Download Chapter 5 - CPO Science

U2
Unit
C5
Chapter
Motion and Force in One Dimension
Chapter 5 Newton’s Laws:
Force and Motion
Objectives:
By the end of this chapter you should be able to:
4Describe how the law of inertia affects the motion of an object.
4Give an example of a system or invention designed to overcome inertia.
4Measure and describe force in newtons (N) and pounds (lb).
4Calculate the net force for two or more forces acting along the same line.
4Calculate the acceleration of an object from the net force acting on it.
4Determine whether an object is in equilibrium by analyzing the forces acting on it.
4Draw a diagram showing an action-reaction pair of forces.
4Determine the reaction force when given an action force.
Key Questions:
When do you encounter Newton’s laws of motion in daily life? How are force, mass, and acceleration related?
What are some common action-reaction force pairs?
Vocabulary
action
force
net force
Newton’s second law
reaction
dynamics
law of inertia
newton (N)
Newton’s third law
statics
equilibrium
locomotion
Newton’s first law
99
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
5.1 The First Law: Force and Inertia
Sir Isaac Newton (1642–1727), an English physicist and mathematician, is one of the most famous
scientists who have ever lived. Before the age of 30, he made several important discoveries in physics
and invented a whole new kind of mathematics—calculus. The three laws of motion discovered by
Newton are probably the most widely-used natural laws in all of science. Together, Newton’s laws are
the model which connects the forces acting on an object, its mass, and its resulting motion. This chapter
is about Newton’s laws, and the first section is about the first law, the law of inertia.
Force
Changing an Suppose you want to move a box from one side of the room to the other. What
object’s motion would you do? Would you yell at it until it moved? “Hey, box, get going! Move to
the other side of the room!” Of course not! You would push or pull it across the
room. In physics terms, you would apply a force to the box.
Force is an A force is what we call a push or a pull, or any action that has the ability to
action that can change an object’s motion. Forces can be used to increase the speed of an object,
change motion decrease the speed of an object, or change the direction in which an object is
moving. For something to be considered a force, it does not necessarily have to
change the motion, but it must have the ability to do so. For example, if you push
down on a table, it will probably not move. But if the legs were to break, the table
could move. Therefore, your push qualifies as a force.
Creating force Forces can be created by many different processes. For example, gravity creates
force. Muscles can create force. The movement of air, water, sand, or other matter
can create force. Electricity and magnetism can create force. Even light can create
force. No matter how force is created, its effect on motion is always described by
Newton’s three laws.
Changes in
motion only
occur through
force
100
Forces create changes in motion, and there can be no change in motion without
also having a force (Figure 5.1). Anytime there is a change in motion, a force must
exist, even if you cannot immediately recognize the force. For example, when a
rolling ball stops by hitting a wall, its motion changes rapidly. That change in
motion is caused by the wall exerting a force that stops the ball.
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
Figure 5.1: Force is the action
which has the ability to change
motion. Without force, the motion
of an object cannot be started
or changed.
NEWTON’S LAWS: FORCE AND MOTION
Inertia
Objects tend to Consider that box you wish to move across the room. What if the box had been
keep doing what moving and you wanted to stop it? Again, yelling a command will not make it
they are doing stop. The only way to stop the box is to apply enough force in a direction opposite
to its motion. In general, objects tend to continue doing what they are already
doing. If they are moving, they tend to keep moving, in the same direction, at the
same speed. If they are at rest, they tend to stay at rest. This idea is known as
Newton’s first law of motion.
Newton’s Newton’s first law states that an object will continue indefinitely in its current
first law state of motion, speed, and direction, unless acted upon by a net force. Intuitively,
you know that the motion of a massive object is harder to change than the motion
of a lighter object. Inertia is a term used to measure the ability of an object to
resist a change in its state of motion. An object with a lot of inertia takes a lot of
force to start or stop; an object with a small amount of inertia requires a small
amount of force to start or stop. Because inertia is a key idea in Newton’s first law,
the first law is sometimes referred to as the law of inertia.
Chapter
5
Which systems in a car
overcome the law of inertia?
The engine supplies force that
allows you to change motion by
pressing the gas pedal.
The brake system is designed to
help you change your motion by
slowing down.
The steering wheel and steering
system is designed to help you
change your motion by changing
your direction.
Inertia is a The amount of inertia an object has depends on its mass. More massive objects
property of have more inertia than less massive objects. Recall that mass is a measure of the
mass amount of matter in an object. Big trucks are made of more matter than small cars;
thus, they have greater mass and a greater amount of inertia. It takes more force to
stop a moving truck because it has more inertia than a small car. This is a
common-sense application of the first law.
