Download 3 newton`s Laws of Motion

chaPTer
3
newton’s Laws of Motion
what Effect Do Forces Have on the Motion
of Objects?
Key concePTs
After completing this chapter you will
be able to
• distinguish between different
types of forces and describe
how they affect the velocity and
acceleration of an object
• explain how Galileo and Newton
advanced our knowledge of
forces and motion
• state and apply Newton’s laws
qualitatively
• use free-body diagrams
to calculate net force
and acceleration
• solve problems involving forces
in one dimension using freebody diagrams and
Newton’s laws
• conduct an inquiry into the
relationship among the
acceleration, net force, and
mass of an object, and analyze
the resulting data
The skier on the opposite page has many different forces acting on him at the
same time. Each force has an effect on his motion. The ground exerts forces
on the skier, gravity is pulling on him, and even the air is pushing him back.
When you combine all of these forces, you can determine how the skier will
move. At times, the skier will move with a constant velocity, while at other
times he will speed up or slow down. The sum of all the forces acting on the
skier determines which of these will occur.
To help increase the speed of the skier, the skis are designed to decrease
the force of friction. The skier can push on the snow-covered ground with his
poles to help him speed up. Even the skier’s clothing and safety equipment are
designed to help increase speed and reduce drag (air resistance). An experienced skier will adjust his or her stance to reduce air resistance.
Extreme velocities are dangerous even to experienced skiers. To help
reduce speed, the skier can plow through the snow or skid with his skis across
the snow, causing the skis to dig into the snow.
Just reading about the physics of skiing will not make you a skilled skier, but
understanding the physics behind skiing can make a good skier even better.
An understanding of the physics of skiing also helps equipment designers
create better skis, poles, and other skiing gear, which help skiers win races.
In this chapter, you will explore different types of forces and discover how
they affect motion. You will learn Newton’s three laws of motion and use them
to explain how and why objects move. You will also solve problems related to
forces and motion.
• assess the environmental and
social impact of technologies
that involve forces
STARTiNg POInTS
Answer the following questions using your current knowledge.
You will have an opportunity to revisit these questions later,
applying concepts and skills from the chapter.
3. What do you think is true about the direction of the total
force acting on the skier if he is slowing down? What if
he is speeding up?
1. List as many forces as you can think of that might be
acting on the skier in the photograph. For each force,
give the direction of the force and suggest what might
be exerting the force.
4. What force or forces do you think would cause the skier to
(a) speed up?
(b) slow down?
2. If the skier is moving slowly at a constant velocity across
a horizontal surface, what forces do you think are acting
on him? How would your answer change if the skier
were moving quickly at a constant velocity?
112
Chapter 3 • Newton’s Laws of Motion
5. The physics of skiing is similar to the physics of
skateboarding.
(a) List three forces that you think act on both a skier
and a skateboarder.
(b) How do you think a skateboarder can speed up and
slow down?
NEL
Mini Investigation
Predicting Forces
Skills: Predicting, Performing, Observing, Analyzing, Evaluating, Communicating
The SI unit of force is the newton. In this chapter, you will be
required to measure forces using a spring scale or a force
sensor. The following activity will help you improve your skills
in estimating and measuring forces. Before performing this
activity, make sure you know how to zero the spring scale or
calibrate the force sensor.
Equipment and Materials: two spring scales or force
sensors; one 100 g object; one 200 g object
1. Hang a 100 g object from a spring scale or a force sensor
and record the reading.
2. Hold a 200 g object in your hand and estimate how much
force is required to hold it up. Record your estimate. Hang
the object from the spring scale or force sensor. Measure
and record the force.
NEL
SKILLS
HANDBOOK
A2.1
3. Predict the reading on the spring scale if you hang both
the 100 g and the 200 g object from it. Record your
prediction. Measure and record the force.
4. Predict the reading on each scale if you use two spring
scales or two force sensors to hold up one 200 g object.
Record your prediction. Test your prediction and record
your results.
A. How accurate were your predictions? How could they be
improved? T/I
B. What can you conclude about forces from your
observations? Write one or two statements that
summarize your observations. T/I C
Introduction
113
3.1
Figure 1 Forces are all around you.
dynamics the study of the causes
of motion
Types of Forces
Forces are all around you, acting on every object that you see. The motion of cars,
trucks, planes, and boats is determined by the forces acting on them. Engineers must
consider forces carefully when designing bridges and buildings. You are always using
forces to move around, to lift objects, or to turn the pages of this book. Forces are
involved in every type of sport and activity. For example, when a pitcher throws a
ball, she exerts a force on the ball that causes the ball to move forward (Figure 1). If
the batter hits the ball, then the bat exerts a force on the ball to change its motion. An
understanding of forces is essential for a scientific description of our environment.
In simple terms, a force is a push or a pull. Forces can cause objects to change their
motion. When you push on a chair to tuck it under a desk, you change the motion of
the chair. The direction of a force is very important. If you push straight down on a
book on a desk, the effect is usually very different than if you push sideways or pull
up. This means that force has direction, making it a vector quantity.
In Unit 1, you studied a branch of mechanics called kinematics. Remember that
kinematics is the study of how objects move without being concerned with why they
move. In this unit, you will study dynamics. Dynamics explains why objects move the
way they do. One way to understand why an object moves is to study the forces acting
on it. These forces can cause the object to start moving, speed up, slow down, or
remain stationary. In this chapter, you will be introduced to different types of forces
and the laws that govern them.
Measuring Forces
newton (N) the SI unit of force
(1 N = 1 kg·m/s2)
Isaac Newton discovered many of the concepts in this chapter. For this reason the
unit of force, the newton, is named after him. The newton (N) is a derived SI unit equal
to 1 kg·m/s2.
To measure force in the laboratory, you can use either a spring scale or a force
sensor. A spring scale has a spring that stretches more when greater forces pull on it.
A needle is attached to the spring to indicate the amount of force. Usually a spring
scale must be zeroed (the reading must be set to zero when not pulling) before use.
Most spring scales can only measure a pulling force. A force sensor is an electronic
device that can be attached to a computer or used independently. This device provides an accurate digital reading of a force and can even graph how the force changes
over time. A force sensor can measure both pushes and pulls.
Force Diagrams
system diagram a simple sketch of all
objects involved in a situation
To understand why an object will remain at rest, start moving, or change its motion,
you need to be able to draw diagrams that show clearly which forces are acting on the
object. These diagrams are essential, especially when several forces are acting on the
object simultaneously. The first type of force diagram is called a system diagram. A
system diagram is a simple sketch of all the objects involved in a situation. For example,
if you are lifting a book up in the air, the system diagram will show your hand pulling
up on the book (Figure 2).
F�a
F�g
Figure 2 A system diagram is a sketch
showing all the objects involved in a situation.
A system diagram helps you determine which
objects push or pull on other objects.
114 Chapter 3 • Newton’s Laws of Motion
Figure 3 The FBD for the book shown in Figure 2.
Since an FBD shows all the forces acting on a single
object, two forces are drawn: the force of the hand
pulling up and the force of gravity pulling down.
NEL
The other type of force diagram is called a free-body diagram (FBD). An FBD is a
simple drawing representing the object being analyzed and all the forces acting on it
(Figure 3). Usually the object is drawn as a rectangle or large dot. The forces are drawn
as arrows originating from the outline of the rectangle or dot and pointing away from
the centre. FBDs are not drawn to scale, but larger forces can be drawn longer than
smaller ones
to help predict the motion of the object. Each force is labelled with the
S
symbol F and an appropriate subscript that indicates the type of force.
free-body diagram (FBD) a simple
drawing of an object showing all the
forces that are acting on it
Everyday Forces
To draw useful force diagrams, you need to be familiar with some common forces
encountered every day. Imagine two children playing outside with a wagon. One
child pulls forward on a rope tied to the front, while the other pushes on the wagon
from behind (Figure 4(a)). What forces act on the wagon? To answer this question,
we first need to study some everyday forces.
First consider the applied forces. An applied force results when one object is in contact
S
with another object and either pushes or pulls on it. The symbol for an applied force is F a.
In our example, the child behind the wagon exerts an applied force forward on the wagon
by pushing on the back. Another force is the tension force (often called tension). Tension
S
is a pulling force exerted on an object by a rope or a string. The symbol for tension is F T.
Ropes and strings are not rigid, which means that they cannot push on an object. If you
try to push with a rope, the rope will just sag down and have no effect on the motion of
the object. An easy way to remember the direction of the tension is that it always pulls the
object toward the rope or the string. The child at the front of the wagon pulls on the rope,
causing tension in the rope. The rope exerts tension on the wagon, pulling it forward.
Notice that in Figure 4(b) both the applied force vector and the tension vector start from
the outline of the rectangle representing the wagon and are directed forward, indicating
the direction of each force.
Whenever an object is in contact with a surface, the surface can exert two different forces on the object. One is called the normal force. The normal force is a
perpendicular force on an object exerted by the surface with which it is in contact.
The normal force is given its name because this force alwaysSacts perpendicular (or
normal) to the surface. The symbol for the normal force is F N. The normal force is
always a push from the surface onto the object. For this reason, the normal force
always points away from a surface. In Figure 4(b), the normal force from the ground
on the wagon starts from the outline of the rectangle and points up, perpendicular
to the ground. In this case, the normal force supports the wagon against the force of
gravity.
The other force exerted by a surface on an object is friction. Friction is a force that
resists the motion or attempted motion of an object. Friction is always parallel to the
surface andSacts opposite to the object’s motion or attempted motion. The symbol for
friction is F f . If the wagon is moving to the right, then the friction on the wagon acts
toward the left, opposite to the motion. If the wagon is at rest even if the children are
pushing and pulling on it, then the friction is left, opposite to the tension and applied
force keeping the wagon at rest.
>
applied force (F a) a force that results
when one object makes contact with
another and pushes or pulls on it
>
tension (F T) a pulling force from a rope
or string on an object that always points
toward the rope or string
>
normal force (F N) a perpendicular force
exerted by a surface on an object in
contact with the surface; the normal force
always points away from the surface
>
friction (F f) opposes the sliding of two
surfaces across one another; friction
acts opposite to the motion or attempted
motion
FN
FT
Ff
(a)
(b)
Fa
Fg
Figure 4 (a) The system diagram of a wagon and the two children pushing and pulling on it
(b) The FBD showing all the forces acting on the wagon
NEL
3.1 Types of Forces 115
>
force of gravity (F g) force of attraction
between any two objects
Notice that all of the forces described on the previous page require one object
to be in contact with another. For this reason, they are called contact forces. Some
forces do not require contact. These forces are known as action-at-a-distance forces
(sometimes called non-contact forces).
The force of gravity, also called the gravitational force, is the force of attraction that
exists between any two objects due to their mass.
The force of gravity is an actionS
at-a-distance force. The symbol for gravity is F g. In this course, you will only learn
about the force of gravity between Earth and other objects close to Earth’s surface. At
Earth’s surface, the force of gravity always points down toward Earth’s centre. Even if
the surface is sloped, such as the side of a mountain, the force of gravity still points
down toward Earth’s centre.
Mini Investigation
Measuring the Force of Gravity
SKILLS
HANDBOOK
Skills: Performing, Observing, Analyzing, Communicating
In this investigation, you will observe the relationship between
mass and the force of gravity. You will also measure and
calculate the magnitude of the force of gravity.
Equipment and Materials: spring scale or force sensor; set of
objects of known mass
1. Create a table with the headings “Mass (kg)” and “Force of
gravity (N)” to record your observations.
2. Select one of the objects. To measure the force of gravity
on the object, hang the object from the spring scale or
force sensor. Hold the object steady before taking a reading.
Record your observations in your table.
A2.1, A6.5
A. Graph your results with the force of gravity (N) on the y-axis
and mass (kg) on the x-axis. T/I C
B. What is the slope of the line of best fit on the graph? What
does the slope represent? (Hint: Think back to the projectile
problems from Unit 1.) T/I C
C. Using your observations, predict the force of gravity
acting on each object below. Use the spring scale or force
sensor to check your predictions. How accurate were your
predictions? T/I C
(i) 0.30 kg
(ii) 0.50 kg
D. Describe how you could calculate the force of gravity (N)
acting on an object if you knew its mass (kg). T/I C
3. Repeat Step 2 for all the objects in the set.
To calculate the magnitude of the force of gravity on an object, you multiply the
mass of the object by the acceleration due to gravity. To calculate the force of gravity,
you can use the equation
>
>
F g 5 mg
S
WEb LInK
To learn more about contact and
action-at-a-distance forces,
g o T o N E L So N SCi E NCE
116
where g 5 9.8 m/s2 [down]. The force of gravity is measured in newtons and the
mass is in kilograms. You will learn more about gravity in Chapter 4.
In this course, you will usually be concerned with external forces. External forces
are those that are caused by one object pushing or pulling on another. An internal
force occurs when an object exerts a force on itself. For example, when skater A pushes
on skater B, the force on skater B is external. If skater B pulls forward on her own arm,
then it is an internal force.
In the following Tutorial, you will use what you have learned about forces to draw
system diagrams and FBDs.
Chapter 3 • Newton’s Laws of Motion
NEL
Tutorial 1 Drawing Force Diagrams
Some force diagrams are easy to draw, while others require more care. The following
Sample Problems will help you to sharpen your skills with force diagrams.
Sample Problem 1
Draw both the system diagram and the FBD for each object
in italics.
(a) A cup is sitting at rest on a table.
(b) Step 1. Identify the objects in the system diagram.
The system diagram shows the trunk, the rope, and
the basement floor.
(b) A large trunk in the basement is pulled by a rope tied to the
right side of the trunk by a person. The trunk does not move.
(c) A baseball player is sliding to the left across the ground.
(d) A desk is pushed to the left across the floor.
Solution
(a) Step 1. Identify the objects in the system diagram.
The system diagram shows the cup and also the desk
because the desk exerts a force on the cup.
Step 2. Identify the forces acting on the trunk for the FBD.
The forces acting on the trunk are tension from the rope,
the normal force, friction, and gravity.
Step 3. Determine the direction of each force.
Step 2. Identify the forces acting on the cup for the FBD.
The forces acting on the cup are the normal force
and gravity.
Step 3. Determine the direction of each force.
The normal force exerted by the desk pushes up on the
cup and the force of gravity pulls the cup down. No one
is pushing the cup so there is no applied force. There
is no friction acting on the cup because the cup is not
moving and friction is not required to keep it stationary.
Step 4. Draw the FBD as a rectangle representing the cup and
the arrows representing each force and its direction. Each
arrow must be labelled with the appropriate force symbol.
The rope can only pull, exerting tension to the right.
The basement floor exerts two forces on the trunk,
the normal force and friction. The normal force is
perpendicular to the surface and is directed up. The
force of friction acts opposite to the applied force to
keep the trunk stationary. The force of gravity on the
trunk is directed down.
Step 4. Draw the FBD as a rectangle representing the trunk and
the arrows representing each force and its direction. Each
arrow must be labelled with the appropriate force symbol.
F�N
F�f
F�T
F�g
F�N
F�g
NEL
3.1 Types of Forces
117
(c) Step 1. Identify the objects in the system diagram.
(d) Step 1. Identify the objects in the system diagram.
The system diagram shows the baseball player and
the ground.
Step 2. Identify the forces acting on the baseball player for the FBD.
The system diagram shows the desk, the person
pushing on it, and the floor.
Step 2. Identify the forces acting on the desk for the FBD.
The forces acting on the desk are an applied force,
the normal force, friction, and gravity.
The forces acting on the baseball player are the normal
force, friction, and gravity.
Step 3. Determine the direction of each force.
Step 3. Determine the direction of each force.
The desk is being pushed to the left, so the applied
force is directed to the left. The normal force pushes up
on the desk. The force of friction is directed to the right,
opposite to the direction of motion. The force of gravity
pulls down on the desk.
The normal force exerted by the ground pushes up
on the baseball player. The force of friction is directed
opposite to the direction of motion. The force of gravity
pulls down on the baseball player.
Step 4. Draw the FBD as a rectangle representing the baseball
player and arrows representing each force and its direction.
Step 4. Draw the FBD as a rectangle representing the desk and
the arrows representing each force and its direction.
F�N
F�N
F�f
F�a
F�g
F�f
F�g
Sample Problem 2
A player kicks a soccer ball that is sitting on the ground. The ball
moves up into the air. Ignore air resistance.
Solution
(a) Step 1. Identify the forces acting on the ball.
(a) Draw the FBD of the ball after it has moved away from the
player but is still in the air.
(b) A student draws the FBD shown in Figure 5 to represent
the soccer ball while it is coming back down. What is wrong
with the FBD? Explain your reasoning.
F�N
The soccer ball has moved away from the player
so there is no applied force. The ball is in the air so
there is no normal force exerted by the ground. The
only force acting on the soccer ball is gravity.
Step 2. Determine the direction of the force.
