Download Unit 4. Forces - Perry County School District 32

Freshman Physics
Name __________________________ Hour______
Unit 4. Forces
Primary Authors:
Meera Chandrasekhar and Dorina Kosztin
Department of Physics and Astronomy, University of Missouri, Columbia
Unit 4: Forces
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Freshman Physics
Lab 1:
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4.1. Practice:
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Unit 4: Forces
Name __________________________ Hour______
Table of Contents
Broom Ball – The Game Lab ................................................................................... 3
What is a Force? ........................................................................................................ 5
Type of Forces ........................................................................................................... 7
Drawing and Analyzing Forces ............................................................................. 9
Force Challenge ...................................................................................................... 13
Measuring Weight .................................................................................................. 15
Gravitational Force and Mass .............................................................................. 19
Forces as vectors ..................................................................................................... 21
Forces as Vectors .................................................................................................... 25
Force Addition and Balancing Forces ............................................................... 27
Drawing Force Diagrams ..................................................................................... 31
Force Diagrams I .................................................................................................... 33
Newton’s First Law ................................................................................................ 35
Force Diagrams II .................................................................................................. 37
Broom Ball Lab Revisited ..................................................................................... 39
Newton’s First Law ................................................................................................ 41
Newton’s Third Law .............................................................................................. 43
Identifying Pairs of Forces.................................................................................... 47
Identifying Pairs of Forces II ............................................................................... 53
Newton’s Third Law Problems ........................................................................... 55
Newton’s Second Law ........................................................................................... 57
Newton’s Second Law Problems ........................................................................ 59
Newton’s Third and Second Laws with Blocks ............................................... 63
Balanced Forces ...................................................................................................... 65
Force Diagrams related to Motion...................................................................... 71
Force Diagrams, Motion Diagrams and Newton’s Laws .............................. 75
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Freshman Physics
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LAB 1: BROOM BALL – THE GAME LAB
Purpose:
What is a force and what does it do?
Materials:
Broom with flexible bristles and a plastic casing at the top of the bristle end.
Bowling ball and soccer ball or basket ball
Large pail containing sand
Course marked off with tape on the floor (see diagram below). Blue painters’ masking tape or
electrical tape work best for tape removal after the activity.
Start/Stop
No touch zone
pail
The rules of the game:
1. Broom Ball is played as a relay race.
2. There are two teams. Half of each team will be stationed at each end of the course.
3. The bowling ball should be at rest at one end of the course and the soccer ball will be at rest at
the other end. Each student will run the course from whichever end he/she is one way using the
bowling ball, and coming back using the soccer ball.
4. The ball may be manipulated only with the bristles of the broom. If any part of the broom other
than the bristles touches the ball that is a penalty. If the ball touches any obstacle in the room,
such as walls, pail, furniture, a student foot, etc. that is a penalty.
5. The clock starts when the first player takes off. Everybody should follow the course. You must
go all the way around the large pail (360 degrees), through the no touch zone without touching
the ball with the broom, around the corner and bring the ball to a complete stop in the starting
box, before the next player takes off reversing the course.
6. After the last team member has completed the course the watch is stopped and a time penalty is
added to the total time for each penalty while the ball was in play.
7. The team with the shortest time wins.
Unit 4: Forces
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Freshman Physics
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Post-lab discussion
1. What three things are the most difficult when it comes to handling the ball?
2. Was there a difference between handling the bowling ball and the soccer ball? Explain.
3. How can a player use the broom to overcome the difficulties mentioned in question 1? (What
strategies would you recommend to a teammate?)
4. How does the ball move in the no-touch zone?
5. What causes the motion of the ball in the no-touch zone?
Unit 4: Forces
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Freshman Physics
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Reading Page: What is a Force?
People often think of force as something you apply using your muscles. When you push or pull on
an object, you apply a force on it. You also apply force when you throw a baseball or kick a soccer
ball, or sit on a soccer ball. Therefore, a force is nothing else than a push or a pull. When you apply a
force on an object, its shape can change, as it might when you sit on a soccer ball, or on a sofa, or
when you squeeze an orange. These are soft objects; but even rigid objects, such as a wall or a car,
can be deformed (have their shape changed) if enough force is applied, such as with a sledgehammer
or in a collision with another car.
Contact Forces Vs Field Forces
Forces cause not only deformations (changes in shape), they can also cause motion – if you push or
pull on a cart, it may move. When you played the broom ball game, you had to push the bowling
ball with the broom to make it move, stop or change its
direction. You had to push harder on the bowling ball
than on the soccer ball because the bowling ball was
heavier than the soccer ball. If you push a cart on a
rough surface, or if the cart is very heavy, you will need
more force to move it than on a smooth surface. If you
sit on a chair, the chair holds you up (you are not falling through it) and applies a force to you: the
longer you sit in that chair, the more you will feel that force. These forces are examples of contact
forces – they arise from physical contact between the applier of the force (called the agent) and the
receiver of the force (called the receiver).
Field forces or long range forces, also called non-contact forces or
forces at a distance, are another class of forces. These forces do not
involve physical contact between the agent and the receiver, but act
through space, through a field. For example, the force of gravity the
Earth applies to us is what keeps us on the planet Earth and does not let
us fly out in space. The effect of the gravitational force on all objects on
the surface of the Earth can be described through a gravitational field. The
Moon goes around the Earth because of the gravitational force between
them; the solar system is kept together by the same force. The Moon itself has a gravitational field,
applies a gravitational force to objects on its surface. Another example of a field force is the
magnetic force: you feel a magnet being attracted or repelled by another magnet even if the two
magnets do not touch each other. The third example of a field force is the electric force, often
observed as static electricity, which causes your socks to stick to your sweaters when you take them
out of the dryer or the hair on your head to stick to your brush or to stand up after brushing it.
While it is convenient to classify forces as field forces and contact forces, on a microscopic level the
distinction is not so clear. For example, the force of friction might seem like a contact force, but it
is caused by repulsive forces between electric charges, which are field forces. It might seem like
there are a lot of forces in nature – gravitational force, friction forces, electric forces, magnetic
forces, push and pull forces, elastic forces …the list is not short. These forces are macroscopic
descriptions of phenomena. These descriptions are useful in designing, say, roller coasters,
furniture, bridges, or highways. The atomic origins of these forces, however, can be traced to just
four forces in nature:
Unit 4: Forces
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1. The gravitational force, which describes the attraction between objects, is based on the mass of each
object and the distance between them, and holds galaxies, stars, and planets together.