Origin of the The word inertia comes from the Latin word inertus, which can be translated to
word inertia mean “lazy.” It can be helpful to think of things that have a lot of inertia as being
Can you think of three parts of a
bicycle that are designed to
overcome the law of inertia?
very lazy when it comes to change. In other words, they want to maintain the
status quo and keep doing whatever they are currently doing.
5.1 THE FIRST LAW: FORCE AND INERTIA
101
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
Applications of Newton’s first law
Seat belts and Two very important safety features of automobiles are designed with Newton’s
air bags first law in mind: seat belts and air bags. Suppose you are driving down the
highway in your car at 55 miles per hour when the driver in front of you slams on
the brakes. You also slam on your brakes to avoid an accident. Your car slows
down but the inertia of your body resists the change in motion. Your body tries to
continue doing what it was doing—traveling at 55 miles per hour. Luckily, your
seat belt or air bag or both supplies a restraining force to counteract your inertia
and slow your body down with the car (Figure 5.2).
Cup holders A cup holder does almost the same thing for a cup. Consider what happens if you
have a can of soda on the dashboard. What happens to the soda can when you turn
sharply to the left? Remember, the soda can was not at rest to begin with. It was
moving at the same speed as the car. When your car goes left, the soda can’s
inertia causes it to keep moving forward (Figure 5.3). The result is quite a mess.
Automobile cup holders are designed to keep the first law from making messes.
The tablecloth Have you ever wondered how a magician is able to pull a tablecloth out from
trick underneath dishes set on a table? It’s not a trick of magic at all, but just physics.
The dishes have inertia and therefore tend to resist changes in motion. Before the
magician pulls on the cloth, the dishes are at rest. So when the tablecloth is
whisked away, the inertia of the dishes keeps them at rest. This trick works best
when the tablecloth is pulled very rapidly and the table is small. It would be quite
difficult to perform this trick with the long table in the diagram. Can you think
why the long table would make the trick hard to do?
Figure 5.2: Because of its inertia,
your body tends to keep moving
when your car stops suddenly. This
can cause serious injury if you are
not wearing a seat belt.
Figure 5.3: Because of its inertia,
a soda can on the dashboard will
tend to keep moving forward when
the car turns left.
102
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
5.2 The Second Law: Force, Mass, and Acceleration
Newton’s discovery of the connection among force, mass, and acceleration was a milestone in our
understanding of science. The second law is the most widely used equation in physics because it is so
practical. This section shows you how to apply Newton’s second law to practical situations.
Newton’s second law of motion
Force is related The acceleration of an object is equal to the force you apply divided by the mass
to acceleration of the object. This is Newton’s second law, and it states precisely what you
already know intuitively. If you apply more force to an object, it accelerates at a
higher rate. If the same force is applied to an object with greater mass, the object
accelerates at a lower rate because mass adds inertia. The rate of acceleration is
the ratio of force divided by mass.
Figure 5.4: An ice-skater can
coast for quite a long time because
motion at constant speed does not
require force. If there was no friction,
a skater could coast at constant
speed forever. Force is required only
to speed up, turn, or stop.
Motion at Force is not necessary to keep an object in motion at constant speed. An ice-skater
constant speed will coast for a long time without any outside force (Figure 5.4). However, the
ice-skater does need force to speed up, slow down, turn, or stop. Recall that
changes in speed or direction always involve acceleration. Force causes
acceleration, and mass resists acceleration.
5.2 THE SECOND LAW: FORCE, MASS, AND ACCELERATION
103
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
The definition of force
What is force?
Pounds In the English system, the unit of force, the pound, was originally defined by
gravity. One pound is the force of gravity pulling on a mass of 0.454 kilograms.
When you measure your weight in pounds on a bathroom scale, you are measuring
the force of gravity acting on your mass.
The simplest concept of force is a
push or a pull.
On a deeper level, force is the
action that has the ability to
create or change motion. Pushes
or pulls do not always change
motion. But they could.
Newtons The metric definition of force depends on the acceleration per unit of mass.
A force of one newton is exactly the amount of force needed to cause a mass of
one kilogram to accelerate at one m/s2. We call the unit of force the newton (N)
because force in the metric system is defined by Newton’s second law. The
newton is a useful way to measure force because it connects force directly to its
effect on matter and motion. A net force of one newton will always accelerate a
1-kilogram mass at 1 m/s2, no matter where you are in the universe.