The force of gravity pulls down on the soccer ball.
Step 3. Draw the FBD as a rectangle representing the ball and
the arrows representing each force and its direction.
F�a
F�g
Ontario Physics 11 U
0176504338
C03-F013-OP11USB
FN
Chapter 3 • Newton’s Laws of Motion
Nesbitt
CO
Figure 5
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118
F�g
NEL
(b) When the soccer ball is in the air, there is no applied force
or normal force. Both of these forces are contact forces.
Since the ball is no longer in contact with the player’s
foot or the ground, these forces no longer act on the ball
and should not be included in the diagram. The FBD that
the student drew in Figure 5 would be appropriate at the
start when the ball is still on the ground and the player is
kicking it.
Practice
1. Draw a system diagram and an FBD for each object in italics. K/U C
(a) A book is at rest on top of a desk.
(b) A basketball falls through the hoop. Ignore air resistance.
(c) A large trunk is pushed horizontally from behind toward the east across a rough floor.
2. Figure 6(a) shows a system diagram of a block sliding up a ramp. A student draws the
FBD for the block (Figure 6(b)). Discuss the validity of the FBD. K/U C
F�N
F�f
(a)
Figure 6
(b)
F�g
Calculating net Forces
In many force problems, you must combine all the forces acting on a single object
into one combined force. The total force is also called the net force or the resultant
force. To determine the net force, you need to use FBDs. Keep in mind that force is a
vector quantity and the direction of each individual force must be
considered before
S
determining the net force. Net force is represented by the symbol F net. In the following
Tutorial, you will draw FBDs to determine the net force acting on an object.
>
net force (F net ) the sum of all forces
acting on an object
Tutorial 2 Using FBDs to Determine Net Force
To determine the net force from the FBD of an object, it is necessary to define the x- and
y-axes and to define which directions are positive. You may omit one axis or the other, if
there are no forces parallel to that axis. In the following Sample Problems, we will practise
this technique.
Ontario 1:
Physics
11 U the Net Force on a Stationary Object
Sample Problem
Calculating
The floor exerts
a normal force of 36 N [up] on a stationary chair.
0176504338
The force ofFN
gravity on the chair isC03-F016B-OP11USB
36 N [down]. Draw the FBD of
the chair andCO
use the FBD to determine
the net force on the chair.
Nesbitt
Solution
4th Pass (1st pass 7381-A)
Pass
Step 1. Draw
the FBD of the object.
Approved
F�N
Not Approved
F�g
NEL
Step 2. Identify which directions are positive.
Define up as the positive y-axis and down as the negative
y-axis. This means the normal force exerted by the floor on
the chair is positive and the force of gravity on the chair is
negative. The values of the forces on the FBD are now
F N � �36 N
F g � �36 N
3.1 Types of Forces
119
Step 3. Add the forces on each axis to determine the net force.
S
S
S
F net 5 F N 1 F g
5 136 N 1 1236 N 2
Fnet 5 0 N
There is no net force on the chair.
Sample Problem 2: Calculating the Net Force When the FBD Is Given
Figure 7 shows all the forces
acting on an object. Use the
FBD to calculate the net force.
52 N [up]
45 N [W]
62 N [E]
52 N [down]
Figure 7
Step 2. Define east and west forces as being along the x-axis.
So up and down forces are along the y-axis.
Add the forces along each axis to determine the
net force.
First, find the sum of all the forces parallel to the
y-axis.
1Fnet2 y 5 152 N 1 1252 N2
50N
The net force on the y-axis is 0 N.
Now find the sum of all the forces parallel to the
x-axis.
Step 1. Identify which directions are positive.
1Fnet2 x 5 162 N 1 1245 N2
Solution
Since the FBD is given, you can skip the drawing step.
Choose up and east as positive. So down and west
are negative. The values of the forces on the FBD
are now
5 117 N
The net force along the x-axis is 17 N [E].
Therefore, the net force on the object is 17 N [E].
�52 N
�45 N
�62 N
�52 N
Practice
Physics 11 U
1. Calculate the net force when each set of forces acts on the same object.
338
Draw an FBD for each object. K/U C
C03-F019-OP11USB
(a) 5.5 N [W], 3.4 N [W], 4.2 N [E] [ans: 4.7 N [W]]
(b) 92 N [up], 35 N [down], 24 N [down] [ans: 33 N [up]]
Nesbitt
(c) 15 N [up], 15 N [down], 35 N [E], 12 N [W] [ans: 23 N [E]]
d
oved
2.Pass
A chain
force of 1200 N [up] on a beam which experiences a force of gravity
5th
(1stexerts
pass a7381-A)
of 1100 N [down]. Draw the FBD of the beam and determine the net force on
the beam. K/U C [ans: 100 N [up]]
3. You push a book across a table to your friend with a force of 6.5 N [E]. The force of
friction on the book is 4.5 N [W]. The normal force and the force of gravity have a
magnitude of 7.5 N. Draw the FBD of the book and calculate the net force on the
book. K/U C [ans: 2.0 N [E]]
120 Chapter 3 • Newton’s Laws of Motion
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NEL
The Four Fundamental Forces
It might seem like there are many different kinds of forces in everyday life and even
more involved with research and technology. Physicists have grouped all known natural forces into four categories called fundamental forces. These four fundamental
forces are the gravitational force, the electromagnetic force, the strong nuclear force,
and the weak nuclear force.
You have already learned a little about the force of gravity, and you will expand
that knowledge in Chapter 4. Not only is the force of gravity responsible for pulling
objects down toward Earth’s centre, but it also exists between any two masses in the
universe. The force of gravity keeps the Moon in orbit around Earth and Earth in
orbit around the Sun. You do not notice the force of gravity between smaller objects
such as a pair of basketballs because the masses are small and the force of gravity is
too weak compared to Earth’s gravity.
The electromagnetic force is caused by electric charges. Electric force exists between
charges, and magnetic force exists between magnets. The electromagnetic force is an
action-at-a-distance force. Unlike gravity, this force can both attract and repel. For
this reason, these forces often cancel each other out. The electromagnetic force holds
atoms and molecules together: it makes concrete hard and a feather soft and governs
the properties of chemical reactions.
In the nucleus of atoms, the positively charged protons are very close and repel
each other. They do not fly apart because the strong nuclear force of attraction
between the neutrons and the protons keeps them in place. In some cases, protons
and neutrons can transform into other particles. The weak nuclear force is responsible for the interactions involved during these particle transformations.
Table 1 gives a brief comparison of the four fundamental forces. The electromagnetic,
strong nuclear, and weak nuclear forces are studied in later physics courses. web Link
To review the four fundamental
forces,
go to nelson sc i ence
Table 1 Comparing the Fundamental Forces
Type of force
Approximate
relative strength
Range
Effect
gravitational
1
infinite
attract only
1020
electromagnetic
infinite
attract and repel
strong nuclear
10
38
less than 10215 m
attract and repel
weak nuclear
1025
less than 10218 m
attract and repel
3.1 Summary
• A force is a push or a pull. Forces are responsible for changes in motion.
• Force is a vector quantity measured in newtons (N).
• There are two types of force diagrams. A system diagram is a simple sketch
of the situation showing the objects involved. A free-body diagram (FBD)
shows all the forces acting on a single object.
• You can use FBDs to calculate the net force on an object. Indicate the
direction of the positive y-axis and the positive x-axis to determine the signs
of each force acting on the object. Add up the forces parallel to each axis to
determine the net force.
S
S
• To calculate the force of gravity, you can use the equation F g 5 mg , where
S
g 5 9.8 m/s2 [down].
• The four fundamental forces are the gravitational force, the electromagnetic
force, the strong nuclear force, and the weak nuclear force.
NEL
3.1 Types of Forces 121
3.1 Questions
1. Assume that you are sitting at your desk facing north with
a book on the desk directly in front of you. K/U
(a) If you push on the side of the book that is closest to
you, in which direction is the applied force?
(b) If you pull on the side of the book that is closest to you,
in which direction is the applied force?
11. Explain the difference between system diagrams
and FBDs. Describe why both are used to solve force
problems. K/U C
2. Name the force or forces that cause these objects to
experience changes in motion. Neglect air resistance. K/U
(a) A ball falls toward the ground.
(b) A person accelerates up in an elevator.
(c) A car gradually slows down while approaching a red
light.
12. For a physics project, you are given a small block of wood,
a paper clip, some masking tape, a balloon, a magnet, and
an elastic band. The objective is to move the block from
one end of a long hallway to the other in the least amount
of time using only the materials listed, without touching the
wood directly. Draw a system diagram showing how you
would complete the task. Draw an FBD of the block
of wood. Include a brief description of what you
would do. T/I C
3. A student forgets to zero the force sensor before
performing an investigation. What effect, if any, will this
have on the data collected during the investigation? T/I
13. Examine Figure 8, showing a spider in a web. The web is
currently under construction and consists of only a few fine
strands. Draw the FBD of the spider. T/I C
4. Some everyday forces are gravity, tension, friction, an
applied force, and the normal force. It is important that you
be able to determine the direction of each of these forces
when drawing an FBD. Create a table or a graphic organizer
to help you remember the direction of these forces. K/U
5. Draw both the system diagram and the FBD for each object
in italics. K/U C
(a) A car is parked on the road.
(b) A small fish is hanging from a fishing line.
(c) A football is falling toward a player.
(d) A puck is being pushed forward across the ice by a
hockey stick.
6. Create a poster to teach students about common everyday
forces. Include at least two system diagrams in your poster
and the corresponding FBDs. You may include several
everyday forces in your poster or concentrate on just
one. K/U C
7. Determine the force of gravity acting on each object. (a) A 2.0 kg object falls straight down.
(b) A 62 kg person stands on the floor.
T/I
C
8. Your teacher says, “Any applied force can also be called a
normal force.” Discuss the validity of this statement. K/U C
9. You tie a long string to a cart on the ground. Explain why
you can only pull the cart forward but cannot push the cart
away with the string. Draw diagrams to help explain your
answer. K/U C
Figure 8
14. A doctor states, “The bones in the human arm can exert
forces that can either push or pull other objects. The
muscles are made of small fibres and can only cause
tension forces.” C A
(a) What does the doctor mean when he says muscles can
only cause tension forces?
(b) Why can bones both push and pull whereas muscles
cannot?
15. Calculate the net force when each set of forces acts on a
single object. T/I
(a) 56 N [up], 35 N [down]
(b) 12.3 N [right], 14.4 N [right], 32.7 N [left]
(c) 45 N [up], 45 N [down], 21 N [W], 21 N [E]
16. (a) List the four fundamental forces from weakest to
strongest.
(b) Describe two ways that gravity is different from the
10. Describe the main difference between contact forces and
other three fundamental forces.
Ontario
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11
U
action-at-a-distance forces. What implication does this
(c) Explain why friction and tension are not fundamental
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difference have when drawing
an FBD? K/U C
forces. K/U C
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122 Chapter 3 • Newton’s Laws of Motion
NEL
3.2
Newton’s First Law of Motion
Every year in Canada, there are about 160 000 car accidents. These accidents cause
many injuries, and about 3000 are fatal. Many of these injuries and deaths involve
motorists who are not wearing seat belts or are driving too fast. An understanding of
Newton’s first law will help you appreciate the importance of safety features in cars
such as seat belts and airbags. Figure 1 shows a crash test designed to help engineers
test and improve the safety features of new cars. What will happen to a crash test
dummy during a collision if it is not wearing a seat belt and no airbag is present?
Newton’s first law will help us answer this question.
Inertia
If you have ever played air hockey, you may know that a small plastic puck moves
with close to uniform velocity after you hit it. In other words, there is very little friction acting on the puck to slow it down. In fact, the net force on the puck is zero
because the upward force on the puck exerted by the air and the downward force of
gravity cancel each other and there is almost no friction. If you do not hit the puck at
all, it will just sit there at rest if the air table is level.
Unfortunately, early scientists and philosophers did not have access to air hockey
tables. They noticed that moving objects would spontaneously slow down for no
apparent reason. They did not know about friction and incorrectly attributed the
decrease in velocity to “lazy” objects. They concluded that a constant net force was
needed to keep an object moving. They thought that larger net forces made things
move at a higher constant velocity and smaller net forces made them move at a lower
constant velocity. If no net force was acting on the object, they thought that the object
would stop.
It was not until the 1600s that Galileo was able to perform experiments to help
clear up these misconceptions. To help explain the results of his experiments, Galileo
used the following thought experiment (Figure 2). Figure 2(a) shows a ball rolling
down an incline, onto a horizontal surface, and up another incline. Galileo reasoned
that if there was no friction acting on the ball, it would continue to roll up the second
incline until it reached the same height as its starting position. If friction were
present, it would not go quite as high on the second slope.
Figure 2(b) shows a situation similar to the first, but the steepness of the second incline
is decreased. Galileo reasoned that the ball would have to roll farther to reach the same
initial height on the second incline. In Figure 2(c), the second incline has been eliminated. In this experiment, the ball will never reach the same height. Galileo concluded
that if there is no friction, the ball will continue to roll forever. It will never reach the
same initial height since it cannot go up another incline. We can verify Galileo’s thought
experiment today using equipment such as air tables, where little friction is present.
Ball starts
here.
descending
ramp
(a)
Ball stops
here.
ascending
ramp
Ball starts
here.
(b)
Ball stops
here.
Ball starts
here.
Figure 1 Crash tests are designed to
test and improve automotive safety.
Ball does
not stop.
(c)
Figure 2 (a) The ball rolls up the steep second ramp until it rises to the same initial height.
(b) The ball rolls up the less steep second ramp, but it still rises to the same height.
(c) There is no second ramp and the ball never stops because it cannot get to the same initial height.
NEL
3.2 Newton’s First Law of Motion 123
inertia the property of matter that causes
it to resist changes in motion; inertia is
directly proportional to the mass of the
object
first law of motion an object will remain
at rest or continue to move at constant
velocity when the net force on the object
is zero
Galileo concluded that once an object starts moving, it will continue moving at a
constant velocity if there is no friction present. Galileo used the concept of inertia
to help explain his conclusion. Inertia is the property of matter that causes it to resist
changes in motion. The inertia of an object depends on the mass of the object. An
object with more mass has more inertia, whereas an object with less mass has less
inertia. In other words, inertia is directly proportional to the mass of the object.
Imagine placing a stuffed animal on the dashboard of a stationary car. If the car
speeds up rapidly, the stuffed animal will resist this change in motion due to its inertia
and end up in your lap. This does not mean the stuffed animal is moving backwards.
The car is moving forward and the stuffed animal is stationary. In other words, the
dashboard is being pulled out from under the stuffed animal. If the car is moving with
uniform velocity and the stuffed animal is placed on the dashboard, the stuffed animal
will stay on the dashboard because there is no change in the velocity of the car. In this
case, inertia does not upset the stuffed animal because inertia only resists changes in
motion. If the stuffed animal is placed on the dashboard and the car suddenly slows
down, the stuffed animal will continue to move forward with uniform velocity due to
its inertia. Again, we are not implying that the stuffed animal jumps forward. It is the
car that is slowing down, not the stuffed animal speeding up. The dashboard slides
under the stuffed animal, causing the windshield to move toward the stuffed animal.
Newton was born in 1642, the year that Galileo died. Newton published Principia
Mathematica, a set of three books which included much of his own work about physics,
as well as a description of Galileo’s law of inertia. The law of inertia is now called
Newton’s first law of motion because it was included with Newton’s other laws of motion.
First Law of Motion
If the net external force on an object is zero, the object will remain at rest or continue to
move at a constant velocity.
Below are some of the important implications of Newton’s first law:
• Anon-zeronetforcewillchangethevelocityofanobject.Th
evelocitycan
change in magnitude, direction, or both.
• Anetforceisnotrequiredtomaintainthevelocityofanobject.
• Externalforcesarerequiredtochangethemotionofanobject.Internalforces
have no effect on the motion of an object.
Tutorial 1 FBDs and the First Law of Motion
The following Sample Problems will help to clarify the meaning of Newton’s first law by
using FBDs.
Sample Problem 1
Use Newton’s first law to explain each situation below.
(a) Why does a computer sitting on a desk remain at rest?
F�N
(b) Why does a hockey puck moving across smooth ice move at
a constant velocity?
(c) Why does a wagon pulled across a rough surface by a child
move at a constant velocity?
Solution
(a) Examine the system diagram and FBD of the computer
shown in Figure 3. Notice that the desk exerts a normal
force up on the computer and the force of gravity pulls down
on the computer. These two forces cancel to give a net force
of zero. According to Newton’s first law, the computer will
remain at rest.
124
Chapter 3 • Newton’s Laws of Motion
(a)
(b)
F�g
Figure 3 (a) System diagram of a computer on a desk
(b) FBD of the computer
NEL
(b) Examine the system diagram and FBD of the hockey puck
shown in Figure 4. Notice that the ice exerts a normal force
up on the hockey puck and the force of gravity pulls down on
the hockey puck. These two forces cancel to give a net force
of zero in the vertical direction. Since no external force acts
in the horizontal direction, according to Newton’s first law,
the hockey puck will continue to move at a constant velocity.