2. The electromagnetic force, which describes the attraction and repulsion between objects due to the
charge on each object and the distance between them, is responsible for the binding of atoms and
molecules.
3. The nuclear strong force is responsible for the binding of neutrons and protons into nuclei.
4. The nuclear weak force is a short-range nuclear force that produces instability in certain nuclei.
Each of these forces is described by a constant, a number, which gives the “strength” of this force.
Ranked using these constants, the strengths of the forces are, in order, strong, electromagnetic, weak and
gravitational. The strong and weak forces have a very short range of action, of the order of the radii
of nuclei. These invisible forces keep things together, but are hard to observe except in the research
laboratory. In everyday life, when we are not dealing with atomic-scale phenomena, the only forces
that impact us are the two long-range forces: gravity and the electromagnetic force. While the
gravitational force may be “weakest,” when one factors in the large masses involved (such as that of
earth, planets or stars), the gravitational force becomes a dominant force in everyday life. Close
behind is the electromagnetic force, which causes static, gives us electrical power, makes cell-phones
work, and makes for the conveniences of modern-day life.
Unit 4: Forces
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Freshman Physics
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Reading Page: Type of Forces
The most common forces we deal with in everyday life and will study in this class are:
Gravitational Forces
Gravitational forces occur because objects have mass. Gravitational forces have
the largest effect when exerted by a large mass, such as the earth, sun, planets or the
moon. Gravitational forces always attract objects. People, trains, and buildings remain “stuck” to
the earth because the gravitational force due to the earth’s mass attracts them. Even when you lift
an object off the earth, the moment you let go, it falls back to the earth because of the earth’s
gravitational attraction. When you go sliding, the force of gravity is responsible for bringing you
down that slide. When you throw a ball up into the air, it always comes back down because of the
force of gravity acting on it. Have you ever held up a heavy object and felt it pulling down toward
the earth? That’s the gravitational force of the earth attracting it! This force acts at a distance, it is a
field force and we say that it acts through a gravitational field. In everyday life, people refer to the
gravitational force the earth exerts on all objects as the weight of that object. (Note: In everyday
language we use the words mass and weight interchangeably, but scientists distinguish between
mass, which measures how much “stuff” an object has, and weight, which measures the force with
which the earth attracts that mass.)
Friction Forces
Friction is often observed when we rub objects together, or when we slide
an object on a surface. It is much easier to drag a box across a smooth
surface than across a rough one. Also, it is much easier to walk (have better traction) if your shoes
have treads on the bottom than if they have a smooth bottom. Generally, rough
surfaces hinder the motion of an object more than a smooth surface does. Although friction may
appear to be caused by surface texture, it is actually caused by electrical forces between molecules.
Frictional forces between two objects depend on the type of surfaces that are in contact with each
other: the rougher the surface, the bigger the friction. One method of reducing friction is to modify
the texture of the contact surface by applying lubricants, such as oil or graphite. While friction is
often considered a hindrance, there are situations where friction is necessary – compare walking on
a dry sidewalk with walking on it on an icy day! Also, put grease on the handle of your spoon and
then try and hold it when you eat; it is much more difficult!
Elastic force (also known as stretching or compressing force)
When you stretch a rubber band, you have to pull on it with a
force. But the rubber band appears to pull back – in fact, you
have to continuously apply the pulling force to keep the rubber
band stretched. When you go bungee jumping, at the bottom of
your jump the bungee cord starts extending and at
one point starts pulling you back up. This “pulling
back” is a manifestation of the elastic force that
exists in the bungee cord or rubber band. If you let go, the rubber band will go back
to its original length too. This elastic force also appears when you compress a spring
– for example, when you push the “Jack in the Box” back in its box, the spring is
compressed and when you open the lid, the elastic force in the spring (due to its
compression) makes the toy pop-up from the box and brings the spring back to its unstretched
length. Objects that stretch or compress when a force is applied to them, and then go back to their
Unit 4: Forces
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original form when the force is removed are called elastic. A force is called elastic force if once
removed allows the object to recover its original form, length, shape. This can happen to things
other than springs, for example, a tree branch can be pulled down and it retracts to its original
position. Have you ever pulled the tip of a ruler back like a catapult and hit a ball? There’s the
elastic force at work again.
Tension (also known as stretching force or pulling force)
Stretching forces or “tension” also occurs when you have
something that is held taut. For example, when you play tugof-war, the string/rope the two teams pull on is stretched
taut and each team applies a force to its end. The force that shows up in the string/rope as the
result of its stretching is called tension force. A picture hanging on the wall has tension force in the
string used to hang it. If the picture is very heavy and the string is not strong enough to support the
tension force, the string will break.
Normal or Support Force
When you sit on your chair, your own weight pushes down on the chair. If so, why
don’t you fall through the chair? Easy – because the chair is supporting you. How
does it do it? Well, the strong material that makes up your chair deforms the chair a
bit, and the molecules of the material that make up the chair feel their bonds
deform a bit too. Just as a spring that is compressed pushes back at you, the springy
bonds between the molecules push back too – and that is the origin of the normal
or support force provided by the chair. The amount of support force is just enough to leave you
sitting where you are. If it were a bit less, you would fall through the chair. If it were more, it
would push you upward. The chair supports you with an equal and opposite force. If you think
about the molecular origin of this force, it makes sense – if the person was heavy and deformed the
chair a lot, the bonds between molecules would be deformed a lot, and the chair would push back a
lot. If it were a light person – small deformation, smaller push-back, smaller support force. Support
forces are pretty clever – they appear only when they are needed, and only in as much amount as
needed. If the person got up from the chair, the deformation of the bonds is gone, and the support
force vanishes! The support force is often called the normal force – normal being perpendicular.
Support forces are always perpendicular to the surface at the point where the object touches it. (If
they were in any other direction they would make the object slide in that direction!).