Converting The newton is a smaller unit of force than the pound. A force of one pound is
newtons and equal to about 4.448 newtons. This means a pound of force can accelerate a
pounds 1-kilogram mass at 4.448 m/s2. Pounds are fine for everyday use here on Earth but
inconvenient for physics because of the conversion factor of 4.448.
104
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
The unit of force is derived from
fundamental quantities of length,
mass, and time. Using the
second law, the units of force
work out to be kg·m/s2.
A force of 1 N causes a 1 kg
mass to accelerate at 1 m/s2. We
could always write forces in
terms of kg·m/s2. This would
remind us what force is. But,
writing kg·m/s2 everywhere would
be a nuisance. Instead we use
newtons. One newton (1 N) is
1 kg·m/s2.
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
Using the second law of motion
Net force The force (F) that appears in the second law is the net force. There are often many
forces acting on the same object. Acceleration results from the combined action of
all the forces that act on an object. When used this way, the word net means
“total.” To solve problems with multiple forces, you have to add up all the forces
to get a single net force before you can calculate any resulting acceleration.
Three forms of The second law can be rearranged three ways. Choose the form that is most
the second law convenient for calculating what you want to know. The three ways to write the law
are summarized below.
Table 5.1: Three forms of the second law
Use...
a=
F
M
F = ma
M=
F
a
if you want to find...
and you know...
The acceleration (a)
The net force (F) and the
mass (m)
The net force (F)
The acceleration (a) and the
mass (m)
The mass (m)
The acceleration (a) and the
net force (F)
Units for the To use Newton’s second law in physics calculations, you must be sure to have
second law units of m/s2 for acceleration, newtons for force, and kilograms for mass. Many
problems will require you to convert forces from pounds to newtons. Other
problems may require you to convert weight in pounds to mass in kilograms.
Remember also that m stands for mass in the formula for the second law. Do not
confuse the variable m with the abbreviation m that stands for meters.
Calculating the acceleration of
a cart on a ramp
A cart rolls down a ramp. Using a
spring scale, you measure a net force
of 2 newtons pulling the car down.
The cart has a mass of 500 grams
(0.5 kg). Calculate the acceleration
of the cart.
1. You are asked for the
acceleration (a).
2. You are given mass (m) and
force (F).
3. Newton’s second law applies.
a=F÷m
4. Plug in numbers. Remember that
1 N = 1 kg·m/s2.
a = (2 N) / (0.5 kg)
= (2 kg·m/s2) / (0.5 kg)
= 4 m/s2
5.2 THE SECOND LAW: FORCE, MASS, AND ACCELERATION
105
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
Finding the acceleration of moving objects
Dynamics The word dynamics refers to problems involving motion. In dynamics problems,
the second law is often used to calculate the acceleration of an object when you
know the force and mass. For example, the second law is used to calculate the
acceleration of a rocket from the force of the engines and the mass of the rocket.
Direction of The acceleration is in the same direction as the net force. Common sense tells you
acceleration this is true, and so does Newton’s second law. Speed increases when the net force
is in the same direction as the motion. Speed decreases when the net force is in the
opposite direction as the motion.
Acceleration from
multiple forces
Three people are pulling on a wagon
applying forces of 100 N, 150 N, and
200 N as shown. Determine the
acceleration and the direction the
wagon moves. The wagon has a
mass of 25 kilograms.
Positive and We often use positive and negative numbers to show the direction of force and
negative acceleration. A common choice is to make velocity, force, and acceleration
positive when they point to the right. Velocity, force, and acceleration are negative
when they point to the left. You can choose which direction is to be positive, but
once you choose, be consistent in assigning values to forces and accelerations.
The sign of When solving problems, the acceleration always has the same sign as the net
acceleration force. If the net force is negative, the acceleration is also negative. When both
velocity and acceleration have the same sign, the speed increases with time. When
velocity and acceleration have opposite signs, speed decreases with time. Careful
use of positive and negative values helps keep track of the direction of forces
and accelerations.
106
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
1. You are asked for the
acceleration (a) and direction.
2. You are given the forces (F) and
mass (m).
3. The second law relates
acceleration to force and mass
(a = F ÷ m).
4. Assign positive and negative
directions. Calculate the net
force then use the second law to
determine the acceleration from
the net force and the mass.