F�N
(a)
F�N
(a)
(b)
F�g
F�f
Figure 4 (a) System diagram of a hockey puck moving
on ice (b) FBD of the hockey puck
F�T
F�g
(b)
Figure 5 (a) System diagram of a child and a wagon (b) FBD of the
child and the wagon
(c) Examine the system diagram and FBD of the wagon shown
in Figure 5. The child applies tension forward on the wagon.
The ground exerts a normal force up, and the force of
friction acts backwards on the wagon. The force of gravity
acts down on the wagon. The two vertical forces cancel
each other and the two horizontal forces cancel each other
to produce a net force of zero. According to Newton’s first
law, the wagon will move at a constant velocity.
Sample Problem 2: Newton’s First Law Applied to Headrests
(Figure 6(a)), there is no force applied to the head. According to
Newton’s first law, your head will continue to remain at rest. Your
head will initially appear to snap backwards relative to your body
as your body accelerates forward, possibly resulting in a neck
injury known as whiplash. The headrest in a modern car helps
push the head forward with the rest of the body (Figure 6(b)).
This helps to prevent whiplash since your neck does not bend
backwards as far during a rear-end collision.
Older cars did not have headrests, but all new cars do. How do
headrests help prevent injuries during a rear-end collision? Use
Newton’s first law to explain your answer.
Solution
Consider the forces acting on a person’s body during a collision.
OP11USB
rio Physics 11 UDuring a rear-end collision, the car will suddenly accelerate
Group
forward and so will your body because the seat exerts a force
504338
owle
directed forward on your torso. In a vintage car with no headrest
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oved
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(b)
Figure 6 (a) No headrest (b) Headrest present
NEL
3.2 Newton’s First Law of Motion
125
Sample Problem 3: Determining the Missing Force
What is the missing force on each FBD shown in Figure 7?
12 N
8N
FN
15 N
28 N
(a)
S
Analysis: 1Fnet 2 y 5 0
22 N
(b)
Figure 7 (a) FBD for an object at rest (b) FBD for an object moving
left at a constant velocity
Solution: 1F net 2 y 5 F N 1 1222 N2
0 5 F N 2 22 N
F N 5 122 N
S
F N 5 22 N [up]
Solution
Now examine the forces along the x-axis.
(a) According to Newton’s first law, since the object is at rest,
the net force must be zero. Choose up as positive. So down
is negative.
Given: 128 N; 215 N
S
Required: F 1
Analysis: 1Fnet 2 x 5 0
Given: two upward forces of 112 N and 18 N
Solution: 1Fnet2 x 5 128 N 1 1215 N2 1 F1
0 5 13 N 1 F1
F1 5 213 N
S
Required: F g
S
Analysis: F net 5 0
Solution: Fnet 5 112 N1 118 N2 1Fg
0 5 20 N 1 Fg
Fg 5 220 N
s 11 U
Given: 222 N
Required: F N
F1
F�g
(b) According to Newton’s first law, the object must have a
net force of zero since it is moving at a constant velocity.
Choose up and right as positive. So down and left is
negative. We can look at (Fnet )y and (Fnet )x separately.
Start with the forces along the y-axis.
S
F 1 5 13 N [left]
Statement: The normal force on the object is 22 N [up].
S
S
F 1 is 13 N [left].
F g 5 20 N 3 down 4
Statement: The force of gravity on the object is 20 N [down].
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Nesbitt Practice
1. Explain why it is unsafe to stand when riding a bus or subway without holding onto
K/U
C
3rd Pass (1stsomething. pass 7381-A)
2. In a demonstration, a teacher places some plates on top of a smooth
1-A)
tablecloth. The teacher then pulls quickly on the tablecloth. If the tablecloth
is a frictionless surface, predict what will happen to the plates. Explain your
reasoning. K/U
3. A driver in a car passes over some black ice, which exerts almost no friction on
the wheels. Explain why the car cannot slow down when the driver pushes on the
brakes. K/U
4. You have some snow stuck on your shovel. Explain how you could apply Newton’s first
law to get the snow off. K/U
5. The FBD in Figure 8 is for a car at rest on the ground. T/I
S
S
S
13 000 N
1250 N
F1
1400 N
Fg
Figure 8
S
(a) Determine F 1 and F g . [ans: F 1 = 2650 N [R]; F g = 13 000 N [down]]
(b)How would your answers change if the car was moving at a constant velocity?
Assume none of the given forces change.
126 Chapter 3 • Newton’s Laws of Motion
NEL
Mini Investigation
Testing Newton’s First Law
Skills: Observing, Analyzing, Communicating
Your teacher will present several situations and ask you to predict what will happen and
explain your reasoning. You will then observe the demonstration and record what happens.
Finally, you will explain what happens and why in terms of Newton’s first law.
Equipment and Materials: coin; playing card; ballistics cart and ball; skateboard; thread;
two standard masses
1. Create a table in your notebook similar to Table 1. The second column in Table 1 shows
a sketch of each demonstration. Summarize your results in the appropriate column of
your table. T/I C Table 1
Situation
Sketch of situation
Prediction/
explanation
Observations
Explanation
A. A coin is on top of a playing
card on the left fist. Hit the card.
C03-F033A-OP11USBS_Sketch.JPG
B. A moving ballistics cart fires a
ball by exerting a force straight up.
C03-F033B-OP11USB.ai
C. A moving skateboard with an
object on top hits a wall.
D. A thread supports an object.
Another thread is underneath. Pull
slowly on the bottom thread.
E. A thread supports an object.
Another thread is underneath. Pull
quickly on the bottom thread.
NEL
3.2 Newton’s First Law of Motion 127
Applications of newton’s First Law
WEb LInK
To learn more about how seat belts
work,
g o T o N E L So N SCi E NCE
A wide range of technologies take advantage of Newton’s first law including automobiles, planes, rockets, and construction. The key idea is that the net force must be
zero for any object to remain at rest or to keep moving with uniform motion.
Consider the physics of a typical seat belt. What will happen if you are not wearing
a seat belt and the car suddenly stops? According to Newton’s first law, you will continue to move forward at a constant velocity until an object exerts a net force on you.
This could be the dashboard or the windshield. If you are wearing a seat belt, the seat
belt will exert a net force on you to slow you down.
One design feature of a seat belt uses the sudden decrease in velocity of the car to
activate a gear mechanism. In this design, the seat belt strap is attached to a spool,
which in turn is attached to a gear (Figure 9). Beneath this gear is a pendulum that
is free to swing back and forth. When the car comes to a sudden stop, the pendulum
swings forward due to inertia. This causes the pendulum to move a metal stop into
the teeth of the gear, locking the seat belt in place.
Before coming to
a sudden stop
After coming to
a sudden stop
pendulum
(a)
(b)
Figure 9 (a) When the vehicle is moving at constant velocity the seat belt pendulum (shown in
green) hangs straight down. (b) After a sudden stop, the pendulum swings, causing the metal stop to
lock into the seat belt gear.
Space and flight technology also takes advantage of Newton’s first law. During
high accelerations in a jet or a rocket, a pilot or astronaut might experience pooling
of blood in certain parts of the body such as the legs. The inertia of the blood often
causes it to move out of the head and into the legs. A G-suit helps to prevent this
condition by exerting pressure on the legs and lower torso. In effect, it is squeezing
the blood out of the legs back up toward the brain.
UNiT TASK BOOKMARK
3.2
Summary
You can apply what you
learned about
Science
Physics 11 • Inertiaisthepropertyofmatterthatcausesittoresistchangesinmotion.
Newton’s first law to the Unit Task
ISBN: ISBN # 0176504338Inertia is directly proportional to the mass of the object.
described on page 204.
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• Newton’sfirstlawcanalsobecalledthelawofinertia.Newton’sfirstlaw
statesIllustration
that if the net force acting on an object is zero, the object will either
Dave McKay
remain at rest or continue to move at a constant velocity.
dhm
• Pass
Th
erearemanyimplicationsofNewton’sfi
rstlaw:objectsatresttend
Fourth
10/09/27
to remain at rest; objects in motion tend to remain in motion; if the
velocity of an object is constant, then the net force is zero; if a net force
acts on an object, the velocity will change in magnitude, direction,
or both.
• Newton’sfirstlawofmotioncanbeappliedinmanysituationstohelp
increase our understanding of motion.
• Newton’sfirstlawofmotionhasmanytechnologicalapplications.
Chapter 3 • Newton’s Laws of Motion
NEL
3.2 Questions
1. Explain how modern technology can help demonstrate
Galileo’s thought experiments. K/U
10. Use Newton’s first law to explain why you should slow down
when going around a curve on an icy highway. K/U C
2. Which has the most inertia, a truck, a desk, or a feather?
Which has the least inertia? How do you know? K/U
11. Figure 11 shows some simple equipment used to test
Newton’s first law. In the experiment, the ring is suddenly
pulled horizontally. T/I C
(a) Predict what will happen to the piece of chalk. Explain
your reasoning.
(b) Why does it help to put some water in the container?
3. Skater 1 has a mass of 45 kg and is at rest. Skater 2 has a
mass of 50 kg and is moving slowly at a constant velocity
of 3.2 m/s [E]. Skater 3 has a mass of 75 kg and is moving
quickly at a constant velocity of 9.6 m/s [E]. Which skater
experiences the greater net force? Explain your reasoning. K/U
4. Explain each statement using inertia or Newton’s first law. K/U
(a) You should not sit in the back (bed) of a pickup truck
when it is moving.
(b) It is hard to get a car moving on very slippery ice.
(c) You should not put objects on the ledge of a car
between the rear windshield and the rear seat.
(d) During liftoff, astronauts are placed horizontally in the
capsule rather than vertically.
5. Headrests and seat belts are two important pieces of safety
equipment used in automobiles. K/U
(a) Will both technologies significantly improve safety if
the car suddenly slows down but keeps moving in a
straight line? Explain your reasoning.
(b) Will both technologies significantly improve safety if the
car suddenly speeds up but keeps moving in a
straight line? Explain your reasoning.
6. Many people buy a coffee or other hot beverage on their
way to work. For safety, the cup usually has a lid and is
placed in a cup holder. Using Newton’s first law, explain
why both of these precautions are necessary. C A
chalk
container Figure 11
12. While on the bus, you throw an apple straight up into the
air. What will happen if the bus
(a) moves at a constant velocity?
(b) slows down?
Explain your reasoning using diagrams. T/I C
13. Determine the indicated forces on each FBD shown in
Figure 12. T/I
(a) statue at rest on a shelf
(b) sled pulled right at a constant velocity
7. Figure 10 shows a string tied to a spike at one end and a puck
at the other. The puck is moving around in a circle on the ice.
Ontario
Physics
Describe what
the puck
will do if11
theUstring is suddenly cut at
the red line.0176504338
Explain your reasoning using a diagram. K/U C
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F�2
54 N
F1
F�1
(a)
86 N
17 N
32 N
(b)
60 N
F2
Figure 12
14. Your physics teacher challenges the class to the following
puzzle. Place eight quarters into a single stack on a desk.
Your task is to take the stack apart one quarter at a time
puck
5th pass (1st pass 7381-A)
Pass spike
using only a thin ruler. You cannot make any contact with
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the quarters but the ruler can. Only quarters at the bottom
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of the pile may be removed. T/I C
(a) Describe how you would complete the task. Carry out
Figure 10
your plan to test whether it works.
8. Use Newton’s first law to explain why the normal force must
(b) Explain why it works.
be equal in magnitude to the force of gravity for an object toOntario Physics 11 U
15. Studies reveal that many people do not use their headrest
remain at rest on a horizontal surface when no other forces 0176504338
properly. Research what most people do wrong and how it
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are acting on the object. K/U C
can be fixed. Prepare a small pamphlet that can be used
Nesbitt
CO
9. You are inside a car moving fast along a sharp turn in the
to make people aware of the problem and how to fix it.
road. Use Newton’s first law to describe what happens to
Include6th
anyPass
useful
that might encourage people to
(1st statistics
pass 7381-A)
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Ontario Physics 11 U
you as you safely make it around the curve. T/I C
T/I
C
make
the
necessary
changes.
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go To N ELS oN S C i EN C E
3.2 Newton’s First Law of Motion
129
3.3
newton’s second law of Motion
Newton’s first law of motion applies to situations when the net force on an object is
zero. When the net force is zero, an object that is at rest will remain at rest and an
object that is in motion will continue to move in a straight line at a constant velocity.
What do these cases have in common? In both cases, the acceleration is zero.
The variables Involved in newton’s Second Law
One way to experience Newton’s second law of motion is in a moving car. A light car
with a powerful engine that can exert a large force will experience a large acceleration (Figure 1(a)). A massive truck experiences small accelerations even if the force is
large (Figure 1(b)). A small economy car experiences smaller accelerations because the
force its engine exerts is smaller (Figure 1(c)). The acceleration is affected by changing
either the mass or the net force. To understand this relationship among acceleration,
net force, and mass, we need to consider these variables more carefully.
(a)
(b)
(c)
Figure 1 (a) A race car speeds up quickly because it has a small mass and experiences a large net force.
(b) A truck accelerates more slowly. Even though a large net force acts on it, the mass is large.
(c) A small economy car also accelerates more slowly. It has a small mass and a small applied force.
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To learn more about how forces are
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Figure 2 The relationship among
acceleration, net force, and mass
(a) A large net force results in a large
acceleration. (b) A small net force
results in a small acceleration.
(c) A small mass results in a large
acceleration. (d) A large mass results
in a small acceleration.
We will first examine the relationship between the net force and the acceleration.
Imagine pushing a large sled with a few small boxes on top across a nearly frictionless icy surface. If you push as hard as you can, the sled starts from rest and attains a
high velocity in little time (Figure 2(a)). If you push with less force on the sled, the
velocity will increase more gradually (Figure 2(b)). These two scenarios imply that
acceleration increases as the net force increases. Now we will examine the effect of
mass on acceleration. If you remove the boxes, the lighter sled is easier to speed up
from rest (Figure 2(c)). If you put more boxes on the sled, the heavier sled is harder
to speed up at the same rate (Figure 2(d)). In other words, acceleration decreases as
mass increases.
(a)
(c)
130
Chapter 3 • Newton’s Laws of Motion
a
a
Fnet
Fnet
(b)
a
a
Fnet
Fnet
(d)
NEL
Newton’s second law of motion is summarized as follows:
Second Law of Motion
If the net external force on an object is not zero, the object will accelerate in the direction
of this net force. The magnitude of the acceleration is directly proportional to the
magnitude of the net force and inversely proportional to the mass of the object.
second law of motion an object will
accelerate in the direction of the net
force; the magnitude of the acceleration is
directly proportional to the magnitude of
the net force and inversely proportional to
the object’s mass
Representing Newton’s Second Law Mathematically
From Newton’s second law, we can derive an equation that connects acceleration, net
force, and mass.
S
S
S
1
S
a ~ F net when m is constant and a ~ when F net is constant
m
Combining the two proportionalities, we get
S
F net
a ~
m
S
We can create an equation relating all three variables if we insert a proportionality
constant k:
S
F net
a 5 k
m
S
If we define the newton as the net force required to accelerate 1 kg at 1 m/s2 or
1 N = 1 kg·m/s2, then k = 1. We can write the equation as
S
F net
a 5
m
S
Solving for the net force, we have
S
S
F net 5 ma
Consider a situation where Sthe mass is kept constant but the net force gradually
S
increases. From the equation F net 5 m a , if mass is kept constant and the net force
on the object increases, the acceleration also increases. If you graph net force versus
acceleration, the relationship is linear (Figure 3).
Consider the slope of the line:
rise
slope 5
run
S
D F net
5
S
Da
The line must pass through the origin. From Newton’s first law, when the acceleration is zero, the net force must also be zero. If we use the origin as the initial point on
the graph, the above slope equation simplifies to
S
slope 5
S
F net2 2 F net1
S
S
5
S
a2 2 a1
F net2 2 0
Fnet
Fnet 2
a2
a
Figure 3 The graph of net force versus
acceleration is linear, and the slope
represents the mass. The line must
pass through the origin, since when the
acceleration is zero the net force must
also be zero.
S
a2 2 0
S
NEL
5
F net2
S
a2
3.3 Newton’s Second Law of Motion 131
B
Physically, what does this slope represent? Using Newton’s second law, we have
S
S
F net 5 ma
a
S
m 5
F net
S
a
The expressions for slope and mass can be equated, so we can conclude that the
slope of the graph of net force versus acceleration is the mass of the object.
Now consider a situation where the net force is kept constant but the mass
m
Figure 4 The graph of acceleration
versus mass is a reciprocal function.