Commonly used symbols to denote the forces we discussed above are:
Symbol Name of the Force Type of Force
Direction of force
Perpendicular to the surface that
FN or Fn Normal force
Contact force
applies it
Gravitational force Non-contact force
Always oriented down toward the
FG or Fg
(or weight)
(field force)
earth
Along the surface in contact; opposes
Ff
Friction force
Contact force
the relative motion of the two surfaces
FT
Tension force
Contact force
Along the rope, always pulling
Along the spring, always opposing the
Fe
Elastic force
Contact force
deformation of the spring
Note: any other contact force that is not one of the forces listed above can be called “applied
force” and denoted with FA.
Unit 4: Forces
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Freshman Physics
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Reading Page: Drawing and Analyzing Forces
A force is always applied by an object or the result of a phenomenon. The object that applies the
force is called the agent. This force is also applied to an object that experiences the force, called the
receiver. And finally, something happens because the agent applied a force to the receiver – the
effect. Let’s see how we can apply this analysis to forces.
A force is a push or a pull and as such when describing a force we must specify not only its
magnitude (how strong the force is) but also the direction of the force (pushing or pulling?). As
such we can represent a force graphically by using an arrow. We place the tail of the arrow on the
object that the force acts on, the receiver, and orient the arrow such that we show the direction of
the force. The length of the arrow should represent the magnitude of the force.
Whenever analyzing forces acting, follow the steps below:
1. Determine the object that is the receiver (has forces applied to it).
2. Identify the agents (objects that apply forces to the receiver).
3. For each agent, identify the force it applies. (Note: remember that we live on Earth and therefore
Earth (agent) always applies a force (gravity) to every single object (receiver) on its surface).
4. Represent the direction of the force with an arrow starting on the
receiver.
5. Describe the effect of the identified forces on the receiver.
g
Example 1
Examine the picture of the Moon going around the Earth: The Moon
goes around the Earth because the Earth (the agent) applies a force to
the Moon (the receiver) and as a result the Moon moves around the
Earth (the effect). The force applied by the Earth is the force of gravity
(Note: This analysis is somewhat simplified in the sense that we have
separated out the agent and the receiver. To produce the attractive gravitational force you need at
least two masses; technically the Earth and the Moon are both agents, and they are both receivers.
However, at this time we chose to examine the Moon as the receiver.)
Example 2
Frequently there is more than one force acting on an object. Let’s look at the picture of the child
on the slide. In this case we consider forces acting on the child, therefore the child is the receiver.
A
B
C
Receiver: Child
Force: Force of Gravity
Agent: Earth
Effect/s: Child slides down
Receiver: Child
Force: Normal Force
Agent: Slide
Effect/s: Supports the child
Receiver: Child
Force: Friction Force
Agent: Slide
Effect/s: Slows down the child
Unit 4: Forces
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Freshman Physics
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The child slides down on the slide because the force of gravity applied by the earth (agent) has the
effect of bringing him down (figure A). The child is also in contact with the slide, thus the slide is
another agent applying forces on the child. The normal force applied by the slide (agent) has the
effect of holding the child from falling through the slide (figure B). The friction force applied by the
slide (agent) has the effect of slowing down the child (figure C). So as you can see, there are three
forces acting on the child (receiver) and they are the result of the interaction between the child and
Earth (long range forces) and the child and slide (contact forces).
Example 3:
Here’s another example of several forces at play: A man pulls on the leash of a dog. In this case we
can choose either the dog or the man as being the receiver. Let’s start with the dog as receiver. All
forces, and their agents and effects are listed in the table below. The effect of all these forces
combined is that the dog does not move as the man pulls on its leash. All forces acting on this dog
are balanced.
Receiver: Dog
Force: Force of
Gravity
Agent: Earth
Effect/s: Tends to
bring to dog down
Receiver: Dog
Force: Normal Force
Agent: Ground
Effect/s: Holds up
the dog
Receiver: Dog
Force: Friction Force
Agent: Ground
Effect/s: Stops the
dog from sliding
Receiver: Dog
Force: Tension
Force
Agent: Rope
Effect/s: Pulls on
the dog
How are things changing if the selected receiver is the man? Look in the table below for all the
forces acting on the man, their agents and effects.
Receiver: Man
Force: Force of
Gravity
Agent: Earth
Effect/s: Tends to
bring to man down
Receiver: Man
Force: Normal Force
Agent: Ground
Effect/s: Holds up
the man
Receiver: Man
Force: Friction Force
Agent: Ground
Effect/s: Stops the
man from sliding
Receiver: Man
Force: Tension Force
Agent: Rope
Effect/s: Pulls on the
man
The effect of all these forces combined is that the man does not move as he pulls on the leash. All
forces acting on this man are balanced.
Unit 4: Forces
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Freshman Physics
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Example 4:
Now let’s go back to the broom ball lab. How did the ball move in the “no touch” zone? It moved
with constant speed. Were there any forces acting on the bowling ball when moving through the
“no touch” zone? Yes, there were! The force of gravity was pulling down on the ball and the
normal force was supporting the ball. The two forces balanced each other, and as a result, the ball
moved with constant speed. Thus we can say that if forces acting on an object are balanced, the
object can be either at rest or moving with constant speed.
FN
Fg
Unit 4: Forces
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Notes:
Unit 4: Forces
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Freshman Physics
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4.1. Practice: Force Challenge
Directions: Follow the 5 steps in the “Analyzing Forces” reading page. Identify one receiver and
one force acting on it. Make sure you don’t use the force of gravity for every example. In some
cases, the receiver or agent is already identified for you.
A.
C.
E.
Receiver:
B.
Receiver:
Force:
Force: Normal
Agent: Earth
Agent:
Effect/s:
Effect/s:
Receiver:
D.
Receiver: tire
Force:
Force:
Agent: Rope
Agent:
Effect/s:
Effect/s:
Receiver: panda
F.
Receiver: Thesaurus
book
Force:
Force:
Agent:
Agent: Dictionary
Effect/s:
Effect/s:
G.
I.
Unit 4: Forces
Receiver: bicycle seat
H.
Receiver:
Force:
Force: Normal
Agent: boy
Agent:
Effect/s:
Effect/s:
Receiver: balloon
J.
Receiver: ball
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
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Freshman Physics
K.