F = –100N – 150 N + 200N
= –50N
a = (–50 N) ÷ (25 kg)
= –2 m/s2
The wagon accelerates 2 m/s2 to
the left.
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
Finding force from acceleration
Amount of force Newton’s second law allows us to determine how much force is needed to cause a
needed given acceleration. Engineers apply the second law to match the force developed
by different engines to the acceleration required for different vehicles. For
example, an airplane taking off from a runway needs to reach a certain minimum
speed to be able to fly. If you know the mass of the plane, Newton’s second law
can be used to calculate how much force the engine must supply to accelerate the
plane to take-off speed.
Force to accelerate a plane
taking off
Forces that The second law also allows us to determine how much force must have been
must have been present to cause an observed acceleration. Wherever there is acceleration there
must also be force. Any change in the motion of an object results from
acceleration. Therefore, any change in motion must be caused by force. When a
tennis ball hits a racquet, it experiences high acceleration because its speed goes
rapidly to zero then reverses direction. The high acceleration is evidence of
tremendous forces between the racquet and the ball, causing the ball to flatten and
the racquet strings to stretch. Newton’s second law can be used to determine the
forces acting on the ball from observations of its acceleration.
A tennis ball contacts the racquet for much less than one second. High-speed photographs show
that the speed of the ball changes from –30 m/s to +30 m/s in 0.006 seconds. If the mass of the
ball is 0.2 kg, how much force is applied by the racquet?
Force on a
tennis ball
striking a
racquet
1. You are asked for force (F).
2. You are given the mass (m), the change in speed (v2 – v1), and the time interval (t).
3. Newton’s second law (a = F ÷ m) relates force to acceleration. Acceleration is the change
in speed divided by the time interval over which the speed changed or a = (v2 – v1) ÷ t.
4. Use the change in speed to calculate the acceleration. Use the acceleration and mass to
calculate the force.
a = (60 m/s) ÷ (0.006 s) = 10,000 m/s2
F = (0.2 kg) × (10,000 m/s2) = 2,000 N. This force is equal to three times the weight of the
tennis player and 1,000 times the weight of the tennis ball!
An airplane needs to accelerate at
5 m/s2 to reach take-off speed before
reaching the end of the runway. The
mass of the airplane is 5,000 kg.
How much force is needed from
the engine?
1. You asked for the force (F).
2. You are given the mass (m) and
acceleration (a).
3. The second law applies.
a=F÷m
4. Plug in the numbers.
Remember that
1 N = 1 kg·m/s2.
F = (5,000 kg) × (5 m/s2)
= 25,000 N
5.2 THE SECOND LAW: FORCE, MASS, AND ACCELERATION
107
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
Finding forces when acceleration is zero
Zero
acceleration
means zero
net force
When acceleration is zero, the second law allows us to calculate unknown forces
in order to balance other forces we know. Think about a gymnast hanging
motionless from two rings (Figure 5.5). The force of gravity pulls down on the
gymnast. The acceleration must be zero if he is not moving. The net force must
also be zero because of the second law. The only way the net force can be zero is
if the ropes pull upward with a force exactly equal and opposite the force of
gravity pulling downward. If the weight of the gymnast is –700 newtons, then
each rope exerts an upward force of +350 newtons.
Equilibrium The condition of zero acceleration is called equilibrium. In equilibrium, all forces
cancel out, leaving zero net force. Objects that are standing still are in equilibrium
because their acceleration is zero. Objects that are moving at a constant speed and
direction are also in equilibrium.
Statics problem A statics problem usually means there is no motion. Most statics problems
involve using the requirement of zero net force, or equilibrium, to determine
unknown forces. Engineers who design bridges and buildings solve statics
problems to calculate how much force must be carried by cables and beams. The
cables and beams can then be designed so that they safely carry the forces that are
required. The net force is also zero for motion at constant speed. Constant speed
problems are treated like statics problems as far as forces are concerned.
A woman is walking two dogs on a leash. If each dog pulls with a force of 80 newtons, how
much force does the woman have to exert to keep the dogs from moving?
A static force
problem
1.
2.
3.
4.
108
You are asked for force (F).
You are given two 80 N forces and the fact that the dogs are not moving (a = 0).
Newton’s second law says the net force must be zero if the acceleration is zero.
The woman must exert a force equal and opposite to the sum of the forces from the
two dogs. Two times 80 N is 160 N, so the woman must hold the leash with an equal and
opposite force of 160 N.
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
Figure 5.5: This gymnast is not
moving so the net force must be zero.