S
F net
gradually increases. From the equation a 5
, if the net force is kept constant
m
and the mass of an object increases, the acceleration decreases. If you graph acceleration versus mass, the graph shows a reciprocal relationship (Figure 4).
S
Tutorial 1 Using Newton’s Second Law
Newton’s second law can be used to solve a variety of problems involving many different
situations. In the following Sample Problems, we will demonstrate how to apply Newton’s
second law.
Sample Problem 1: Determining Acceleration
Sample Problem 2: Calculating Net Force
A net force of 36 N [forward] is applied to a volleyball of mass
0.24 kg. Determine the acceleration of the volleyball.
A 64 kg runner starts walking at 3.0 m/s [E] and begins to speed
up for 6.0 s, reaching a final velocity of 12.0 m/s [E]. Calculate
the net force acting on the runner.
S
Given: F net 5 36 N [forward]; m 5 0.24 kg
S
Required: a
S
S
S
S
Analysis: F net 5 ma . Choose forward as positive.
Solution: F net 5 ma
S
F net
a 5
m
S
136 N
0.24 kg
a5
a 5 1150 m/s2
>
a 5 150 m/s2 3 forward 4
Statement: The acceleration of the volleyball is
150 m/s2 [forward].
S
S
Given: m 5 64 kg; v 1 5 3.0 m/s [E]; v 2 5 12.0 m/s [E]; ∆t 5 6.0 s
S
Required: F net
S
S
Analysis: F net 5 ma , but first we have to calculate the
>
>
> v2 2 v1
acceleration using the kinematics equation a 5
.
Dt
Choose east as positive.
>
>
> v2 2 v1
Solution: a 5
Dt
a5
112.0 m/s 2 113.0 m/s2
6.0 s
a 5 11.5 m/s2
>
a 5 1.5 m/s2 3 E 4
Now we can calculate the net force.
>
>
F net 5 ma
Fnet 5 164 kg2 111.5 m/s2 2
Fnet 5 196 N
>
F net 5 96 N 3 E 4
Statement: The net force on the runner is 96 N [E].
132 Chapter 3 • Newton’s Laws of Motion
NEL
Sample Problem 3: Calculating Net Force and Acceleration Using an FBD
A 9100 kg jet moving slowly on the ground fires its engines,
resulting in a force of 22 000 N [E] on the jet. The force of
friction on the jet is 3800 N [W].
(a) Draw the FBD for the jet.
(b) Calculate the net force acting on the jet.
(c) Calculate the acceleration of the jet.
Solution
(a) Choose up and east as positive. So down and west
are negative.
S
(c) Given: F net 5 18 200 N [E]; m 5 9100 kg
S
Required: a
>
>
Analysis: F net 5 ma
>
>
Solution: F net 5 ma
F�N
F f � �3800 N
(b) The normal force and gravity will cancel when the jet is on
horizontal ground. The net force is east since the applied force
is greater than the force of friction. To find the net force, we
add all the horizontal forces.
>
>
>
F net 5 F a 1 F f
Fnet 5 122 000 N 1 1238002 N
Fnet 5 118 200 N
>
F net 5 18 200 N 3 E 4
The net force on the jet is 18 200 N [E].
S
F net
a 5
m
118 200 N
a5
9100 kg
a 5 12.0 m/s2
S
a 5 2.0 m/s2 3 E 4
F a � �22 000 N
S
F�g
Statement: The acceleration of the jet is 2.0 m/s2 [E].
Practice
1. A net force of 126 N [S] is applied to a 70 kg sprinter. Determine the acceleration of
the sprinter. T/I [ans: 1.8 m/s2 [S]]
2. A car accelerates at 1.20 m/s2 [forward]. The net force on the car is 1560 N [forward].
What is the mass of the car? T/I [ans: 1300 kg]
3. A cyclist starts to pedal vigorously, increasing her velocity from 6.0 m/s [E] to 14.0 m/s [E]
in 6.0 s. The total mass of the cyclist and the bicycle is 58 kg. Find the net force acting
on the cyclist and bicycle. T/I [ans: 77 N [E]]
4. During a road test, a driver brakes a 1420 kg car moving at 64.8 km/h [W]. The car
slows down and comes to a stop after moving 729 m [W]. T/I
(a) Calculate the net force acting on the car. [ans: 316 N [E]]
(b)What is the force of friction acting on the car while it is slowing down? Explain
your reasoning. [ans: 316 N [E]]
5. For each FBD shown below, determine the net force applied to the object and its
acceleration. T/I
(a) m 5 8.0 kg [ans: 36 N [left], 4.5 m/s2 [left]] (b) m 5 125 kg [ans: 1000 N [up], 8 m/s2 [up]]
24 N
11 U
31 N
C03-F044-OP11USB
Nesbitt
19 N
1200 N
600 N
1100 N
600 N
1300 N
5th Pass (1st pass 7381-A)
6. In a two-person bobsled competition, athlete 1 pushes forward on the sled with 310 N and
athlete 2 pushes forward with 354 N. A force of friction of 40 N [backwards] is acting on
the bobsled. The mass of the bobsled is 390 kg. Calculate the acceleration of the bobsled. T/I [ans: 1.6 m/s2 [forward]]
NEL
3.3 Newton’s Second Law of Motion 133
The line weight of the arrows is the same as those in part (a).
newton’s Second Law and Gravity
F�g
Figure 5 This FBD shows an object in
free fall, with no air resistance acting
on it. The net force on the object is the
force of gravity. The acceleration of the
object is equal to the acceleration due
to gravity.
In Section 3.1, you learned that you can calculate the force of gravity by multiplying
the mass by the acceleration due to gravity. We can now justify the equation
S
S
F g 5 m g using Newton’s second law.
Consider an object in free fall with no air resistance acting on it (Figure 5).
Free fall is motion of an object toward Earth with no other forces acting on it. The
only force acting on the object is the force of gravity. In this situation, the force of
gravity is equal to the net force. We also know that the object accelerates down at
S
a 5 9.8 m/s2 [down]. Combining these two facts, we have
S
S
F g 5 F net
S
5 ma
S
S
Then, because a 5 g ,
S
S
F g 5 mg
You will use the equation for the force of gravity to help you complete
Investigation 3.3.1. To prepare for the investigation, read the following Tutorial and
complete the Practice questions.
Tutorial 2 Acceleration of Falling Objects
Recall that strings can only pull on objects when they exert tension. A pulley is a small
wheel that changes the direction of the tension in a rope or string without changing its
magnitude. We will assume throughout the text that all pulleys are frictionless and light.
Sample Problem 1
In an investigation, students place a 0.80 kg cart on a table. They
tie one end of a light string to the front of the cart, run the string
over a pulley, and then tie the other end to a 0.20 kg hanging
object (Figure 6). Assume that no friction acts on either object.
(a) Determine the magnitude of the acceleration of the cart and
the hanging object.
0.80 kg
0.20 kg
Figure 6
(a) Step 1. Draw the FBD for each object.
FBD of cart
m1
F�T
F�g
1
The hanging object will accelerate down, so choose
down as positive. The equation for the net force acting
on the hanging object is
Fnet 5 Fg2 2 FT
Because Fnet 5 m2a and Fg2 5 m2g,
m2a 5 m2g 2 FT (Equation 2)
Step 3. Add the equations to solve for the acceleration.
F�T
The tension acting on the cart and on the hanging object
is the same. Adding equations 1 and 2 will cancel the
tension.
F�g
m1a 1 m2a 5 FT 1 m2g 2 FT
m 1 a 1 m2 a 5 m2 g
1m 1 1 m2 2 a 5 m2 g
10.80 kg 1 0.20 kg2 a 5 10.20 kg2 19.8 m/s22
a 5 1.96 m/s2
a 5 2.0 m/s2
FBD of hanging object
F�N
The cart is on the table, so the normal force and gravity
cancel each other. The cart will accelerate to the right,
so choose right as positive. The equation for the net
force acting on the cart is
Fnet 5 FT
Because Fnet 5 m1a,
m1a 5 FT (Equation 1)
(b) Calculate the magnitude of the tension.
381-A)
Step 2. Identify which directions are positive. Determine the net
force acting on each object.
m2
2
The magnitude of the acceleration of the cart is 2.0 m/s2.
134
Chapter 3 • Newton’s Laws of Motion
NEL
(b) To calculate the tension, substitute the acceleration into
equation 1.
m1a 5 FT
FT 5 10.80 kg2 11.96 m/s22
FT 5 0.16 N
The magnitude of the tension in the string is 0.16 N.
Practice
1. Calculate the acceleration of the cart in Figure 7, given the following assumptions. T/I
(a) No friction is acting on the cart. [ans: 3.3 m/s2 [right]]
(b) A force of friction of 0.50 N acts on the cart opposite to the motion. [ans: 3.0 m/s2 [right]]
1.20 kg
0.60 kg
Figure 7
2. In an experiment, objects are placed on top of a cart as shown in Figure 8.
motion sensor
T/I
2.0 kg
0.40 kg
Figure 8
(a) Calculate the acceleration of the cart. Assume that no friction acts on the cart. [ans: 1.6 m/s2 [right]]
(b) What will happen to the acceleration of the cart if the mass of the objects on top of
the cart increases? Explain your reasoning.
(c) What will happen to the acceleration of the cart if an object is taken from the top
of the cart and tied to the hanging object? Explain your reasoning.
s 11 U
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CrowleArt Group
3.3 Summary
Deborah Crowle
2nd pass
• AccordingtoNewton’ssecondlaw,whenanon-zeronetforceactson
Investigation
an object, the object will accelerate in the direction of the net force.
The acceleration is directly proportional to the net force and inversely
proportional
to the mass. The equation representing Newton’s second
S
S
law is F net 5 ma .
• Ifthenetforceonanobjectincreasesandthemassisconstant,thenthe
11 U
acceleration increases. If the net force on an object is constant and the mass
increases, then the acceleration decreases.
C03-F050-OP11USB
• Whensolvingproblemswheremorethanoneforceactsonasingleobject,
CrowleArt Groupmake sure you draw an FBD. You canSadd all the forces to calculate the net
S
Deborah Crowle force. You can also use the equation F net 5 ma .
S
3.3.1
Investigating Newton’s Second
Law (p. 150)
Now that you have learned about
Newton’s second law, you can
perform Investigation 3.3.1. You
will explore how changing the net
force acting on a system affects the
acceleration of the system. You will
also explore how changing the mass
of the system affects the acceleration
of the system.
S
• Forafallingobject,Newton’ssecondlawcanbeusedtojustifythat F g 5 m g .
4th pass
NEL
3.3 Newton’s Second Law of Motion
135
3.3 Questions
9. A long, heavy, metal chain is held at rest on a table with
part of the chain hanging over the edge (Figure 9). The
chain is released and it starts to accelerate. K/U
1. Calculate the net force in each situation. T/I
(a) A 72 kg rugby player accelerates at 1.6 m/s2
[forward].
(b) A 2.3 kg model rocket accelerates at 12 m/s2 [up].
2. Calculate the acceleration in each situation. T/I
(a) A cannon exerts a force of 2.4 3 104 N [E] on
a 5.0 kg shell.
(b) A hockey stick hits a 160 g puck forward with a force
of 24 N.
Figure 9
(a) In which direction will the chain accelerate? What
causes the acceleration? Explain your reasoning.
(b) What will happen to the acceleration of the chain as
more chain moves over the edge of the table? Explain
your reasoning.
3. Determine the mass of the object in each situation. T/I
(a) A driver brakes and the car accelerates at 1.2 m/s2
[backwards]. The net force on the car is 1400 N
[backwards].
(b) A woman throws a shot put with a net force of
33 N [forward] with an acceleration of 6.0 m/s2
[forward].
10. Three students push horizontally on a large 80 kg crate
sitting on the floor. Two of them push to the left on the
crate, each with a force of 170 N. The third pushes to the
4. A 54 kg skier starts from rest at the top of a snow-covered
right on the crate with a force of 150 N. Assume that no
11 U the net
hill, reaching a velocity ofOntario
12 m/s inPhysics
5.0 s. Calculate
friction acts on the crate. T/I
T/I
force acting on the skier. 0176504338
(a) What is the acceleration of the crate?
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5. A dynamics cart is pulledFN
from rest by a net force
of
(b) What will happen to the net force and acceleration if a
CrowleArt
1.2 N [forward]. The cartCO
moves 6.6 m, reaching
a velocityGroup
fourth student jumps on top of the crate? Explain your
of 3.2 m/s [forward]. Determine the mass of the
cart. T/ICrowle
Deborah
reasoning.
6. During a parachute jump,Pass
a 58 kg person opens
thepass
1st
11. A string can hold up 12 kg without breaking. You tie the
parachute and the total drag
force
acting
on
the
person
is
string to a 30 kg object sitting on ice and use it to pull
Approved
720 N [up]. T/I
the object horizontally for 22 m. Calculate the minimum
Not Approved
(a) Calculate the net force acting on the person.
possible time to complete the task. T/I
(b) Determine the acceleration of the person.
12. Examine the data in Table 1. T/I C
7. A net force of magnitude 36 N gives an object of mass
(a) Copy and complete the table.
S
S
m1 an acceleration of 6.0 m/s2. The same net force gives
(b) Graph F a versus a and draw the line of best fit. What
m1 and another object of mass m2 fastened together
does the y-intercept represent? Explain.
S
an acceleration of 2.0 m/s2. What acceleration will m2
S
(c)
Graph
F
net versus a and draw the line of best fit.
T/I
experience if the same net force acts on it alone? Calculate the slope of the line. What does the slope
8. A 1300 kg car accelerates at 1.6 m/s2 [E]. A frictional force
represent? Explain.
of 3800 N [W] is acting on the car. T/I C
(a) Draw the FBD of the car.
(b) Determine the applied force acting on the car.
Table 1
Mass (kg)
Friction (N) [W]
Applied force (N) [E]
4.0
9.0
9.0
4.0
9.0
13.0
4.0
9.0
4.0
9.0
136 Chapter 3 • Newton’s Laws of Motion
Net force (N) [E]
Acceleration (m/s2) [E]
8.4
3.5
NEL
3.4
Newton’s Third Law of Motion
Examine the photograph in Figure 1 of an Atlas V rocket during liftoff. What forces
are acting on the rocket? An obvious one is gravity pulling the rocket down. The
rocket is accelerating upward in the picture. This means that the net force must be
up according to Newton’s second law. What is this upward force? You might suggest
that the ground is pushing up on the rocket with the normal force. This cannot be
the answer because the normal force is a contact force and the rocket is no longer in
contact with the ground. In this section, you will learn about this upward force as you
learn about Newton’s third law of motion.
Action and Reaction Forces
If you reach out and push this book away from you, you can actually feel the book
pushing back on you. This is an example of a set of action and reaction forces. The
action force is you pushing on the book, and the reaction force is the book pushing
back on you. An easy way to experience action and reaction forces is by pushing on
the boards when you are skating in an ice rink. When you push on the boards (the
action force), the boards push back on you (reaction force). It is the reaction force
that causes you to accelerate away from the boards.
These action and reaction forces are all around us and go unnoticed most of the
time. When you push a door open, the door pushes back on you. When you walk
forward across the floor, you push backwards on the ground and the ground pushes
forward on you. In fact, whenever one object exerts a force on another, the second
object exerts another force back.
Another simple way to demonstrate action and reaction forces is to have a person
standing at rest on a skateboard suddenly step forward (Figure 2). When this happens, the person and the skateboard will accelerate in opposite directions. According
to Newton’s second law, both the person and the skateboard have net forces acting on
them because they are accelerating. What causes these forces?
The net force on the skateboard is caused by the person’s feet pushing backwards
on the skateboard. The person’s feet exert the action force on the skateboard. The net
force on the person is caused by the skateboard pushing forward on the person. The
skateboard exerts the reaction force on the person.
Keep in mind that these action and reaction forces are simultaneous. It is incorrect to
imply that the action force happens first and then the reaction force happens. These are
contact forces, and both the action and reaction forces start whenever contact is made.
Newton’s third law of motion deals with these action and reaction forces. For this
reason, it is sometimes called the action–reaction law.
V of person
V of skateboard
Figure 2 As a person jumps off
a skateboard in one direction, the
skateboard will accelerate in the other
direction.
Third Law of Motion
For every action force, there is a simultaneous reaction force that is equal in magnitude,
but opposite in direction.
We can now explain how a rocket can accelerate up off the launch pad. During
liftoff, the rocket engines burn rocket fuel, creating tremendous pressure, which causes
the expanding hot gases to accelerate from the bottom of the rocket (action force).
At the same time, the expanding hot gases push up on the rocket (reaction force),
causing the rocket to accelerate up. According to Newton’s third law, the action force
caused by the expanding hot gases is equal in magnitude to the reaction force of the
expanding hot gases on the rocket. If the reaction force up on the rocket from the
expanding hot gases is greater than the force of gravity pulling the rocket down, then
the rocket will accelerate up. In the following Tutorial, you will apply Newton’s third law
to problems involving motion.