M.
O.
Q.
S.
Unit 4: Forces
Name __________________________ Hour______
Receiver:
L.
Receiver: ball
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
Receiver:
N.
Receiver: girl
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
Receiver: toolbox
P.
Receiver: chair
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
Receiver: doorknob
R.
Receiver:
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
Receiver:
T.
Receiver:
Force:
Force:
Agent:
Agent:
Effect/s:
Effect/s:
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Reading Page: Measuring Weight
One of the simplest methods of measuring a force is to use a spring scale. If you pull on
the hook of a spring scale with a force, the spring inside the scale stretches. The amount
a spring stretches is proportional to the amount of force applied. For example, if we
apply a force of 40 N and we find that a spring gets 8 cm longer than its original length,
then we know that if we apply 20 N of force, it should get 4 cm longer. This allows us to
construct a scale (10 N = 2 cm of stretch). Once we have a scale, we can measure other
amounts of force.
A common use of a spring scale is to measure weight, the amount of gravitational force applied by
the earth. In everyday language we think that weight is a measure of how much “stuff” an object
contains. Scientists distinguish between mass, which measures how much “stuff” an object has, and
weight, which measures the force with which the earth attracts that mass. Since the force with
which the earth attracts all objects scales with the mass of the object, the mass and weight of an
object are proportional to one another. The mathematical relationship between the gravitational
force applied by Earth (or weight) and the mass of the object is:
𝐹𝑜𝑟𝑐𝑒 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 (𝑜𝑟 𝑤𝑒𝑖𝑔ℎ𝑡 )
𝑁
= 9.8
𝑚𝑎𝑠𝑠
𝑘𝑔
This is also known as the “gravitational field strength” or the acceleration due to gravity and it is
denoted with the letter “g”. We can then rewrite the above mathematical relationship using
symbols, as:
g
Fg
m
where g = 9.8 N/kg on Earth
From the above expression, we can calculate the gravitational force Fg (or weight) on Earth as:
Fg  mg or Weight (in N) = mass (in kg) x 9.8 (in N/kg)
The numerical factor of 9.8 will change if we use different units.
For example, in the cm-mg-sec system,
Weight (dynes) = mass (mg) x 980 (dyne/mg)
In the British system,
Weight (lbs) = mass (slugs) x 32 (lb/slug)
Because weight and mass are related just by a numerical factor, we can use the same device to
measure both and just mark the device with the appropriate scales. Spring scales often have
markings to measure both mass and weight. When you go to the store to buy apples, and you want
to check how much mass the apples have, you are using a spring scale. The reading of the scale is in
lb (pounds) which is a unit of force.
Unit 4: Forces
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A bathroom scale is another device to measure weight – a person has to stand on
it, his/her mass is pulled down toward the earth due to the earth’s gravity, and the
person pushes down on the scale. A spring inside the scale gets compressed due
to this force, and rotates a dial or displays a number that displays this force. The
force may be displayed in pounds of force, or it may be rescaled and displayed as
kilograms of mass. Or it could equally have been displayed as slugs of mass or
newtons of force! Marking equivalent units is not unusual – many car
speedometers have speed displayed as km/hour and miles/hour; thermometers
may also read Celsius or Fahrenheit. Spring scales are a bit different in that the two units are for
different factors – mass and weight, but the principle is the same. In a digital balance (like the ones
used in class), the weight of the object compresses a spring or a strain gauge inside the balance. The
amount of compression is related to the mass of the object. In a classical beam balance, the weight
in the left pan is balanced by the weight in the right pan.
How can you tell mass and weight apart?
Mass and weight have different units. Weight is a force and it is measured in units of newtons
(abbreviated N) in the metric system, or pounds (lb) in the British system. Mass is a measure of how
much stuff an object contains and it is measured in units of grams or kilograms (g or kg) in the
metric system and slugs in the British system. Mass will remain the same on the Earth or the Moon
or anywhere else. Weight, however, is the force with which the object is attracted. If the object
were on the Moon, it would be attracted by a different amount of force than on the Earth, since the
gravitational field strength of the Moon is smaller than the gravitational field strength of the Earth
(the mass of the moon is smaller than that of the earth, and the object is also closer to the center of
the moon). So its weight would be different (in fact it would be about 1/6 as much). Below you
have a table with the gravitational field strength of each planet in the Solar System:
Planet
Gravitational
Strength
Unit 4: Forces
Earth
Moon
Sun
Mars
Jupiter
Pluto
9.8 N/kg
1.6 N/kg
273.4 N/kg
3.7 N/kg
25.8 N/kg
0.6 N/kg
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4.1. Practice: Gravitational Force and Gravitational Strength
1. Many unit conversion tables contain the following conversion: 1 kg = 2.2 pounds. Explain what
is wrong with this “equation.” Write a statement that includes the terms “1 kg” and “2.2 pounds”
that is correct.
2. It is commonplace to find statements on food cans such as “Net Weight: 16 oz. (454g)” Why do
most people find this acceptable? Why do “physics types” object to such statements?
3. When you step on a bathroom scale here is US, your weight is given in pounds. Is this a correct
unit for such a scale? What would happen to the reading on this device if you were to stand on it
while on the moon? Is this what the scale should read? Why are all these standards and
measurements used so often?
Unit 4: Forces
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Unit 4: Forces
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4.2. Practice:
Name __________________________ Hour______
Gravitational Force and Mass
1. A box has a mass of 8.00 kg. Knowing that the gravitational field strength on Earth is 9.8 N/kg,
calculate the force of gravity on the box.
2. A box of cereal has a mass of 250 g. What is the force of gravity on the box, knowing that the
gravitational field strength on Earth is 9.8 N/kg?
3. The Earth exerts a gravitational force of 500 N on Amy. What is Amy’s mass in kg?
4. The Earth exerts a gravitational force of 850 N on John. What is John’s mass in g?
5. A rock has a mass of 5.00 kg on the moon. What is the mass of the rock on the earth?
6. The gravitational field strength on the Moon is 1.6 N/kg. If a rock on the moon weighs 200 N,
how much does the same rock weigh on the earth?
Unit 4: Forces
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7. Using the information provided below, fill out the table:
g
(N/kg)
9.8 N/kg
Mass on
Earth
(m)
A.