If the weight of the gymnast is
700 N, then each rope must pull
upward with a force of 350 N in
order to make the net force zero.
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
5.3 The Third Law: Action and Reaction
This section is about the often-repeated phrase “For every action there is an equal and opposite
reaction.” This statement is known as Newton’s third law of motion. Newton’s first and second laws
of motion discuss single objects and the forces that act on them. Newton’s third law discusses pairs of
objects and the interactions between them. This is because forces in nature always occur in pairs, like
the top and bottom of a sheet of paper. You cannot have one without the other.
Forces always occur in action-reaction pairs
Moving in space The astronauts working on the space station have a serious problem when they
is a problem need to move around in space: There is nothing to push on. How do you move
Figure 5.6: An astronaut can
move in space by throwing an object
in the direction opposite where the
astronaut wants to go.
around if you have nothing to push against?
Forces always The solution is to throw something opposite the direction you want to move. This
come in pairs works because all forces always come in pairs. If this seems like a strange idea,
think through the following example. Suppose an astronaut throws a wrench.
A force must be applied to the wrench to accelerate it into motion. The inertia of
the wrench resists its acceleration. Because of its inertia, the wrench pushes back
against the gloved hand of the astronaut. The wrench pushing on the astronaut
provides a force that moves the astronaut in the opposite direction (Figure 5.6).
Forces on Forces also come in pairs when objects are not moving. For example, consider this
objects at rest book. It is probably lying open on a table. The weight of the book exerts a force on
the table, the same as it would exert on your hands if the book was resting on your
hands. The table pushes back upward on the book with a force equal and opposite
the book’s weight. A chain of force pairs keeps going because the table pushes
down on the floor and the floor pushes back up on the table (Figure 5.7). The
floor pushes down on the walls and Earth pushes back up on the walls to hold up
the floor.
Action-reaction The two forces in a pair are called action and reaction. Anytime you have one,
pairs you also have the other. If you know the strength of one you also know the
strength of the other since both forces are always equal. The two forces in an
action-reaction pair always point in exactly opposite directions. They do not
cancel each other because they act on different objects.
Figure 5.7: Forces always come in
action-reaction pairs. The two forces
in a pair are equal in strength and
opposite in direction.
5.3 THE THIRD LAW: ACTION AND REACTION
109
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
Newton’s third law of motion
The first and The first and second laws apply to single objects. The first law states that an object
second laws will remain at rest or in motion at constant speed and direction until acted upon by
an external force. The second law states that net force causes acceleration and
mass resists acceleration.
The third law In contrast to the first two laws, the third law of motion applies to pairs of objects
operates on because forces always come in pairs. Newton’s third law states that for every
pairs of objects action force there has to be a reaction force that is equal in strength and opposite in
direction. For example, to move on a skateboard you push your foot against the
ground (Figure 5.8). The reaction force is the ground pushing back against your
foot. The reaction force is what pushes you forward, because it is the force that
acts on you. Your force against the ground pushes against Earth; however, the
planet is so large that there is no perceptible motion resulting from your force.
Action-reaction Action and reaction forces act on different objects, not on the same object. For
forces act on example, the action-reaction pair that is required to move a skateboard in the
different objects traditional way includes your foot and Earth. Your foot pushing against the ground
Figure 5.8: All forces come in
pairs. When you push on the ground
(action), the reaction of the ground
pushes back on your foot.
is the action force. The ground pushing back on your foot is the reaction force. The
reaction force makes you move because it acts on you (Figure 5.8). Why doesn’t
your foot make the ground move? Simply because the force is too small to
accelerate Earth’s huge mass. Even though the reaction force that acts on you is
the same size, you are much less massive than Earth. The same size reaction force
is big enough to accelerate you.
Stopping action It is easy to get confused about action and reaction forces. People often ask,
and reaction “Why don’t they cancel each other out?” The reason is that the action and reaction
confusion forces act on different objects. The action force of your foot acts on Earth and
Earth’s reaction force acts on you. The forces cannot cancel because they act on
different objects.
Action and It does not matter which is the action force and which is the reaction. Whichever
reaction force you call the action makes its counterpart the reaction. The important thing is
to recognize which force acts on which object (Figure 5.9). To apply the second
law properly, you need to identify the forces acting on the object for which you are
trying to find the acceleration.
110
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
Figure 5.9: It does not matter
which force you call the action or the
reaction. The action and reaction
forces are interchangeable.