NEL
Figure 1 An Atlas V rocket was
launched in June 2009. As the rocket
lifted up off the launch pad, what force
caused it to accelerate upward?
third law of motion each action force
has a reaction force that is equal in
magnitude and opposite in direction
3.4 Newton’s Third Law of Motion 137
Tutorial 1 Explaining Motion Using Newton’s Third Law
In the following Sample Problem, we will clarify Newton’s third law and demonstrate how it
can be used to explain motion when objects exert forces on each other.
Sample Problem 1
Explain each event in terms of Newton’s third law.
(a) A swimmer moves through the water.
(b) A small balloon releases air and flies around the classroom.
(c) You start walking across the floor.
(b) As the rubber in the balloon contracts, it forces air out the
back of the balloon (action force). According to Newton’s
third law, the reaction force is caused by the air pushing
back on the balloon, which accelerates the balloon
forward.
Solution
(c) The bottom of your shoe exerts a horizontal backward action
force on the floor. According to Newton’s third law, the
reaction force is caused by friction when the floor pushes
forward on your feet. Friction causes you to accelerate
forward.
(a) The swimmer’s arms and legs exert an action force
backwards on the water, causing the water to accelerate
backwards. According to Newton’s third law, the water
exerts an equal but opposite force forward on the swimmer,
propelling the swimmer forward through the water.
Practice
1. Explain each event in terms of Newton’s third law.
(a) A rocket can accelerate in outer space.
(b) A motorboat accelerates east in the water.
(c) Football player 1 tackles football player 2.
K/U
Mini Investigation
Demonstrating the Third Law
SKILLS
HANDBOOK
Skills: Predicting, Performing, Observing, Analyzing, Communicating
In this investigation, you will perform and observe several actions
that involve Newton’s third law. Your task is to predict what will
happen at each station, observe carefully what actually happens,
and explain why it happens.
Equipment and Materials: office chair with wheels; bathroom
scale; desk; ballistics cart; fan cart with removable sail
1. Create a table similar to Table 1 to record your observations.
Add six rows to the table.
Table 1
Activity
Prediction
Observation
3. Perform activities (a) to (g) (or observe a classmate
performing these activities). Record your observations.
(a) Sit on an office chair and push gently against a wall with
both hands.
(b) Sit on the chair, not touching the wall. Use your hands to
pull horizontally on your own shoulders, away from the wall.
138
(c) Stand on a bathroom scale placed beside a desk. Put
your hands on the desk and push down.
(d) Stand on a bathroom scale. Push down on your own
head with your hands.
(e) Use a spring-loaded ballistics cart to fire a ball
horizontally.
(f) Obtain a fan cart (Figure 3(a)) with no sail. Direct the
fan away from the cart. Turn the fan cart on.
(g) Obtain a fan cart (Figure 3(b)) with a sail. Direct the fan
toward the sail. Turn the fan cart on.
sail
Action and reaction
forces
2. Read through the descriptions of activities (a) through (g).
For each activity, predict what you think will happen and
record your predictions in your table.
Chapter 3 • Newton’s Laws of Motion
A2.1
(a)
(b)
Figure 3
A. Use Newton’s third law to describe the action and reaction
forces you observed in each activity. T/I
NEL
You may have noticed that objects will not always accelerate or the reading on a
scale will not always change when a force is applied to an object. What is different
about these situations? The difference is that in each of these situations there is no
external net force acting on the object.
Does this mean that action and reaction forces cancel and we can never accelerate?
Definitely not. Action and reaction forces always act on different objects, or different
parts of a single object. When two objects are involved, the two forces are not added
together and each object can accelerate.
For example, if a ballistics cart pushes backwards on a ball (action force), the
ball accelerates backwards because the applied force causes a net force on the ball.
According to Newton’s third law, the ball will also cause a reaction force on the cart
in the opposite direction. This reaction force causes a net force on the cart, making
it accelerate the other way. The action and reaction forces do not cancel because they
do not act on the same object. When you draw the FBD for each object, the action
and reaction forces will appear in separate FBDs (Figure 4).
FBD of ball
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technician and a forensic scientist,
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FBD of cart
F�N
F�N
F�g
F�g
(a) before
FBD of ball
FBD of cart
F�N
F�N
F�a
F�a
F�g
F�g
(b) after
Figure 4 (a) Diagram and FBDs of a ball inside a ballistics cart before firing (b) Diagram and FBDs
after firing the ball. The action and reaction forces do not cancel because they act on different
objects.
Tutorial 2 Using Newton’s Third Law in Calculations
tario Physics 11 U
In the following Sample Problem, we will clarify Newton’s third law and demonstrate how it
76504338
can be used to explain motion when objects exert forces on each other.
C03-F057a-OP11USB
Nesbitt
Sample Problem 1: One Skater Pushing on Another
Two skaters are standing on ice facing each other (Figure 5).
4th Pass (1st pass 7381-A)
Skater 1 pushes on skater 2 with a force of 70 N [E]. Assume
that no friction acts on either skater. The mass of skater 1 is
50 kg and the mass of skater 2 is 70 kg.
(a) State the action and reaction forces.
(b) Draw the FBD of each skater.
(c) Describe what will happen to each skater.
(d) Calculate the acceleration of each skater.
ntario Physics 11 U
76504338
NEL
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N
ss
proved
t Approved
skater 1
skater 2
Figure 5
3.4 Newton’s Third Law of Motion
139
Solution
(a) The action force is skater 1 pushing with 70 N [E] on
skater 2. The reaction force is skater 2 pushing with 70 N
[W] on skater 1.
(b) Choose east as positive. So west is negative.
skater 2
skater 1
F�N1
F�N2
(d) For each skater, the normal force and the force of gravity
cancel. This means that the applied force is equal to the net
force. For skater 1,
S
S
F net 5 F a
m1a1 5 270 N
150 kg2 a1 5 270 N
a1 5 21.4 m/s2
The acceleration of skater 1 is 1.4 m/s2 [W].
Similarly, for skater 2,
F a � �70 N
F a � �70 N
S
S
F net 5 F a
m2a2 5 170 N
F�g
1
170 kg2 a2 5 70 N
a2 5 11.0 m/s2
F�g
2
(c) Skater 1 will accelerate west and skater 2 will accelerate east.
The acceleration of skater 2 is 1.0 m/s2 [E].
Notice that the two skaters accelerate in opposite directions
and with different accelerations. The accelerations do not have
the same magnitude because the skaters’ masses are different.
Practice
1. Given the action force, describe the reaction force for each
situation. K/U C
(a) You push forward on a book with 5.2 N.
(b) A boat exerts a force of 450 N [W] on the water.
(c) A hockey player hits the boards with a force of 180 N
[toward the boards].
3. A horse is tethered to a cart to pull it forward. A student
claims, “According to Newton’s third law, when the horse
pulls forward on the cart, the cart will also pull backwards
on the horse. The two objects are attached together, so they
cannot accelerate.” Discuss the validity of this statement.
2. Nobel and Maaham are wearing inline skates. Nobel has
a mass of 62 kg and pushes on Maaham, whose mass is
54 kg. Maaham accelerates at 1.2 m/s2 [left]. Assume that
no friction acts on either person. T/I
(a) Determine the force that Nobel exerts on Maaham.
4. A student stands on a skateboard and pushes on a wall with
a force of 87 N [S]. The total mass of the student and the
skateboard is 58 kg. K/U T/I
(a) Calculate the acceleration of the student. [ans: 1.5 m/s2 [N]]
(b) Explain why the wall does not move.
K/U
C
[ans: 65 N [left]]
s 11 U
(b) Determine Nobel’s acceleration. [ans: 1.0 m/s2 [right]]
C03-F059b-OP11USB
81-A)
Nesbitt
UNiT TASK BOOKMARK
5th Pass (1st pass 7381-A)
You can apply what you have learned
about Newton’s third law to the Unit
Task on page 204.
140
3.4 Summary
• Newton’sthirdlawalwaysinvolvessituationswheretwoobjectsexertforces
on each other.
• Newton’sthirdlawstatesthatforeveryactionforcethereisasimultaneous
reaction force equal in magnitude but opposite in direction.
• WhenapplyingNewton’sthirdlaw,theactionandreactionforceswillappearon
separate FBDs. Since they are on separate FBDs, they are not added together.
Chapter 3 • Newton’s Laws of Motion
NEL
3.4 Questions
1. Given each action force, state the reaction force.
(a) A tire pushes on the road with a force of
240 N [backwards].
(b) You pull on a desk with a force of 25 N [N].
K/U
2. Explain each event below in terms of Newton’s third law.
(a) A squid moves through the water by taking in water
and expelling it.
(b) Walking on a wagon is dangerous.
(c) A helicopter can hover above the ground.
K/U
3. During a space walk, an astronaut notices that her tether
is not attached and she is drifting away from the space
station. Explain each statement below using Newton’s
third law. K/U C
(a) She can pull herself back to the space station if she
can reach the space station and pull on it.
(b) She cannot push herself back to the station by pulling
forward on her space suit.
(c) She can get back to the space station even if she
cannot reach it if she is holding a tool.
6. A toy car (200 g) moves by shooting a plastic ball (50 g)
horizontally out the back. The average acceleration of the
car is 1.2 m/s2 [E] and there is negligible friction acting on
each part of the toy. T/I C
(a) Draw an FBD for each object.
(b) Identify the action and reaction forces on each part
of the toy.
7. Two figure skaters are moving east together during a
performance. Skater 1 (78 kg) is behind skater 2 (56 kg)
when skater 2 pushes on skater 1 with a force of
64 N [W]. Assume that no friction acts on either
skater. T/I
(a) Determine the acceleration of each skater.
(b) What will happen to the motion of each skater?
Explain your reasoning.
8. A milk carton filled with water is hanging from a string
(Figure 8). What will happen if you punch two holes in
opposite sides of the carton at the opposite corners?
Explain your reasoning. T/I
4. Figure 6 shows a photograph of an early naval cannon tied
to a ship. Explain why the ropes are necessary. A
Figure 6
5. Figure 7 shows a fan cart. K/U
(a) Explain why the fan cart cannot accelerate.
(b) Explain why the fan cart can accelerate if the rigid sail
is removed.
sail
Figure 8
9. A male astronaut (82 kg) and a female astronaut (64 kg)
are floating side by side in space. T/I
(a) Determine the acceleration of each astronaut if the
woman pushes on the man with a force of 16 N [left].
(b) How will your answers change if the man pushes with
16 N [right] on the woman instead?
(c) How will your answers change if they both reach out
and push on each other’s shoulders with a force of
16 N?
Figure 7
NEL
3.4 Newton’s Third Law of Motion
141
3.5
using newton’s laws
Newton’s three laws of motion apply to many different situations everywhere around
you. They can be used to determine if a train locomotive can make it through a
mountain pass while pulling many cars behind it. The laws can also be used to design
devices such as prosthetic limbs and bridges (Figure 1). To understand how to design
these types of devices, you need to know how to apply all three of Newton’s laws, and
you need to know how they are related to each other. For example, forces act on a
prosthetic leg to accelerate it so a person can walk. The tension in suspension bridge
cables helps to hold up the roadway against the force of gravity.
CAREER LInK
To learn about becoming a civil
engineer,
g o T o N E L So N SCi E NCE
Figure 1 Newton’s three laws of motion
are used to design devices such as
(a) prosthetic limbs and (b) bridges.
(a)
(b)
In this section, you will practise using all three laws together to solve more complex and interesting problems involving forces and motion. In addition, you will learn
more about forces, such as tension, and how to use kinematics to understand motion
problems more clearly.
Tension and newton’s Laws
Recall that tension is a pulling force exerted by a device such as a rope or a string.
In this course, you may assume that the ropes or strings are light and do not stretch.
This means that you do not have to include the mass of the string when calculating
the acceleration of two objects tied together. It also means that the tension is uniform
throughout the rope or string and pulls with the same force at both ends. Keep in
mind that ropes and strings can only pull. This means that tension always acts on the
object directed toward the rope or the string.
For example, two masses are tied together with a string, and a horizontal applied force
pulls m1 to the right (Figure 2). If the string exerts a tension of 20 N [left] on m1, then it
also exerts a tension of 20 N [right] on m2. This is a direct consequence of Newton’s third
law and the fact that the string does not stretch and has negligible mass.
How can we measure tension directly? One way is with a force sensor or a spring
scale. If you tie opposite ends of a string to two separate force sensors and then pull
on the string in opposite directions, you can easily see that the readings on both
sensors are the same (Figure 3). Again, this is a direct consequence of Newton’s third
law and our assumptions about strings. A single force sensor or spring scale can be
used to measure the tension in strings if it is tied between two strings (Figure 4).
CAREER LInK
To learn about becoming a crane
operator,
g o T o N E L So N SCi E NCE
m2
FT FT
m1
Fa
force sensor
Figure 2 Two objects tied together with
a string. The tension force at both ends
of the string is the same.
142
Chapter 3 • Newton’s Laws of Motion
Figure 3 Two force sensors tied
together with a string. The readings on
the sensors will be equal according to
Newton’s third law.
Figure 4 Force sensors can be used to
measure tension in strings.
NEL
Keep in mind that when two objects are tied together with a single string, if you
drag one object forward, the other will also move forward once the string becomes
taut. This means that the two objects will move with the same acceleration when
they are pulled in a straight line. In this case, tension is an internal force and can be
ignored if you are calculating the acceleration of both objects.
Since the tension is the same throughout the string and the tension pulls in
opposite directions at the ends, we often just calculate the magnitude of the tension
and refer to the FBD for the direction. The following Tutorial will help you to practise
solving problems that involve tension and Newton’s laws.
Tutorial 1 Solving Tension Problems
To solve the following Sample Problems, we will use Newton’s laws and our knowledge of
tension. Each problem will help clarify some of the concepts about tension.
Sample Problem 1: Objects Hanging from Strings
Each object in Figure 5 has a force of gravity of 120 N [down]
acting on it. Determine the tension in each string.
(b)
(a)
(c)
Figure 5
Solution
(a) First draw the FBD of the object. Choose up as positive.
F�T
F g � �120 N
The object is at rest, so it is not accelerating. Newton’s first
law implies that the net force must be zero.
>
>
>
F net 5 F T 1 F g
Fnet 5 FT 1 12120 N2
0 5 FT 2 120 N
FT 5 1120 N
The tension in the string is 120 N [up].
(b) In this diagram, the force of gravity has not changed and
the object is at rest. This means that the FBD is the same
and we will find the same tension. This example reinforces
the concept that pulleys only change the direction of force
without changing the magnitude of the force.
(c) In this balanced system, both objects are at rest. By
drawing an FBD for either object, you will get exactly the
same result for the tension. This result is contrary to what
most people would expect. Most people would incorrectly
say the string is holding up twice as much mass and
should have twice the tension. Others incorrectly think the
tension is zero since both forces of gravity pull the string at
each end and they should cancel. Neither statement is true.
The second object is just providing the force necessary to
hold up the first object. In other words, the second object
is just doing the job of the wall or beam, but otherwise the
situation is unchanged.
Please choose whichever size works best.
Please choose whichever size works best.
Please choose whichever size works best.
Bottom version is larger.
NEL
3.5 Using Newton’s Laws
143
Sample Problem 2: Objects Connected Horizontally by Strings
S
Three sleds are tied together and pulled east across an icy
surface with an applied force of 120 N [E] (Figure 6). The
mass of sled 1 is 12.0 kg, the mass of sled 2 is 11.0 kg, and
the mass of sled 3 is 7.0 kg. You may assume that no friction
acts on the sleds.
sled 3
rope A
sled 2
rope B
sled 1
S
(b) Calculate the magnitude of the tension in rope A.
(c) Calculate the magnitude of the tension in rope B.
Solution
(a) All three sleds will move together with the same acceleration,
so we can treat them as one single object. The total mass of
all three sleds is mT = 12.0 kg + 11.0 kg + 7.0 kg = 30.0 kg.
There is no need to consider
F�N
the tension at this point
because it is an internal force
and will not contribute to the
acceleration of the total mass.
Choose east as positive. So
F a � 120 N [E]
west is negative.
S
1 120 N 5 130.0 kg2 a
1120 N
a5
30.0 kg
a 5 14.0 m/s2
F�g
F�N
F�N
F a � 120 N [E]
F�TB
(a)
F�g
F�TB
(b)
F�g
Figure 7 (a) FBD of sled 1 (b) FBD of sleds 2 and 3
Ontario Physics 11 U
S
S
F net 5 F TB
0176504338
FN
CO
The acceleration of all three sleds is 4.0 m/s2 [E].
(b) We could use the FBD for either sled 2 or sled 3 to calculate
Pass
the tension in rope A. We will use the FBD for sled 3
Approved
because it is slightly simpler—it only has rope A pulling on
Not Approved
it, whereas sled 2 has both rope A and rope B pulling
on it.