9.8 N/kg
1.6 N/kg
273.4 N/kg
3.7 N/kg
25.8 N/kg
Weight on
Earth (Fg)
Weight on
Moon
Weight on
Sun
Weight on
Mars
Weight
on Jupiter
0.2 kg
B.
6000 N
C.
D.
45000 N
30 N
E.
F.
500 N
89000 N
8. If you were to drop a 5 kg rock on your toe, would you rather be on Mars or on Jupiter? Explain.
9. Do you think it is easier or harder to hammer a nail into a floorboard on the Moon than on
Earth? Explain.
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Reading Page: Forces as vectors
The word “force” makes us think of pushing, pulling, holding up, dragging down – all phrases that
have a feeling of direction associated with them. You can push away from yourself, or pull toward
you. Other forces that one encounters, like the force of friction may not intuitively tell us the
direction involved – until we realize that friction always slows things down. Friction resists motion
– so it has a direction too! All forces have a direction associated with them. They belong to the
family of vectors, for which we need to know both the amount and the direction.
A vector is a physical quantity for which both the amount and the direction should be
specified. A scalar has only the amount specified, but not the direction.
Not all things in nature are vectors. For example, mass (e.g., 56 grams) does not have a direction.
To say “56 grams south” does not mean anything. Thus mass is always a scalar – it does not have a
vector equivalent. Similarly, temperature is always a scalar (34°C north east is meaningless). In
contrast, a force can be push or pull, up or down, left or right – thus forces are vectors. Some
physical quantities, like speed and velocity have different names for the scalar and vector forms.
Others, like force, do not have scalar counterparts.
The direction of a vector can be specified in many ways. We can represent a force graphically by
using an arrow. We place the tail of the arrow on the object that the force acts on, the receiver, and
orient the arrow such that we show the direction of the force. The length of the arrow should
represent the magnitude of the force and the arrow should indicate the direction of the force.
Let’s look at an example and see how we can use this new information
when representing forces. In the picture on the left you have a bear sitting
at rest on a very smooth table. If the bear is the receiver, then there are
two forces acting on the bear. The force of gravity, Fg, (agent: Earth) is
always oriented vertically down. The normal force, FN, (agent: table) is
always oriented perpendicular to the surface that applies it, in this case,
perpendicular to the table, and upward. The two forces are represented by
two arrows, each one indicating the direction of the force. The lengths of
the two arrows indicate the strength (magnitude) of each force. In this
case, because the bear is sitting on the table at
rest, the two forces balance each other out,
which means their lengths are the same.
Why is it useful or necessary to have vectors? Because just giving the
force amount information does not paint the whole picture! I am
telling you now that an additional force of 50 N is applied to the bear,
so you know the amount of force applied. Is that enough information
to determine what happens to the bear? No, you also need to know in
which direction this force is applied. If the force is upward, the bear will
lift off the table, if it is to the right, the bear will move to the right. So
as you can see, the direction of the force is also very important to
specify. Now, if the pulling force of 50 N is applied to the right, how
can you keep the bear from moving to the right? Of course, you must
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apply a force that is also 50 N oriented to the left, meaning you must balance the forces along the
horizontal direction.
Do you remember how the bowling ball form Broom Ball Lab moved in the “no touch” zone? The
only forces acting on the bowling ball were the force of gravity and the normal force, and they
balance each other out. There were no forces along the horizontal direction, and still the ball moved
with a constant speed. So we can say that when all forces acting on an object are balanced, the
object is either at rest or moving with a constant speed.
The direction of a vector can be specified in many ways. Here are some:
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Examples: Adding Forces in 2D
Rita and Manny pull on a sack of candy. Rita
pulls toward the north with a force of 26 N, while
Manny pulls toward the east with a force of 40 N.
Draw the total force on the sack.
1. Set up your graph paper: Define the northeast-south-west directions with a compass
rose. The axes on the graph paper should be
along north-south and east-west. Choose your
scale – decide how many cm will represent 10
N. Mark off the axes. In the figure we show
marks every 10 cm. (box 8)
2. Set the sack at the center of the graph paper as
before. Draw Manny’s force, 40 N toward the
east (let’s call it force ⃗A). Draw Rita’s force, 26
⃗ ). (Box 9).
N toward the north (force B
3. To add vectors, we add them one after
another. This means that you draw force ⃗A,
and at the end of force ⃗A, draw force ⃗B. Since
we represent force ⃗A as going from 0 to 40
(which is where the tip of the arrowhead is
⃗ is placed at the “40” mark,
drawn), force B
which is the end point of force ⃗A. To do so,
⃗ so it still points north, (and is
we move force B
still the same length) but its starting point is at
the tip of force ⃗A. The arrows representing
the vectors need to be placed tip-to-tail. (Box
10).
4. The vector that represents the sum of ⃗A and ⃗B
now starts from the tail (the beginning) of the
first vector to the tip (the end) of the last one.
The total force ⃗A + ⃗B is shown by the dashed
arrow in box 11.
Note:
⃗ you would
In order to find the length of ⃗A + B
need to use Pythagorean theorem. We will not be
using this at this level.
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A Note On Defining Angles:
After you have drawn your vector diagram for adding forces, your answer must define both the
amount of the force and the angle it makes. Here are two common conventions for defining angles:
Convention #1 – useful when your vector diagram is drawn with a North-East-South-West grid.
Two equivalent methods of defining the angle of the vector (dashed line):
Measure your angle starting from one of the
axes. We started from the east and measured the
angle in the northward direction (see arrow).
The angle is defined as 35˚ North of East or 35˚
North from East. This angle is between the east
axis and the vector.
OR: The angle can be measured starting from
the north axis and measured in the eastward
direction (see arrow). This angle is defined as
55˚ East of North or 55˚ East from North. This
angle is between the north axis and the vector.
Convention #2: Useful when you have an x-y Cartesian grid.
Two equivalent methods of defining the angle of the vector (dashed line):
As with convention #1, measure your angle
starting from any one of the four axes. Usually
one starts from one of the nearby axes. Above,
we start at the +x axis and measure 30˚ in the
clockwise (CW) direction. The angle is defined
as 30˚ CW from +x, and is the angle between
the +x axis and the vector.