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
Solving problems with action-reaction forces
Thinking about
which force
is acting on
which object
In many physics problems, you are asked to determine the acceleration of a
moving object from the forces acting on it. In the last section, you learned that the
net force is the total of all forces acting on an object. Very often one of the forces
will be a reaction force to a force created by the object. For example, consider a
small cart attached to a spring (Figure 5.10). When you push the spring against a
wall, a force is created. When you let the cart go, the force from the spring
accelerates the cart away from the wall. But the force from the spring is pushing
on the wall, so what force accelerates the cart? The answer is the reaction force of
the wall pushing back on the spring. A force created by an object cannot accelerate
the object itself, but the reaction force can.
Three people are each applying 250 newtons of force to try to move a heavy cart. The people
are standing on a rug. Someone nearby notices that the rug is slipping. How much force must be
applied to the rug to keep it from slipping? Sketch the action and reaction forces acting between
the people and the cart and between the people and the rug.
Determining the
reaction forces
from people
pushing a cart
Figure 5.10: Analyzing the action
and reaction forces for a cart
launched off a wall by a spring.
1.
2.
3.
4.
You are asked for how much force (F) it takes to keep the rug from slipping.
You are given that three forces of 250 N each are being applied.
The third law says that each of the forces applied creates a reaction force.
Each person applies a force to the cart and the cart applies an equal and opposite force to
the person. The force on the rug is the sum of the reaction forces acting on each person. The
total force that must be applied to the rug is 750 N in order to equal the reaction forces from
all three people.
5.3 THE THIRD LAW: ACTION AND REACTION
111
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
Locomotion
Locomotion The act of moving or the ability to move from one place to another is called
locomotion. Any animal or machine that moves depends on Newton’s third law
to get around. When we walk, we push off the ground and move forward because
of the ground pushing back on us in the opposite direction.
In the water When something swims, it pushes on water and the water pushes back in the
opposite direction. As a result, the animal, submarine, or even microscopic
organism moves one way, and a corresponding amount of water moves in the
opposite direction. The movement of a boat through water results from a similar
application of Newton’s third law. When a lone paddler in a kayak exerts an action
force pushing the water backward, the reaction force acts on the paddle, pushing
the paddle and the kayak forward (Figure 5.11).
In the air Whether insect, bat, bird, or machine, any object that flies under its own power
moves by pushing the air. Living creatures flap their wings to push air, and the air
pushes back, propelling them in the opposite direction. Jets, planes, and
helicopters push air, too. In the specific example of a helicopter, the blades of the
propeller are angled such that when they spin, they push the air molecules down
(Figure 5.12). According to Newton’s third law, the air molecules push back up on
the spinning blades and lift the helicopter.
Figure 5.11: Action and reaction
forces for a kayak moving through
the water.
The natural Squid use jet propulsion to move quickly. A squid fills a large chamber in its body
jet engine in with water. The chamber has a valve the squid can open and close. To move
a squid quickly, the squid squeezes the water inside its body with powerful muscles, then
opens the chamber valve and shoots out a jet of water. The squid moves with a
force equal and opposite in direction to the water jet that leaves its body.
Figure 5.12: Action and reaction
forces on
a helicopter.
112
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
Biomechanics
Biomechanics is the science of how physics is applied to muscles and motion. Many athletes use
principles of biomechanics to improve their performance. People who design sports equipment use
biomechanics to achieve the best performance by matching the equipment design to the athlete’s body.
Physicians, carpenters, people who build furniture, and many others also use biomechanics in their
work. Any machine that relies on forces from the human body also relies on biomechanics.
The force A force platform is a very sophisticated scale that can record how forces change
platform over time. Instead of containing springs, as your bathroom scale might, a force
platform contains strain gauges (Figure 5.13). When a person steps or jumps on
the platform, each strain gauge produces a reaction force and also a signal
proportional to the strength of the reaction force. The force readings given off by
the platform are referred to as ground reaction forces or GRFs.
Measuring force There are usually 12 strain gauges, three in each corner of a force platform
in three oriented along the x-, y-, and z-axes. When force is applied to the platform,
directions electrical signals from all 12 strain gauges are sent to a computer. The computer
converts the signals to 12 separate force readings. From these readings, data is
generated regarding the magnitude, direction, and sequence of GRFs being
produced. Based on the relative magnitude of forces on each gauge, the center of
pressure, or location of the force, can also be calculated.
Figure 5.13: A force platform has
12 strain gauges arranged to
measure forces in the x, y, and z
directions at each of the corners.