S
S
C03-F070-OP11USB
1m2 1 m32 a 5 F TB
Nesbitt
118.0 kg2 114.0 m/s22 5 F TB
F 5 172 N
3rd Pass (1st passTB7381-A)
The magnitude of the tension in rope B is 72 N.
Practice
1. Examine each diagram in Figure 8. In each situation,
which rope will have the greater tension? Explain your
reasoning. K/U
rope A
rope B
2. A locomotive with a mass of 6.4 3 105 kg is accelerating
Physics 11 U
Ontario
Physics
11aUtrain car with aOntario
2
at 0.12 m/s
[W] while
pulling
mass of
(a)
5
5.0 3 100176504338
kg. Assume that negligible friction is0176504338
acting on
Physics 11 U the train.FNT/I
C03-F071b-OP11USB
FN
C03-F071a-OP11USB
rope A
338
Nesbitt
CO
Nesbitt
CO
(a) Calculate the net force on the entire train.
Fa
C03-F069-OP11USB
[ans: 1.4 3105 N [W]]
(b)
Nesbitt
(b) Determine
of thePass
tension
the
3rd Pass (1st pass 7381-A)
Pass7381-A)
(1stbetween
pass
Pass the magnitude 4th
Figure 8
locomotive
and
the
train
car.
[ans: 6.0 3104 N]Approved
Approved
ed
roved
F�TA
The magnitude of the tension in
rope A is 28 N.
F�g
(c) To calculate the tension in rope B,
we can use the FBD of sled 2, but
our answer will depend on the accuracy of the calculated
tension in rope A. To avoid this problem, you can either
use the FBD of sled 1 or the FBD of sleds 2 and 3
(Figure 7). We will choose the latter since it is slightly
simpler. In this calculation, we will use a mass of
m2 + m3 = 18.0 kg.
(a) Determine the acceleration of the sleds.
S
F�N
S
m3 a 5 F TA
17.0 kg2 114.0 m/s22 5 F TA
FTA 5 128 N
120 N [E]
Figure 6
F net 5 m T a
S
Fnet 5 F TA
4th Pass (1stNot
pass
7381-A)
Approved
144
Chapter 3 • Newton’s Laws of Motion
rope B
Not Approved
NEL
Kinematics and Newton’s Laws
When using any of the kinematics equations from Unit 1, it is essential that the
acceleration remain constant. Now we can extend this restriction by stating that the
net force on an object must also remain constant if you use oneSof the kinematics
S
equations. This is a direct consequence of Newton’s second law, F net 5 m a , which
shows that net force is constant when the acceleration is constant.
Imagine that you start moving east due to a constant net force acting on you. You
might start walking, but you gradually speed up and start running. Then your net force
drops to zero and you move at a constant velocity. Finally, another constant net force
acts in the opposite direction and slows you down until you eventually come to rest.
During the three separate parts of the trip, your acceleration was constant because
the net force was constant. This means that you can use a kinematics equation during
one part of the trip but not a single equation for the entire trip. The following Tutorial
will clarify how to use kinematics concepts with Newton’s laws.
Tutorial 2 Newton’s Laws and Kinematics
When solving the following Sample Problems, keep in mind that the acceleration is
constant when the net force is constant, according to Newton’s second law.
Sample Problem 1: Skater Pushing on the Boards
Starting from rest, an ice skater (54.0 kg) pushes the boards with
a force of 130.0 N [W] and moves 0.704 m. He then moves at a
constant velocity for 4.00 s before he digs in his skates and starts to
C03-F054-OP11USB.ai
slow down. When he digs in his skates, he causes a net force of 38.0
N [W] to slow him down until he stops.
(a)
(b)
Determine the acceleration of the skater
(i) when he is pushing on the boards
(ii) just after he stops pushing on the boards
(iii)when he starts to slow down
How far does he move?
F�N
238.0 N 5 154.0 kg2 a
38.0 N [W]
238.0 N
54.0 kg
a 5 20.704 m/s2
a5
The acceleration of the skater
is 0.704 m/s2 [W] when he is
slowing down.
Solution
Use FBDs to solve this problem.
(a) (i)When the skater pushes the boards
with a force of 130.0 N [W], the
boards push back on the skater
with an equal and opposite force
of 130.0 N [E]. Choose east as
positive. So west is negative.
>
>
F net 5 ma
>
>
F net 5 ma
F�N
130.0 N [E]
F�g
F�g
(b) During part (i), the skater moves 0.704 m [E], but we
need to calculate his final velocity in order to calculate
his displacement during the other sections of the
motion.
S
S
S
Given: v 1 5 0; Dd 5 0.704 m [E]; a 5 2.407 m/s2 [E]
S
Required: v 2
Analysis: v22 5 v12 1 2aDd
Solution: v22 5 v12 1 2aDd
v22 5 102 2 1 2 112.407 m/s22 110.704 m2
v2 5 1.841 m/s (one extra digit carried)
Now we can calculate the displacement for the other
sections of the motion. For part (ii),
S
S
1130.0 N
D d 5 v Dt
a5
54.0 kg
Ontario Physics 11U
5 (11.841 m/s)(4.00 s)
2
a 5 2.407 m/s2 1one extra digit carried
0176504338
Dd 5 7.364 m (one extra digit carried)
C03-F074-OP11USB
The acceleration of the skater is 2.41 m/s2 FN
[E] when he
For part (iii),
Nesbitt
CO
is pushing on the boards.
v 2 5 v 2 1 2aDd
1130.0 N 5 154.0 kg2 a
2
1
(ii) When he stops pushing on the boards, the net force
3rd Pass
02 5(1st
(11.841
m/s)2 1 2(20.704 m/s2)Dd
pass 7381-A)
Pass
acting on him is zero. According to Newton’s first law,
Dd 5 1.981 m (one extra digit carried)
Approved
his acceleration will also be zero.
Statement: The total distance travelled by the skater is
Not Approved
(iii)Now the skater is slowing down and the net force is
0.704 m 1 7.364 m 1 1.981 m 5 10.1 m
opposite to the direction of motion.
NEL
3.5 Using Newton’s Laws 145
Sample Problem 2
A worker pushes two large boxes across the floor from rest with
an applied force of 160.0 N [right] on the larger box (Figure 9).
The boxes are touching. The mass of the larger box is m1 5 32.0 kg
and the mass of the smaller box is m2 5 8.0 kg. The force of
friction on the large box is 80.0 N [left] and the force of friction
on the smaller box is 20.0 N [left].
(b) The force from the large box on the smaller box is an
internal force. To calculate this force, we need to draw the
FBD for just one box. Either box will do but we will use the
smaller one because it has fewer forces acting on it. Again,
the normal force and the force of gravity cancel.
F�N
(a) Calculate the acceleration of the two boxes. Assume that the
boxes start to move.
(b) Determine the force exerted by the larger box on the smaller box.
(c) Determine the velocity of the boxes after 4.0 s.
�20.0 N
F�1 on 2
160.0 N
m1
F�g
m2
Figure 9
(a) Both boxes must move together with the same acceleration,
so for now we will treat them like one single object with a
total mass of mT 5 32.0 kg 1 8.0 kg 5 40.0 kg. From the
FBD for both boxes, the normal force and gravity cancel.
Choose right as positive. So left is negative.
Fnet 5 F 1 on 2 1 1220.0 N2
m 2a 5 F 1 on 2 2 20.0 N
18.0 kg2 111.5 m/s22 5 F1 on 2 220.0 N
F 1 on 2 5 132.0 N
The force exerted by the larger box on the smaller box
is 32.0 N [right].
FN
20.0 N
160.0 N
S
S
(c) Given: v 1 5 0; ∆t 5 4.0 s; a 5 1.5 m/s2 [right]
S
Required: v 2
80.0 N
Fg
S
S
F net 5 m T a
1
2
1
1160.0 N 1 280.0 N 1 220.0 N2 5 m T a
160.0 N 5 140.0 kg2 a
S
S
S
S
S
S
Analysis: v 2 5 v 1 1 a Dt
Solution: v 2 5 v 1 1 a Dt
5 0 1 111.5 m/s22 14.0 s2
v 2 5 16.0 m/s
160.0 N
Statement: The final velocity of both boxes is 6.0 m/s [right].
a5
40.0 kg
504338
Ontario Physics
11 Um/s2
5 11.5
03-F075-OP11USB
The acceleration of both0176504338
boxes is 1.5 m/s2 [right].
ave McKay Illustration
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FN
hm
Nesbitt
CO
Practice
ourth Pass 10/09/30
1. Two dynamics carts are placed end to end. Cart 1 (1.2 kg) is stuck to cart 2 (1.8 kg).
4th Pass
Cart 1 is pushed with a Pass
force of 18.9 N [W], causing
cart(1st
1 topass
push 7381-A)
cart 2 forward.
T/I
Ignore the force of friction.
Approved
(a) Calculate the acceleration
of each cart. [ans: 6.3 m/s2 [W]]
Not Approved
(b) Calculate the force that cart 1 exerts on cart 2. [ans: 11 N [W]]
(c) Would your answers change if cart 2 were pushed with an equal but opposite force
instead of cart 1? If your answers change, calculate the new results.
[ans: 6.3 m/s2 [E]; 7.6 N [W]]
2. A 1200 kg car is moving at 95 km/h when the driver notices a deer down the road. He
immediately moves his foot toward the brake pedal, taking only 0.50 s before the car starts
-F076-OP11USB
slowing down. The brakes cause a net force of 2400 N [backwards] on the car for 2.0 s.
bitt
The deer then jumps out of the way and the driver lifts his foot off the brake pedal. How far
does the car move in the 2.5 s starting from when the driver sees the deer? T/I [ans: 62 m]
Pass (1st pass 7381-A)
146
Chapter 3 • Newton’s Laws of Motion
NEL
3.5 Summary
• Th
etensionsatbothendsofastringoraropeareequalinmagnitude.
• Tensioncanbemeasuredwithaspringscaleoraforcesensor.
• Th
ekeyequationsofmotionfromtheKinematicsunitandNewton’slawscan
be used together to solve motion problems.
3.5 Questions
1. You hold one end of a rope and pull horizontally with a
force of 65 N. Calculate the tension in the rope if the other
end is
(a) tied to a wall
(b) held by a friend who pulls with 65 N in the opposite
direction
(c) tied to a 12 kg object on smooth ice T/I
2. A 72 kg sled is pulled forward from rest by a snowmobile
and accelerates at 2.0 m/s2 [forward] for 5.0 s. The force of
friction acting on the sled is 120 N [backwards]. The total
mass of the snowmobile and driver is 450 kg. The drag
force acting on the snowmobile is 540 N [backwards]. T/I
(a) Determine the tension in the rope.
(b) Calculate the force exerted by the snowmobile that
pushes the sled forward.
3. Two people, each with a mass of 70 kg, are wearing inline
skates and are holding opposite ends of a 15 m rope. One
person pulls forward on the rope by moving hand over hand
and gradually reeling in more of the rope. In doing so, he
exerts a force of 35 N [backwards] on the rope. This causes
him to accelerate toward the other person. Assuming that
the friction acting on the skaters is negligible, how long will
it take for them to meet? Explain your reasoning. T/I
4. A 1200 kg car pulls an 820 kg trailer over a rough road. The
force of friction acting on the trailer is 650 N [backwards].
Calculate the force that the car exerts on the trailer if
(a) the trailer is moving at a constant velocity of
30 km/h [forward]
(b) the trailer is moving at a constant velocity of
60 km/h [forward]
(c) the trailer is moving forward at 60 km/h and starts
accelerating at 1.5 m/s2 [forward]
(d) the trailer is moving forward at 60 km/h and starts
accelerating at 1.2 m/s2 [backwards] T/I
5. An old rope can now only safely suspend 120 kg. When the
rope is tied to a beam, it hangs down with a vertical length
of 12.0 m. Calculate the minimum time required for an
85 kg person starting from rest to climb the entire length of
the rope without breaking it. T/I
NEL
6. Three dynamics carts have force sensors placed on top of
them. Each force sensor is tied to a string that connects all
three carts together (Figure 10). You use a sixth force sensor
to pull the three dynamics carts forward. The reading on force
sensor 2 is 3.3 N. Assume that the force sensors are light and
that there is negligible friction acting on the carts. T/I
2.2 kg
1
2.5 kg
2
1.8 kg
3
4
5
6
Figure 10
(a) What is the acceleration of all the carts?
(b) What is the reading on each force sensor?
(c) What force are you applying to force sensor 6?
7. A locomotive (6.4 × 105 kg) is used to pull two railway
cars (Figure 11). Railway car 1 (5.0 × 105 kg) is attached
to railway car 2 (3.6 × 105 kg) by a locking mechanism.
A railway engineer tests the mechanism and estimates
that it can only withstand 2.0 × 105 N of force. Determine
the maximum acceleration of the train that does not
break the locking mechanism. Explain your reasoning.
Assume that friction is negligible. T/I C
car 2
car 1
Figure 11
8. A skier (68 kg) starts from rest but then begins to move
downhill with a net force of 92 N for 8.2 s. The hill levels
out for 3.5 s. On this part of the hill, the net force on the
skier is 22 N [backwards]. T/I
(a) Calculate the speed of the skier after 8.2 s.
(b) Calculate the speed of the skier at the end of the
section where the hill levels out.
(c) Calculate the total distance travelled by the skier before
coming to rest.
3.5 Using Newton’s Laws
147
Physics JOURNAL
3.6
Galileo, Newton, and Hawking
ABSTRACT
In his book Principia Mathematica, Newton realized that the laws governing
the motion of planets could be applied to all physical phenomena. Newton’s
predictions have had an impact on many fields of science and technology.
Einstein’s theory of relativity and Stephen Hawking’s work on the nature of
gravity and black holes are grounded in Newton’s laws. Newton’s work in
Principia Mathematica may be the greatest achievement in physics.
On July 5, 1687, Newton (Figure 1) first published his
landmark book Principia Mathematica. This work consisted
of three volumes and included many mathematical discoveries, as well as his famous laws of motion. He also used
some of Galileo’s earlier work to help formulate some of his
own ideas, such as the concept of inertia.
The primary focus of Principia Mathematica is on massive objects in motion, such as planets in our solar system.
Newton realized that the rules governing the motion of
large objects in the universe could be used to study how
other fundamental forces act on objects.
In Newton’s time, the other fundamental forces were
either not well understood (such as electromagnetic force)
or completely unknown (such as the strong and weak
nuclear forces). Yet in Principia Mathematica, Newton predicted that the laws of physics would somehow be able to
account for all physical phenomena.
Figure 1 Isaac Newton
Newton and the Foundations of Physics
Today we know that not only was Newton on the right
track with his prediction, but his discoveries have had
148 Chapter 3 • Newton’s Laws of Motion
impacts on fields of study and technology that no one
could have predicted in Newton’s time. His laws of motion
and his ideas about gravity are used to construct buildings
and bridges, design cars and planes, and launch satellites
into orbit.
Newton’s laws of motion are also the foundation of
physics wherever forces are a factor. Albert Einstein wrote,
“To the Master’s honour all must turn, each in its track,
without a sound, forever tracing Newton’s ground.” This is
an eloquent way of stating that Newton’s laws of motion are
so all-inclusive that any other endeavour in physics can be
traced back in some way to Newton’s work.
Einstein: Extending Newton’s Ideas
Einstein’s work on relativity followed a path very similar
to Newton’s laws. Einstein’s special theory of relativity
extended Newton’s first law to deal with the special case of
objects moving at a very fast, constant velocity. Einstein’s
theory of general relativity extended Newton’s second and
third laws to deal with accelerating objects and gravity.
Newton’s third law deals with action and reaction forces.
The most obvious example of these is contact forces. If you
push on an object, it will push back on you with an equal
but opposite force. Newton also stated that this was true of
gravity, which is an action-at-a-distance force. For example,
when you jump up into the air, the force of gravity exerted
by Earth pulls you back down. There is also a reaction force
on Earth exerted by you, pulling up on Earth.
What about the other action-at-a-distance forces? Does
Newton’s third law still apply to those forces? For example,
when a positive charge exerts a force on another charge,
is there an equal and opposite reaction force? What about
magnetism? When a north pole of one magnet exerts a force
on a north pole of another magnet, is there also a reaction force? This is what Newton was thinking about in the
preface of Principia Mathematica. The answer to all of these
questions is yes. Newton’s third law works for any actionat-a-distance force, as well as any contact force. This makes
the third law even more general and all-encompassing than
he had imagined.
NEL
Stephen Hawking: Standing on the
Shoulders of Giants
Physicist Stephen Hawking has continued with the work
started by Galileo, Newton, and Einstein (Figure 2) in his
study of the universe. His work deals mainly with extending
the concepts explored by Newton and Einstein to topics such
as black holes and the nature of gravity. One of his most
widely known accomplishments is the idea that even black
holes can lose mass through Hawking radiation (Figure 3).