Unit 4: Forces
OR: The same angle can be measured starting
from the -y axis: start from the -y axis and
measure the angle in the counter-clockwise
(CCW) direction (see arrow). This angle is
defined as 60˚ CCW from -y, and is the angle
between the -y axis and the vector.
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4.3. Practice: Forces as Vectors
1) Knowing that the size of one square is 10 N by 10 N, draw force vectors to represent the
following:
a) 20 N south
b) 45 N south
c) 15 N east
N
W
E
S
2) What is different about these two vectors: a force that is 5 Newtons, west, and a force that is
25 Newtons, north? Explain in words and draw the arrows.
3) Karina is pulling on her toy truck with a force of 25 N. At the same time, her brother Lovell
pulled on it with a force of 20 N. Can you think of three different diagrams (scenarios) that
represent the forces described above? Explain what happens in each scenario as the result of
the two forces acting on the truck.
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4) If you want everybody to interpret the forces on the truck the same way, what important
piece(s) of information should you specify?
5) Can you figure out the total force acting on these objects? (Show what you understood by
total force and how you figured it out, this can be an equation.)
6) If all the forces acting upon an object are balanced, then the object:
a) must not be moving.
b) must be moving with a constant velocity.
c) must not be accelerating.
d) none of these
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4.4. Practice:
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Force Addition and Balancing Forces
1. Describe the angles below in words (i.e., 12˚ North of West, etc). Give two equivalent
descriptions for each angle.
a)
Original angle
Equivalent angle
Equivalent angle
b)
Original angle
Equivalent angle
Equivalent angle
c)
Original angle
Equivalent angle
Equivalent angle
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2. Describe the angles below in words (i.e., 12˚ CW of +y, etc). Give two equivalent descriptions
for each angle.
a)
Original angle
Equivalent angle
Equivalent angle
b)
Original angle
Equivalent angle
Equivalent angle
c)
Original angle
Equivalent angle
Equivalent angle
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3. Draw diagrams on graph paper, mark the angles and figure out equivalent descriptions (e.g., 30˚
North of East is equivalent to 60˚ East of North) for:
a) 24˚ North of East
d) 34˚ CCW from –x
b) 52˚ West of South
e) 60˚ CW from -y
c) 38˚ South of East
f) 25˚ CCW from +y
4. (a) Shawna pulls on a mule with a force of 8.0 N toward
the north, while Tammy pulls on it with a force of 4.0
N toward the east. Draw a diagram of the forces and
show the resultant vector of the two directions.
(b) If the mule is stubborn and does not want to move,
in which direction, and with how much force, must it
resist (give the two specific directions and draw the
resultant vector).
5. Julie pushes a box with a force of 2.0 N toward the
west, while Martha pushes it with a force of 4.0 N
toward the north. Draw a diagram of the forces.
Draw the total (resultant vector) of these two forces
on the box?
6. Farmer Tim is trying to get his pony loaded on a
train, and has a crane helping him lift the pony.
He pushes on a pony with a force of 800 N to the
right, while a crane pulls on the pony with a force
of 2000 N upward.
(a) Draw a diagram of the forces. Show the vector
sum (resultant) of the two forces.
(b) If Jackie wanted the pony not to move, what must Jackie’s force be?
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Reading Page: Drawing Force Diagrams
What is a force diagram? A force diagram (often called a free-body diagram) is a tool to represent all
the forces acting on an object. In some situations it might be easy to identify all the forces that act
on an object. However, situations tend to get complicated quickly, especially if there are both
contact and long-range forces. Therefore it is a good idea to have a process that helps us identify all
the forces in situation. Here is a method that works well:
1. Draw a picture of the problem, showing the object and everything in the environment that
touches the object – ropes, tables, springs are all part of the environment.
2. Identify the receiver – which is the object or objects of interest – by drawing a closed curve
around the receiver, with the object inside the curve and everything else (environment) outside
the curve.
3. Locate every point in the receiver at the boundary of the curve where the environment touches
the receiver and identify by name all the contact forces at each point of contact (there may be
more than one force), then give each one an appropriate symbol.
4. Identify any long-range forces acting on the receiver. Name the force and write its symbol in
the picture.
5. Draw the force diagram. Start by representing the receiver with a dot. Draw all forces with the
tail on the dot and keep the direction of those forces the same.
Example 1: A flamingo stands on the ground. Draw the force diagram for the flamingo.
1. The picture
2. Identify the receiver with a closed
curve around it.
5. Make the force
diagram
Fg
3. Identify all contact forces.
4. Identify all long range forces.
Force of gravity, Fg
Normal force, FN
Unit 4: Forces
FFNg
Normal force, FN
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Example 2: A sled on level ground is being pulled by a rope. Draw the force diagram for the sled.
1. The picture
2. Identify the receiver with a
closed curve around it.
5. Make the force
diagram
FN
FT
3. Identify all contact forces.
4. Identify all long range forces.
Ff
Fg
Example 3: A dog is being pulled by her leash on level ground. Draw the force diagram for the
dog.
Note: one might think that we need to have four normal forces, and four friction forces, one for
each paw. However, we are going to represent the dog by a point in the force diagram, so it is all
right to represent the normal force and the friction force at one point (paw) only.
1. The picture
2. Identify the receiver with a
closed curve around it.
5. Make the force
diagram
FN
FT
3. Identify all contact forces.
4. Identify all long range forces.
Tension force, FT
Tension force, FT
Ff
Fg
Friction force, Ff
Friction force, Ff
Force of gravity, Fg
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4.5. Practice: Force Diagrams I
Identify your receiver with a dotted line. Be aware that if you cannot identify the agent for a force, it
means that there is no force!
1. Draw a force diagram for a bird sitting
motionless on a branch.
2. Draw a force diagram for a lamp that is
suspended from the ceiling.
3. Draw a force diagram for Sarah as she
clears a high jump.
4. Draw a force diagram for the ball used
as a book end.
5. Draw a force diagram for the skier and
skies during his jump. Ignore air resistance.
6. Draw a force diagram for the sled and
boxes together. Note that the child pulls
on the sled at an angle.