Who uses force Force platforms are used in many different fields including medicine and athletics.
platforms? Physicians, technicians, and therapists use force platforms in clinical settings to
help in the diagnosis and rehabilitation of walking disorders. Biomechanists,
including athletic trainers, use force platforms for research and to help athletes
improve their technique. Equipment designers and manufacturers use information
from force platforms in the design of sports equipment such as running shoes.
The center of The center of pressure is the place on your foot at which the average force is
pressure exerted against the ground. The center of pressure moves as your foot changes its
contact point with the ground during walking or running. Force platform analysis
is often used to evaluate the differences caused by various types of shoes, different
track surfaces, walking versus running, and changes in gait patterns before and
after surgery (Figure 5.14).
Figure 5.14: The center of
pressure for two runners with
different running styles.
5.3 THE THIRD LAW: ACTION AND REACTION
113
Force from a vertical jump
Jumping is The vertical jump is a common sport skill. Vertical jumps are seen in many
a common different sports including basketball, volleyball, soccer, football, baseball, and
sports skill tennis. A force platform makes an excellent tool to analyze the forces between the
jumper’s foot and the floor.
Measuring the To start the experiment, the athlete stands motionless in the middle of the platform
forces from a (Figure 5.15). The “standing still” data is used to measure the weight of the
vertical jump athlete. That weight is converted to mass, using the second law (m = F ÷ g). The
mass data is stored for later use. When given the command by the researcher, the
athlete bends and jumps as high as possible. The force platform measures the force
from each strain gauge at a rate of 250 to 1,000 measurements per second.
The force versus The biomechanist uses the data to generate a force versus time graph. A typical
time curve force versus time curve for a vertical jump is shown at the bottom of Figure 5.15.
The total force recorded is the combination of the athlete’s weight and the force
produced during the jump. In this case, the athlete weighs 550 newtons. The peak
GRF recorded is approximately 1,340 newtons. The time from the start of the
jump until the athlete leaves the platform is just about one second. Once the
athlete takes off and no longer touches the force table, the force readings drop to
zero until the athlete lands back on the platform. The total time that the force is
zero corresponds to the time in the air, a piece of information that allows other
calculations to be made later.
Other
characteristics
of jumping
motion
The force table data can be used to calculate many characteristics of the jumping
motion. The total energy used can be calculated, as well as the maximum height
reached. The force generated by the athlete’s legs can also be determined along
with maximum acceleration, and the balance of force between right and left legs.
Other The technique of electromyography monitors the nerve signals to muscles and can
biomechanical determine the relative strength and sequence of contractions in the muscles being
techniques used in jumping. When combined with video equipment, the force, position, and
time data can give a complete analysis of the motion that an athlete can watch to
improve or evaluate her technique.
114
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
Figure 5.15: A force platform can
be used to measure the vertical force
exerted during a vertical jump.
NEWTON’S LAWS: FORCE AND MOTION
Chapter
5
Chapter 5 Assessment
Vocabulary
Concept review
Select the correct term to complete the sentences.
1.
A glass of milk sits motionless on the kitchen table.
a. Describe the forces acting on the glass of milk. Include their direction
in the description.
b. What word describes the state of motion of the glass of milk?
2.
Name two units commonly used to measure force. How are they related?
3.
Are the following statements true or false? Explain your answers using
an example.
a. Applying a force to an object will make it move.
b. To keep an object moving, a force must be applied.
c. A force must be applied to change the direction of a moving object.
4.
To tighten the head of a hammer on its handle, it
is banged against a surface as shown to the right.
Explain how Newton’s first law is involved.
5.
How can rolling a bowling ball help you to
determine the amount of matter in the ball?
6.
List at least three parts of an automobile that are
designed to overcome the effects of Newton’s
first law. Briefly explain the function of each.
7.
State Newton’s second law in words. Write an equation expressing the law.
8.
Explain how the unit of force used by scientists, the newton, is defined.
9.
In a space shuttle orbiting Earth, where objects are said to be weightless, an
equal arm balance could not be used to measure the mass of an object. How
could you measure the mass of an object in this situation?
force
Newton’s first law
equilibrium
locomotion
reaction
inertia
net force
statics
newton (N)
Newton’s third law
law of inertia
dynamics
Newton’s second law
action
1.
The measure of the ability of an object to resist a change in its state of
motion is called __________.
2.
Any action which has the ability to change an object’s motion must be
a(n) __________.
3.
Newton’s first law is sometimes referred to as the __________.
4.