(a)
(b)
Figure 2 (a) Albert Einstein (b) Stephen Hawking
To put the contributions and accomplishments of Newton
into perspective, Hawking wrote,
Einstein is the only figure in the physical sciences with
a stature that can be compared with Newton. Newton
is reported to have said: “If I have seen further than
other men, it is because I stood on the shoulders of
giants.” This remark is even more true of Einstein
who stood on the shoulders of Newton. Both Newton
and Einstein put forward a theory of mechanics and
a theory of gravity but Einstein was able to base
General Relativity on the mathematical theory of
curved spaces that had been constructed by Riemann
while Newton had to develop his own mathematical
machinery. It is therefore appropriate to acclaim
Newton as the greatest figure in mathematical physics
and the Principia is his greatest achievement.
Figure 3 Hawking radiation from a black hole. Until Hawking
showed otherwise, people thought that nothing could escape a
black hole.
Further Reading
Greene, B. (1999). The Elegant Universe. New York: W. W.
Norton & Company.
Hawking, S. (1988). A Brief History of Time. New York:
Bantam Dell.
Hawking, S. (2001). The Universe in a Nutshell. New York:
Bantam Books.
Hawking, S., & Israel, W. (Eds.). (1987). 300 Years of
Gravitation. New York: Cambridge.
3.6 Questions
1. Explain the meaning of the statement, “Great physicists are
often influenced by the great physicists of the past.” K/U C
2. Describe, using an example, how Newton’s laws of motion
have affected your own life. C A
3. Explain why Hawking places Newton ahead of Einstein as
the greatest figure in mathematical physics. K/U C
NEL
4. Research some of the other topics and concepts covered in
Principia Mathematica not outlined in this section. For one
of these topics, write a short report on its significance and
T/I
C
A
applications. go to nelson sc i ence
3.6 Physics Journal: Galileo, Newton, and Hawking 149
chaPTer
3
Investigations
Investigation 3.3.1
conTrolled eXPerIMenT
• Questioning
• Researching
• Hypothesizing
• Predicting
Investigating newton’s
Second Law
In this investigation, you will perform two controlled
experiments. In Part A, you will measure the acceleration
of a cart using different net forces while keeping the total
mass constant. In Part B, you will measure the acceleration
of a cart using different total masses while keeping the net
force constant.
Testable Questions
• Howdoestheaccelerationofacartdependonthenet
force acting on the cart if the total mass is constant?
• Howdoestheaccelerationofacartdependonthe
total mass if the net force is constant?
Hypothesis/Prediction
SKILLS
HANDBOOK
A2.2
After reading through the experiment, write a hypothesis
to answer each Testable Question.
variables
Identify the independent (sometimes called manipulated)
and dependent (sometimes called responding) variables
in this experiment. Describe how you will measure these
variables. What variables must be controlled?
Experimental Design
There are many different ways to perform this activity.
Figure 1 shows one simple way to apply a constant force
to a cart.
ticker tape timer
SKILLS MEnU
• Planning
• Controlling
Variables
• Performing
• Observing
• Analyzing
• Evaluating
• Communicating
Keep in mind that the force of gravity acting on the
hanging object is the net force on the total mass. The total
mass includes the hanging object, the cart, the string, and
any objects on top of the cart. If you want to change the
force and keep the total mass constant, take an object off
the cart and hang it from the string. If you want to change
the mass and keep the net force constant, change the
objects on top of the cart but do not change the hanging
objects.
Discuss with your group members how you will safely stop
the cart before performing the investigation.
Equipment and Materials
•
•
•
•
•
•
•
•
dynamicscart
electronicbalance
tickertapetimer,motionsensor,orsimilardevice
three100gobjects
three1.0kgobjects
pulley
string
tickertape
Procedure
Part A: Acceleration and net Force
1. Create a table to record your observations similar to
Table 1.
cart with masses
Table 1
pulley
Total
mass
Hanging
mass
Net force
Acceleration
Net force/
total mass
Figure 1
150
Chapter 3 • Newton’s Laws of Motion
NEL
2. Measure the mass of the cart.
(d)
Use
yourBOOKMARK
results from Part A to plot a graph of net
UNiT
TASK
force
(y-axis)
versus acceleration (x-axis). Draw a
3. Set up the equipment as shown in Figure 1 or as
As you
plan
tobest
carryfitoutand
the Unit
Task (page
XXX), consider
line
of
calculate
its slope.
Whatwhat
doesyou
directed by your teacher. Make sure everything is
havethis
learned
about
synthesis
and
decomposition
reactions
in
this
graph indicate about the relationship between
working properly by allowing the cart to accelerate
section.
acceleration and net force? What does the slope
once or twice.
represent? T/I C
4. Put one 1.0 kg object and two 100 g objects on top of
(e) Use your results from Part B to plot a graph of
the cart. You might need to tape them down. Hang
acceleration (y-axis) versus total mass (x-axis). Draw
a 100 g object from the string. Allow
the
motion
CONTROLLED EXPERIMENT
Skills Menu
a smooth curve through the points. What
does
to occur and obtain the data required to find the
S
this
graph
indicate
about
the
relationship
between
•
Questioning
•
Planning
•
Observing
acceleration ( a 1).
• acceleration
Researching
• Controlling
and total
mass? T/I C • Analyzing
5. Take one of the 100 g objects from on top of the cart
• Hypothesizing
Variables
• Evaluating
(f) • Use
your results from
Part B to plot a• graph
of
and hang it from the string. Allow the motion to
Predicting
• Performing
Communicating
acceleration
(y-axis)
versus
the
reciprocal
of
the
occur and obtain the data required to find the new
S
total
mass
(1/m;
x-axis).
Draw
a
line
of
best
fit
and
acceleration ( a 2).
calculate
its
slope.
What
does
this
graph
indicate
6. Take the last 100 g object from the top of the cart
about the relationship between acceleration and total
and hang it from the string. Allow the motion to
mass? What does the slope represent? T/I C
occur and obtain the data required to find the new
S
(g) Answer the Testable Questions. T/I
acceleration ( a 3).
Investigation 5.1.2 Part B: Acceleration and Mass
S
7. Use the data for a 3 from Step 6 as the first set of data
for this experiment.
8. Using the same cart setup as in Step 6, add one
1.0 kg object to the cart. Allow the motion to
occur and obtain the data required to find the
S
new acceleration ( a 4).
9. Add an additional 1.0 kg object to the cart. Allow the
motion to occur and obtain the data required to find
S
the new acceleration ( a 5).
Analyze and Evaluate
(a) In terms of the variables in this investigation, what
type of relationship was being tested? T/I
(b) Calculate the acceleration for each trial. T/I
(c) Calculate the ratio of the net force to the total
mass. What does this ratio represent? Explain your
reasoning. K/U T/I
NEL
(h) Comment on the accuracy of your hypothesis. C
(i) List some possible sources of error. How could you
modify the investigation to avoid or reduce these
sources of error? T/I
Apply and Extend
(j) Describe how you could determine if friction had any
effect on the results of this investigation. T/I
(k) Explain why a graph of net force versus acceleration
must pass through the origin when the total mass is
constant. T/I
(l) Explain why a graph of acceleration versus the
reciprocal of the total mass must pass through the
origin when net force is constant. T/I
(m) Commercial airlines are limiting the number of pieces
and the mass of luggage that passengers can bring
onto an aircraft. Use what you have learned in this
investigation to explain why. C A
Chapter 3 Investigations 151
chaPTer
3
SUMMARY
Summary Questions
1. Create a study guide for this chapter based on the
Key Concepts listed in the margin on page 112. For
each point, create three or four subpoints that provide
further information, relevant examples, explanatory
diagrams, or general equations.
2. Look back at the Starting Points questions on
page 112. Answer these questions using what you
have learned in this chapter. Compare your latest
answers with those that you wrote at the beginning
of the chapter. Note how your answers have
changed.
3. You may use several different forms of active
transportation, such as bicycles, skateboards, and
inline skates. Using the concepts of this chapter,
analyze the safety issues of one of these forms of
transportation. Make sure you use all of Newton’s laws
in your explanations. Also provide some safety tips
that will help reduce the chance of serious injury.
vocabulary
>
applied force (F a) (p. 115)
>
tension (F T) (p. 115)
>
normal force (F N) (p. 115)
>
friction (F f) (p. 115)
dynamics (p. 114)
newton (N) (p. 114)
system diagram (p. 114)
free-body diagram (FBD) (p. 115)
>
force of gravity (F g) (p. 116)
>
net force (F net) (p. 119)
first law of motion (p. 124)
second law of motion (p. 131)
third law of motion (p. 137)
inertia (p. 124)
CAREER PATHwAYS
Grade 11 Physics can lead to a wide range of careers. Some require a college diploma
or a bachelor of science degree. Others require specialized or post-graduate degrees.
This graphic organizer shows a few pathways to careers related to topics covered in
this chapter.
1. Select an interesting career that relates to forces and Newton’s laws of motion.
Research the educational pathway you would need to follow to pursue this career.
2. What is involved in the career you have chosen? Research at least two programs,
and design a poster or pamphlet to display your findings.
forensic
technician
B.Sc.
M.Sc.
SKILLS
HANDBOOK
A7
materials scientist
Ph.D.
rocket scientist
forensic scientist
prosthesis designer
sports footwear designer
aeronautics engineer
12U Physics
B.Eng.
OSSD
civil engineer
11U Physics
accident reconstructionist
college diploma
crane operator
mechanic
go T o N ELSoN SC i EN C E
152
Chapter 3 • Newton’s Laws of Motion
NEL
CHAPTER
3 SELF-Quiz
K/U
Knowledge/Understanding For each question, select the best answer from the four
alternatives.
1. Which of the following best describes a normal force?
(3.1) K/U
(a) a force that resists the motion or attempted
motion of an object
(b) a perpendicular force exerted by a surface on an
object in contact with the surface
(c) the pull between two objects at a distance
(d) the force in a string or rope when pulled
2. Which force is responsible for the interactions during
particle transformations? (3.1) K/U
(a) electromagnetic
(b) gravitational
(c) weak nuclear
(d) strong nuclear
3. Which object, when stationary, has the least inertia?
(3.2) K/U
(a) a desk
(b) a pen
(c) a computer
(d) a feather
4. A 60.0 kg object accelerates with a magnitude of
2.0 m/s2. What is the magnitude of the net force
acting on this object? (3.3) T/I
(a) 30 N
(b) 60 N
(c) 120 N
(d) 180 N
5. What is the mass of a rock that experiences a
gravitational force of magnitude 11.8 N? (3.1) T/I
(a) 1.1 kg
(b) 1.3 kg
(c) 1.2 kg
(d) 1.0 kg
6. Which statement best describes Newton’s third law?
(3.4) K/U
(a) For every action force, there is a reaction force of
lesser magnitude and in the same direction.
(b) For every action force, there is a reaction force of
equal magnitude but opposite in direction.
(c) For every action force, there is a reaction force of
equal magnitude and in the same direction.
(d) For every action force, there is a reaction force of
lesser magnitude but in the opposite direction.
T/I
Thinking/Investigation C
Communication A
Application
7. An ice skater pushes off a railing. Which of the
following is the reaction force? (3.4) K/U
(a) the force of the skater pushing off the railing
(b) the force of the railing pushing back on the skater
(c) the force of friction from the ice
(d) the force of gravity
8. What important realization did Newton describe in
Principia Mathematica? (3.6) K/U
(a) Forces are governed by the theory of relativity.
(b) The rules governing the motion of large objects
in the universe can be used to study how
fundamental forces act on objects.
(c) Black holes lose mass through a special type of
radiation.
(d) Apples fall from trees due to gravitational force.
Indicate whether each statement is true or false. If you think
the statement is false, rewrite it to make it true.
9. Forces are measured in newtons. (3.1) K/U
10. The normal force is the force resisting the motion or
attempted motion of an object. (3.1) K/U
11. A free-body diagram is a simple sketch of all the
objects involved in a situation. (3.1) K/U
12. All forces require objects to be in contact and cannot
act at a distance. (3.1) K/U
13. The net force on an object is the sum of all the forces
acting on it. (3.1) K/U
14. Massive objects have more inertia than less massive
objects. (3.2) K/U
15. An object can change its motion even if the net force
acting on it is zero. (3.2) K/U
16. If the net force on an object is constant and the mass
decreases, then the acceleration increases. (3.3) K/U
17. Newton’s third law states that for every action force,
there is a simultaneous reaction force of equal
magnitude acting in the same direction. (3.4) K/U
To do an online self-quiz,
go t o nelso n sc ience
NEL
Chapter 3 Self-Quiz 153
CHAPTER
3 Review
K/U
Knowledge/Understanding Knowledge
For each question, select the best answer from the four
alternatives.
1. Which of the following symbols is used for a tension
force? (3.1) K/U
>
(a) F a
>
(b) F net
>
(c) F T
>
(d) F f
2. In which direction does friction act? (3.1) K/U
(a) parallel to the surface and opposite to an object’s
motion or attempted motion
(b) perpendicular to the surface and opposite to an
object’s motion or attempted motion
(c) parallel to the surface and in the same direction
as an object’s motion or attempted motion
(d) normal to the surface and opposite to an object’s
motion or attempted motion
3. Which of the following symbols is used to represent
the sum of all forces acting on an object? (3.1) K/U
>
(a) F N
>
(b) F a
>
(c) F T
>
(d) F net
4. Which force holds the protons together in the nucleus
of an atom? (3.1) K/U
(a) electromagnetic
(b) gravitational
(c) weak nuclear
(d) strong nuclear
5. You have your seat belt on in the passenger seat of a
car. The car suddenly accelerates. Which statement
best describes your motion? (3.2) K/U
(a) Your body will suddenly move forward with
respect to the seat.
(b) Your head will suddenly move forward with
respect to your body.
(c) Both your body and your head will move forward
at the same rate.
(d) Your head and your body will suddenly move
backwards with respect to the seat.
154 Chapter 3 • Newton’s Laws of Motion
T/I
Thinking/Investigation C
Communication A
Application
6. Which of the following correctly states Newton’s
second law? (3.3) K/U
>
>
a
(a) F net 5 > m>
(b) mF net 5 a >
>
(c) F net 5 ma
>
>
(d) F net , ma
7. A boy jumps off a skateboard. What is the reaction
force? (3.4) K/U
(a) the force exerted by the boy pushing off the
skateboard
(b) the force exerted by the skateboard pushing back
on the boy
(c) the force of friction exerted by the road on the
skateboard
(d) the force of gravity causing the boy to land on the
ground
8. Which device could be used to measure tension?
(3.5) K/U
(a) a bathroom scale
(b) a balance
(c) a spring scale
(d) a sliding scale
Indicate whether each statement is true or false. If you think
the statement is false, rewrite it to make it true.
9. One newton is equal to 1 kg·m/s. (3.1) K/U
10. A tension force is a perpendicular force acting on an
object that is exerted by the surface with which it is in
contact. (3.1) K/U
11. Friction is a force that resists the motion or attempted
motion of an object. (3.1) K/U
12. Forces that do not require contact are called actionat-a-distance forces. (3.1) K/U
13. To determine the net force, you do not need to
consider the direction of each force acting on an
object. (3.1) K/U
14. An object with less mass has more inertia. (3.2) K/U
15. If there is a net force acting on an object, then the
motion of the object will change. (3.2) K/U
16. If the net force on an object is constant and the mass
increases, then the acceleration decreases. (3.3) K/U
17. Newton’s third law states that for every action force
there is a simultaneous reaction force of lesser
magnitude in the opposite direction. (3.4) K/U
NEL
Match each term on the left with the most appropriate
description on the right.
18. (a) weak nuclear
(i)
(b) normal
(ii)
(c) friction
(iii)
(d) tension
(iv)
(e) gravity
(v)
a pulling force from a rope
or a string
a force that resists the
motion or attempted
motion of an object
the force responsible for
interactions during particle
transformations
the force of attraction
between two objects because
of their mass
a perpendicular force
exerted by a surface on an
object (3.1) K/U
Write a short answer to each question.
19. What is the rate of acceleration due to gravity? (3.1) K/U
20. In your own words, describe what it means for an
object to have inertia. (3.2) K/U C
21. In your own words, describe Newton’s third law and
give an example that demonstrates this law. (3.4) K/U C
Understanding
22. A book sits on a desk. Draw a free-body diagram of
all the forces acting on the book. (3.1) K/U
23. The free-body diagram in Figure 1 represents a block
Ontario
Physicsvelocity
11 U across a rough
being dragged
at constant
surface. Copy
Figure 1 into your notebook and draw
0176504338
in the missing
sure to indicate its
C03Q-F02-OP11USB
FN force vector. Be
direction and magnitude relative to the other forces
Nesbitt
CO
shown. (3.1) K/U
24. The free-body diagram in Figure 2 represents a block
sitting motionless on a ramp. Is the FBD complete?