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7. Draw a force diagram for the picture
hanging on the wall.
8. Draw a force diagram for Henry who
hangs motionless from a tree branch.
9. Draw a force diagram for the toolbox.
10. Draw a force diagram for the chair that
the cowboy sits on.
11. Draw a force diagram for a balloon
floating stationary in the air.
12. Draw a force diagram for the worker
sitting motionless on a sloped roof.
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Reading Page: Newton’s First Law
To explain in the most general way how force and motion are connected Newton came up with
three physics laws.
NEWTON’S FIRST LAW
Newton's first law of motion is also known as the law of inertia. It states that:
An object moving with constant velocity continues to do so unless acted upon by a nonzero net force.
This law may sound simple but it has many nuances that must be clarified in order to be
understood.
1) The phrase “moving with constant velocity” in the statement of this law means that the object is
traveling in a straight line, with constant speed, i.e. it is neither speeding up, nor slowing down, nor
changing direction. This law says that the natural state of motion is that of constant velocity. Since
the law does not distinguish the constant velocity of zero (at rest) from any other constant velocity,
it says that all constant velocities are equivalent.
Newton’s First Law can be restated as:
An object in constant velocity motion, or at rest, will continue its constant velocity motion, or remain at rest, unless
acted upon by a net force.
2) Newton’s First Law can seem counterintuitive: in real life objects in motion stop moving sooner
or later. Prior to Newton, people believed that the “natural state” of an object was at rest.
Example: push your physics textbook across the table. As long as you keep pushing it (applying a
force to it), the book will move and as soon as you stop pushing, it will start slowing down and
eventually stop moving. It may seem that the only force acting on your book is the force applied. In
reality there is another force that acts on the book: the force of friction between the book and the
table. The book comes to a stop once the pushing force is gone not because rest is its “natural
state” but because the force of friction is still there acting on the book. If the same book was
pushed along a smooth icy surface it would travel much farther before it stops. Now imagine an
ideal case where there is no friction: the book would continue to move forever as a result of one
push from your hand.
3) The word inertia describes the tendency of all objects to continue with their previous motion
when the net force is zero. We correlate the inertia of an object with its mass. Mass can be thought
of as a measure of the matter content of an object; but for motion, mass is a measure of its inertia.
It is harder to make an object with a lot of mass (lot of inertia) deviate from its path than an object
with less mass (and less inertia).
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Newton’s First Law can be restated as:
An object with a lot of inertia (i.e. a lot of mass) is harder to deviate from its trajectory (i.e. it takes a lot of force to
change its motion) than an object with less inertia.
4) Now let’s get back to the example of your book moving forever if there is no friction acting on
it. Newton’s First Law actually says two things: a) in the absence of a net force, an object keeps
moving as it was moving and b) in the presence of a net force, a body changes its motion.
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4.6. Practice: Force Diagrams II
Identify your receiver with a dotted line. Be aware that if you cannot identify the agent for a force, it
means that there is no force! Draw a force diagram in the space provided and discuss if forces
acting on the receiver are balanced or not.
Force Diagram
Are forces balanced or not?
A. Draw a force diagram for the
hockey player sliding at constant
speed across the ice.
B. Draw a force diagram for the
bowling ball after it left Dan’s
hand.
C. Draw a force diagram for the
ascending balloon.
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D. Draw a force diagram for Allie
(and sled) speeding down the hill.
E. Draw a force diagram for Dan
who slides down the slide.
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4.7. Practice: Broom Ball Lab Revisited
Broom ball is the physics game you played at the beginning of this unit. The objective is to use a
broom to cause a bowling ball to move along a specific course in the smallest amount of time
without leaving the boundaries of the course. Consider the course shown below, where you start at
A and stop at H.
Assignment:
For each of the lettered positions (A through H) on the diagram above, you will be asked to do the
following:
1. Draw the force applied by the broom on the ball.
2. Draw the direction of the velocity of the ball at that position.
3. Describe the motion of the ball as one or more of the following: at rest, speeding up, slowing
down, constant speed, changing directions.
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After completing the table above, answer the following questions:
1. At which points is the direction of the force the same as the direction of motion (direction of
the velocity)?
2. What is the effect of a force applied in the same direction as the direction of motion of the
object?
3. Between what points did the direction of the force change? Did the direction of motion also
change between those points? Is there a connection between these two changes?
4. At which points is the direction of the force different than the direction of motion (direction of
the velocity)?
5. What is the effect of a force applied in a different direction than the direction of motion?
6. Was there a place where no force was applied by the broom? How did the ball move at that
place? Explain your answer.
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4.8. Practice: Newton’s First Law
1. A sheet of paper can be withdrawn from under a container of milk without toppling it if the
paper is jerked quickly. This best demonstrates that
a) the milk carton has no acceleration.
b) gravity tends to hold the milk carton secure.
c) the milk carton has inertia.
d) none of the above.
Explain your answer:
2. A school bus is moving at constant velocity. Inside the bus, a student drops a tennis ball from
his hand. The ball hits the floor
a) exactly below the student’s hand.
b) ahead of the student’s hand.
c) behind the student’s hand.
d) more information is needed to solve this problem.
e) none of the above.
Explain your answer:
3. If your automobile runs out of fuel while you are driving, the engine stops but you do not come
to an abrupt stop. The concept that most explains why this occurs is
a) inertia.
b) gravity.
c) acceleration.
d) resistance.
Explain your answer:
4. According to Newton's law of inertia, a rail road train in motion should continue going forever
even if its engine is turned off. We never observe this because railroad trains
a) move too slowly.
b) are much too heavy.
c) must go up and down hills.
d) always have forces that oppose their motion.
Explain your answer:
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5. Whirl a rock at the end of a string and it follows a circular path in a horizontal plane. If the
string breaks, the tendency of the rock is to
a) continue to follow a circular path.
b) follow a straight-line path.
c) increase its speed
d) revolve in a smaller circle
Explain your answer:
6. When a rocket ship accelerating in outer space runs out of fuel it
a) accelerates for a short time, then slows down to a constant velocity.
b) accelerates for a short time, slows down, and eventually stops.
c) no longer accelerates.