The law of motion which states that all objects tend to resist changes in
motion is known as __________.
5.
A problem in which there is no motion is described as __________.
6.
The acceleration of an object is proportional to the net force applied to the
object according to __________ .
7.
The total force applied to an object as the result of many applied forces is
called the __________.
8.
A(n) __________ problem is one involving motion.
9.
The force needed to accelerate a mass of one kilogram at a rate of 1 m/s2 is
one __________.
10. When the net force acting on an object is zero, the condition of zero
acceleration is called __________.
11. Forces always occur in pairs. One force is called the __________ force, the
other is called the __________ force.
12. “For every action force there is an equal and opposite reaction force,” is a
statement of __________.
13. The act of moving can be called __________.
10. Explain the difference between mass and weight. State common units for each.
11. What is the difference between the terms force and net force?
12. In physics problems, velocities, accelerations, and forces often appear with
positive (+) or negative (–) signs. What do those signs indicate?
13. How does the sign of the force applied to an object compare with the sign of
the acceleration?
14. What do motionless objects have in common with objects that are moving in
a straight line with constant speed?
CHAPTER 5 ASSESSMENT
115
Chapter
5
NEWTON’S LAWS: FORCE AND MOTION
15. What is the difference between dynamics problems and statics problems?
Give an example of each.
16. You and your little 6-year-old cousin are wearing ice skates. You push off
each other and move in opposite directions. How does the force you feel
during the push compare to the force your cousin feels? How do your
accelerations compare? Explain.
17. You jump up. Earth does not move a measurable amount. Explain this
scenario using all three of Newton’s laws of motion.
10. A baseball player strikes the ball with his 1-kg bat. The bat applies an
average force of 500 N on the 0.15-kg baseball for 0.20 seconds.
a. What is the force applied by the baseball on the bat?
b. What is the acceleration of the baseball?
c. What is the speed of the baseball at the end of the 0.20 seconds?
11. The graph represents the motion of a 1,500-kg car over a 20-second interval.
a. During which interval(s) is the net force on the car zero?
b. What force is being applied to the car during interval C–D?
Problems
1.
The box pictured is being pulled to the right at
constant speed along a level surface.
a. Draw a diagram with arrows to represent
the size and direction of all the forces
acting on the box.
b. Draw a diagram with one arrow to
represent the size and direction of the net force acting on the box.
2.
Calculate
a. the weight in pounds of a 16-newton object.
b. the weight in newtons of a 7-pound object.
c. the weight in newtons of a 3-kilogram object on Earth.
d. the mass in kilograms of an object that weighs 12 newtons on Earth.
3.
How does the inertia of a 200-kg object compare to the inertia of a
400-kg object?
4.
A constant force is applied to a cart, causing it to accelerate. If the mass of
the cart is tripled, what change occurs in the acceleration of the cart?
5.
If the net force acting on an object is tripled, what happens to its acceleration?
6.
On Venus, the acceleration due to gravity is 8.86 m/s2. What is the mass of a
man weighing 800 N on the surface of that planet?
7.
A 60-kilogram boy on a 12-kilogram bicycle rolls downhill. What net force
is acting on the boy and his bicycle if he accelerates at a rate of 3.25 m/s2?
8.
A young girl whose mass is 30 kilograms is standing motionless on a 2-kg
skateboard holding a 7-kg bowling ball. She throws the ball with an average
force of 75 N.
a. What is the magnitude of her acceleration?
b. What is the magnitude of the acceleration of the bowling ball?
9.
On Mercury, a person with a mass of 75 kg weighs 280 N. What is the
acceleration due to gravity on Mercury?
116
UNIT 2 MOTION AND FORCE IN ONE DIMENSION
12. Two forces are applied to a 2-kilogram block on a frictionless horizontal
surface as shown in the diagram. Calculate the acceleration of the block.
Applying your knowledge
1.
When a sled pulled by a horse accelerates, Newton’s third law says that the
sled and horse exert equal and opposite forces on each other. If the horse and
sled apply equal but opposite forces on one another, explain how the sled can
be accelerated under these circumstances.
2.
A bowling ball is positioned near the front of a stationary wagon. If the
wagon is suddenly pulled forward, the bowling ball appears to move
backwards in the wagon. Use each of Newton’s three laws to explain what is
actually happening to the wagon-ball system.
3.
A 0.1-kilogram ball held at waist height is dropped and bounces back up
toward the student’s hand. Include all of the words from the chapter
vocabulary list in describing the motion of the ball.