Explain. Include an FBD in your answer. (3.1) T/I C
F�f
F�g
Figure 2
25. Draw a free-body diagram for the first two situations.
Then answer (c). (3.1) T/I C
(a) A student pulls a large box across a smooth floor
to the right.
(b) A student pushes a large box across a smooth
floor to the right.
(c) Are there any differences between your diagrams
for (a) and (b)? Explain.
26. The engines of a plane exert a horizontal force
of magnitude 37 850 N while the plane is flying
northward. A wind blowing to the south also exerts
a horizontal force of magnitude 850 N on the plane.
What is the net horizontal force on the plane? (3.1) T/I
27. The engines of a plane flying westward exert a
horizontal force of magnitude 35 000 N. A wind
blowing westward exerts a horizontal force of
magnitude 1200 N. What is the net horizontal force
on the plane? (3.1) T/I
28. A trap door that opens in the middle is stuck half
open with a box sitting on it (Figure 3). Draw a
free-body diagram for the box. (3.1) T/I
2nd Pass (1st pass 7381-A)
Pass F�N
Approved
Not ApprovedF�a
box
doors
F�g
Figure 1
Figure 3
NEL
Chapter 3 Review
155
29. Use Newton’s first law to explain why the normal force
39. The cart in Figure 4 has a mass of 2.3 kg and is
must be equal in magnitude to the force of gravity
attached to a 1.7 kg object. Calculate the acceleration
for an object to remain at rest on a horizontal
of the cart given the following assumptions: (3.3) T/I
surface when no other forces are acting on the
(a) The force of friction is negligible.
object. (3.2) K/U C
(b) The frictional force acting on the wheels of the
cart has a magnitude of 0.6 N.
30. Four children are playing tug-of-war. The two
children on the right pull with forces of magnitude
84 N and 86 N, and one of the children on the left
is able to pull with a force of magnitude 83 N. If the
rope remains stationary, how hard is the second child
on the left pulling? (3.2) T/I
31. A student is trying to push a box across the floor with
20 N of force, but the box does not move. What is
Figure 4
the magnitude of the frictional force exerted by the
ground on the box? (3.2) T/I
40. Assume the cart in Figure 4 has an acceleration of
magnitude 2.5 m/s2 and a mass of 1.8 kg. Calculate
32. Answer each question below using Newton’s second
the mass of the attached object given the following
law. Explain your answers. (3.3) K/U C
assumptions: (3.3) T/I
(a) Two cars have the same net force acting on them,
(a) The force of friction is negligible.
but one has more mass than the other. Which car
(b) A frictional force of magnitude 0.4 N acts on the
will have the greater acceleration?
wheels of the cart.
(b) A heavy box of sand is on top of a cart. A person
pulls the cart forward with a constant net force
41. Explain each situation using Newton’s third law. (3.4) K/U
while the sand leaks out of the box and onto the
(a) A boat is able to float on water.
ground. What will happen to the acceleration of
(b) A dolphin can jump out of the water by pushing
the cart?
down on the water.
33. Calculate the net force in each situation. (3.3) T/I
(c) A raft glides to the left when a student jumps off
(a) A 69 kg sprinter accelerates at 2.1 m/s2 [forward].
the raft to the right.
(b) A 620 g basketball falls through the net.
42. When a cannon fires, it rolls backwards. Use your
T/I
Ontario
Physics
11 (3.3)
U
knowledge of Newton’s laws to explain why this
34. Calculate the net acceleration
in each
situation.
happens. (3.4) K/U C
0176504338
(a) A 260 kg boat crew paddles
north with a net
force of magnitude 468
43. A student stands on a skateboard and pushes on a
C03Q-F03-OP11USB
FNN.
(b) A 70.0 kg skydiver opens
his
parachute
and
CrowleArt Group wall with a force of magnitude 89 N. The total mass of
CO
the student and the skateboard is 58 kg. Assume that
experiences a net force of 236 N [up].
Deborah Crowle
the force of friction is negligible. (3.4) T/I C
35. A student pushes a 10 kg Pass
box and lets it slide1st
across
pass
(a)
Calculate the acceleration of the student.
the floor. The magnitude of the frictional force acting
Approved
(b) Explain why the wall does not appear to move.
on the box is 40 N. What is the acceleration of the
Not Approved
box? (3.3) T/I
44. A girl is ice skating and pushes off a rail with a force
of magnitude 75 N. The total mass of the girl and her
36. A 175 g hockey puck slows down at a rate of 1.5 m/s2
skates is 62 kg. (3.4) T/I C
as it slides across the ice. Determine the frictional
force acting on the puck. (3.3) T/I
(a) Calculate the acceleration of the girl while she
is pushing if the ice exerts a frictional force of
37. The engines of an airplane exert a net force of
magnitude 4.0 N on the skates.
magnitude 800 000 N during takeoff, causing the
(b) Explain why the rail does not appear to move.
plane to accelerate at a rate of 8.0 m/s2 [forward].
What is the mass of the plane? (3.3) T/I
45. A 3.0 kg object hangs from a string inside an elevator.
Calculate the tension in the string for the following
38. A batter hits a baseball with a mass of 145 g.
situations. (3.5) T/I
After impact, the ball experiences a net force of
3
1.80 3 10 N [S]. What is the acceleration of the ball?
(a) The elevator is stationary.
(3.3) T/I
(b) The elevator is accelerating at 1.2 m/s2 [up].
(c) The elevator is accelerating at 1.4 m/s2 [down].
156
Chapter 3 • Newton’s Laws of Motion
NEL
11 U
Analysis and Application
>
55. The box in Figure 6 has a mass of 85 kg. F a = 10 N [up],
>
>
>
F b 5 30 N [right], F c 5 25 N [right], F d = 10 N [down],
>
and F e 5 22 N [left]. (3.3) T/I
46. Wind is blowing a flag to the east. What other forces
are acting on the flag if it remains attached to a pole?
Include an FBD of the flag in your answer. (3.1, 3.2) T/I
Fa
47. A skydiver has a mass of 71.5 kg. What is the force of
gravity acting on him
(a) when he jumps?
Fb
T/I
(b) after he has landed? (3.1)
Fe
48. A 45.0 kg girl is sitting on a bench. What is the
Fc
magnitude of the force with which the bench pushes
against the girl? (3.1, 3.4) K/U
Fd
49. A boulder rolls off the edge of a cliff and initially falls
Figure 6
with a force of magnitude 1100 N. What is the mass
(a) What is the net force acting on the box in both
of the boulder? (3.1) K/U
the vertical and horizontal directions?
50. A student weighs out 7.6 N of water into a beaker.
(b)
What is the acceleration of the box?
What is the mass of the water? (3.1) K/U
56. Suppose the box in Figure 6 has a net acceleration
51. A T-shirt launcher is capable of shooting shirts at
>
>
of magnitude 5.5 m/s2. F a 5 13 N [up], F b 5 12 N
35 m/s horizontally. If the time it takes to accelerate
>
>
the shirts to this speed is 0.50 s and each shirt has
[right], F c 5 19 N [right], F d 5 26 N [down], and
>
a mass of 250 g, how much force does the launcher
F e 5 31 N [left]. (3.3) T/I
exert on the shirts? Assume that the friction in the
(a) What is the net force acting on the box in both
tube is negligible. (3.3) T/I
the vertical and horizontal directions? In which
52. A 72 kg runner is jogging at a rate of 6.0 m/s and then
direction does the box move?
begins to sprint, reaching a full speed of 15 m/s after
(b) What is the mass of the box?
3.0 s. What is the net force acting on the runner? (3.3) T/I
57. Suppose the box in Figure 6 has a mass of 12 kg.
>
>
>
53. Two boxes of mass 30.0 kg and 10.0 kg are at rest side
F a 5 220 N [up], F b 5 82 N [right], F d 5 220 N
2
by side (Figure 5). You apply a force of 3.0 3 10 N on
>
[down], and F e 5 112 N [left]. The magnitude of the
the first box for 5.0 s, and they both slide across the
acceleration of the box is 1.5 m/s2. (3.3) T/I C
floor. The larger box has a force of friction of 180 N,
and the smaller box
has a force
of friction
(a) If the box is moving
to the right, what is the
Ontario
Physics
11 U of 60.0 N.
>
(3.3, 3.4) T/I C
magnitude of F c?
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(b) If the box is moving
to the left, what is the
>
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magnitude of F c?
10 kg
30 kg CO
Nesbitt
58. A dogsled team has four dogs that pull a person and a
sled with a combined mass of 100 kg. (3.3) T/I
2nd Pass (1st pass 7381-A)(a) They start from rest and reach a speed of 45 km/h
Pass
Figure 5
Approved
in 2.5 s. What is the average force applied by
(a) Calculate theNot
acceleration
of the boxes during the
each dog?
Approved
first 5.0 s.
(b) Suppose each dog can pull with a force of
(b) If the applied force is removed, the boxes will
magnitude 150 N. What is the frictional force
slow down and stop. Explain why.
acting on the sled?
(c) Calculate the total distance travelled by the boxes.
59. The Moon is much smaller than Earth, so the
gravitational strength of the Moon is only about one54. Four students are playing tug-of-war. The two
sixth that of Earth. (3.3) T/I A
students on the right pull with forces of magnitude
55 N and 65 N, and weigh 60 kg and 62 kg. The two
(a) What is the acceleration due to gravity on the Moon?
students on the left pull with forces of magnitude 58 N
(b) How much would a 72 kg person weigh on the
and 70 N, and weigh 59 kg and 64 kg. What are the
Moon?
magnitude and direction of the acceleration of the
(c) If an object falls with a force of 700 N [down] on
students? (3.3) T/I
Earth, what would the force on the same object
be if it fell on the Moon?
NEL
Chapter 3 Review
157
60. A girl is standing on a raft floating on the water and
jumps off to the right with a force of magnitude 100 N.
The mass of the girl is 55 kg, and the mass of the raft
is 120 kg. (3.4) T/I C
(a) Describe the action and reaction forces in this
situation.
(b) Determine the acceleration of both the girl and
the raft.
61. A boy and a girl are standing on skateboards. The
boy pushes off the girl to the left with a force of
magnitude 74 N. The mass of the boy is 62 kg and the
mass of the girl is 59 kg. Ignore friction. (3.4) T/I C
(a) State the action and reaction forces in this situation.
(b) Determine the magnitude and direction of the
acceleration of each skateboarder.
62. Two ice skaters are playing a game. Skater A pushes off
skater B. Skater A has a mass of 75 kg and accelerates
with a magnitude of 1.2 m/s2. Skater B accelerates with
a magnitude of 0.80 m/s2. Ignore friction. (3.4) T/I C
(a) Based on their accelerations, which skater has
more mass?
(b) State the action and reaction forces and calculate
their values.
(c) Calculate the mass of skater B.
63. Students are performing an experiment about Newton’s
third law using skateboards. Student A has a mass
of 58 kg and pushes off student B with a force of
magnitude 80.0 N. Student B has a mass of 55 kg and
has placed a block of unknown mass with him on his
skateboard. (3.4) T/I C
(a) Calculate the acceleration of student A.
(b) If the magnitude of the acceleration of student B
is greater than that of student A, what range of
values could the mass of the block have? What if
the magnitude of the acceleration of student B is
less than that of student A?
(c) If student B accelerates with a magnitude of
1.25 m/s2, what is the mass of the block?
64. A male astronaut (82 kg) and a female astronaut
(64 kg) are floating side by side in space. (3.4) T/I C
(a) Determine the acceleration of each if the woman
pushes on the man with a force of 16 N [left].
Ontario Physics 11 U
(b) How will your answers change if the man pushes
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with 16 N [right] on the woman instead?
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65. A locomotive with a mass of 6.4 3 105 kg is
NGI
accelerating CO
with a magnitude of
0.12 m/s2 while
pulling a train car of mass 5.3 3 105 kg. Assume that
negligible friction
2ndtrain.
pass(3.5) T/I
Pass is acting on the
(a) CalculateApproved
the net force on the entire train.
(b) Determine
tension between the locomotive
Notthe
Approved
and the train car.
158
Chapter 3 • Newton’s Laws of Motion
Ontario Physics 11 U
66. Two objects are hung from strings (Figure 7). The top
object (m1) has a mass of 18 kg and the bottom object
(m2) has a mass of 12 kg. (3.5) T/I
(a) Calculate the tension in each string.
(b) Calculate the tension in each string if you pull
down on m1 with a force of 45 N [down].
(c) Calculate the tension in each string if you pull
down on m2 with a force of 45 N [down].
(d) Compare your answers to parts (b) and (c) and
explain any differences.
(e) If you keep increasing the downward force on
m2, which string will most likely break first?
Explain your reasoning by assuming that both
strings are identical.
string A
m1
string B
m2
Figure 7
67. The blocks in Figure 8 are pulled to the right and
accelerate with a magnitude of 1.1 m/s2. If m1 5 4.0 kg,
m2 5 2.3 kg, and m3 5 3.4 kg, calculate the tension in
each string. Assume that friction is negligible. (3.5) T/I
string A
m1
string B
m2
string C
m3
Figure 8
68. Suppose the blocks in Figure 8 are pulled to the right
with a force of magnitude 15 N. If m1 5 4.3 kg,
m2 5 5.5 kg, and m3 5 3.1 kg, calculate the tension in
each string and the acceleration of the blocks. Ignore
friction. (3.5) T/I
69. Suppose the blocks in Figure 8 are pulled to the right
with a force of magnitude 24 N. The tension in string
B is twice that of the tension in string A. If m1 5 10 kg
and m3 5 8 kg, calculate the tension in each string
and the mass of m2. Ignore friction. (3.5) T/I
NEL
11 U
70. A student has tied together two sleds with a rope. Two
of his friends, with masses of 55.0 kg and 60.0 kg, are
riding in the sleds, one in each (55.0 kg in the back,
60.0 kg in front). The student uses another rope to
pull the sleds with a horizontal force of magnitude
230 N. The sleds accelerate with a magnitude of
1.02 m/s2. The front sled experiences a force of
friction of magnitude 58.8 N. Assume that the
masses of the sleds are negligible. (3.5) T/I
(a) What is the frictional force on the back sled?
(b) What is the tension in the rope connecting the sleds?
(c) The student pulling the sleds starts from rest,
runs for 3.00 s, and then lets the sleds go.
How far will the sleds travel after he lets them go?
Evaluation
71. The planets are constantly changing position around
the Sun and have been closely following the same paths
for millennia. However, the Sun has a small wobble in
its position. Use Newton’s first law and the concept of
inertia to explain why this is so. (3.2) T/I C
72. The gravity of Earth attracts the Moon, just as it does
objects near Earth. By Newton’s third law, the force
that attracts the Moon to Earth is the same force that
attracts Earth to the Moon. (3.4) T/I A
(a) Are objects on Earth attracted to the Moon?
(b) Why does nothing fly off toward the Moon?
73. Figure 9 shows a fan cart with the fan running but
without the cart accelerating. (3.4) K/U
Ontario Physics 11 U sail
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Crowle Art Group
CO
Deborah Crowle
Pass
Approved
Not Approved
1st pass
Figure 9
(a) Explain why the fan cart cannot accelerate.
(b) The sail is removed and the cart begins to
accelerate. Explain why.
NEL
74. Two blocks are hung on opposite ends of a pulley
system, as shown in Figure 10. The left block has a
mass of 35.2 kg and the right block has a mass of
36.4 kg. (3.5) T/I
Figure 10
(a) Is it possible for the blocks to remain stationary?
What forces could be causing this to happen?
(b) What would happen if one of the blocks were
tapped downward?
Reflect on Your Learning
75. A student claims, “If action and reaction forces are
equal in magnitude and opposite in direction, then
when you add them together, you will always get zero
and nothing will ever accelerate.” Discuss the validity
of this statement. C
Research
go To N ELS oN S C i EN C E
76. When two positively charged particles are close
together, they repel each other, and the closer the
particles are, the stronger this repulsion is. However,
in atoms, protons are so close together that the strong
nuclear force is able to overcome the electromagnetic
repulsion. Write a one-page report describing the
strong nuclear force and how strong it has to be in
order to hold the nucleus of atoms together. Compare
this with the strength of the electromagnetic repulsion
acting at the same distance. What happens in heavier
elements where there are a lot of protons and thus an
even stronger electromagnetic repulsion? T/I C
77. Newton is reported to have said, “If I have seen
further than other men, it is because I stood on the
shoulders of giants,” meaning that he could not have
made the discoveries that he did without the previous
work of other scientists. Prepare a presentation in a
format of your choice describing the knowledge of
science at the time and who the primary influences
were for Isaac Newton. What discoveries did they
make, what observations did they make, and what
experiments did they perform that helped lead
Newton to his discoveries? T/I C
Chapter 3 Review
159