Explain your answer:
7. Compared to a 1-kg block of solid iron, a 2-kg block of solid iron has twice as much
a) inertia.
b) mass.
c) volume.
d) all of the above.
e) none of the above.
Explain your answer:
8. If one object has twice as much mass as another object, it also has twice as much
a) inertia.
b) velocity.
c) acceleration due to gravity.
d) all of the above.
Explain your answer:
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Reading Page: Newton’s Third Law
What is the connection between forces acting on two objects interacting with each other? Let’s
consider the simple interaction between a hammer and a nail. The hammer exerts a force on the nail
as it drives it into the wall. At the same time, the nail exerts a force on the hammer. If you are not
sure that it does, imagine hitting the nail with a banana or a glass hammer. It is the force of the nail
on the banana that pokes holes into it or shatters the glass.
Let’s look now at the picture on left: a mom is pulling on her son,
trying to get him away from his computer. The mom interacts with
her son, and her son interacts with the computer. We have already
learned how to identify all the forces acting on the boy, or on the
mom or on the computer. But how do we deal with objects that
interact with each other, such as the mom and the boy, or the boy
and the computer?
Newton’s Third Law explains how two objects/systems interact with each other. Every time an
object A pushes or pulls on an object B, object B pushes or pulls back on object A. When the mom
pulls on the boy, the boy pulls back (and she feels this in her arms). The two objects, mom and boy,
are interacting. An interaction is the mutual influence of two systems on each other. The boy and
mom are also interacting with the ground/earth.
Let’s analyze all forces acting on the mom:
And now let’s analyze all forces acting on the boy:
The pulling force applied by the mom on the boy is the action force, and the pulling force applied
by boy on his mom’s arms is the reaction force. Although we name one force the action and the
other force the reaction for convenience, these two forces occur simultaneously and one cannot
strictly specify which one is the “action” and which one is the “reaction”. An action/reaction pair
of forces exists as a pair, or not at all. Also, paired action and reaction forces have (a) the same
magnitude, (b) act in opposite directions and (c) act on different objects.
But how about the rest of the forces acting on the boy and mom? Are they part of an
action/reaction pair? Yes, all forces in the universe are part of action/reaction pairs – there are no
forces that act alone. If you look only at the forces acting on the boy it may seem that these forces
are isolated but that is because we have chosen our system to be one single object: the boy. All
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forces acting on the boy arise from his interaction with the environment (which is outside for the
chosen system). To be able to identify all the action reaction forces we must consider the expanded
system which consists of boy, his mom and the ground.
Let’s now identify all the action reaction pairs that act in the system. In the diagram below the
action reaction forces are connected through a dotted line.
For each force applied on the boy, there is a force the boy applies to another object. The same
holds true for the mom. All interaction forces between boy and mom, boy and ground, and mom
and ground are contact forces. The exception is the weight applied by earth, which is a long range
force.
How do action reaction pairs work for long range forces?
If you let a ball fall, it will move down toward the earth because the earth pulls on it with a
force called weight, the action force. But does the ball pull on the earth? Is there a “reaction”
force acting on the earth? Indeed there is. The ball also attracts the earth with the same
amount of force – the weight of the object. Does the earth then fall toward the ball? Yes, it
does. But since the earth is huge and the ball is very small what one observes is a larger
effect on the small ball. A similar effect occurs with two magnets: two magnets attract or
repel each other through a long range force that can act at a distance. If you hold a magnet
in each hand, you can feel the force acting on each magnet because long range forces come
in pairs too.
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There is only one force in the boy + mom + ground diagram for which a force pair is not drawn:
the friction force applied by the keyboard on the boy’s fingers. Is there no pair for this force? Yes,
there is: the force with which the boy’s fingers act on the keyboard. We have not drawn the reaction
for that force intentionally. Whenever we deal with Newton’s Third Law we must define the system
of interacting object. In our case the system was boy + mom + ground/earth. The computer was an
external object to our system and thus the force applied by the computer to the boy’s fingers is
considered an external force.
Newton’s Third Law states that:
1. Every force occurs as one member of an action/reaction pair of forces.
2. The two members of an action/reaction pair act on two different objects.
3. The two members of an action/reaction pair point in opposite directions, and are equal in magnitude.
Rules to follow when identifying action/reaction pairs:
1. Identify the objects that are systems of interest. Other objects whose motion you don’t care
about are part of the environment.
2. Draw each object separately. Place them in the correct position relative to other objects.
Don’t forget to include objects like the earth that may not be mentioned in the problem.
3. Identify every force. Draw the force vector on the object on which it acts. Label each with a
subscripted label. The usual force symbols can be used.
4. Identify the action/reaction pairs. A force goes with a force. Connect the two force vectors
of each action/reaction pair with a dotted line. When you’re done, there should be no
unpaired forces.
5. Draw a free-body diagram for each object within the system. Include only the forces acting
on the objects in your system, not forces that the objects in your system exert on other
objects.
Newton’s third law is one of the fundamental symmetry principles of the universe. Since we have
no examples of it being violated in nature, it is a useful tool for analyzing situations which are
somewhat counter-intuitive. For example, when a small truck collides head-on with a large truck,
your intuition might tell you that the force on the small truck is larger. Not so! Both cars experience
the same force. But why does the small car sustain much more damage than the truck? That has to
do with Newton’s Second Law!
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Notes:
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4.9. Practice: Identifying Pairs of Forces
1. Wherever there is an action force, there must be a reaction force which
a) always acts in the same direction.
b) is slightly smaller in magnitude than the action force.
c) is slightly larger in magnitude than the action force.
d) is exactly equal in magnitude.
Explain:
2. An archer shoots an arrow. Consider the action force to be exerted by the bowstring against the
arrow. The reaction to this force is the
a) combined weight of the arrow and bowstring.
b) air resistance against the bow.
c) friction of the ground against the archer's feet.
d) grip of the archer's hand on the bow.
e) arrow's push against the bowstring.
Explain:
3. A player catches a ball. Consider the action force to be the impact force of the ball against the
player's glove. The reaction to this force is the
a) player's grip on the glove.
b) force the glove exerts on the ball.
c) friction of the ground against the player's shoes.
d) muscular effort in the player's arms.
e) none of these
Explain:
4. A player hits a ball with a bat. The action force is the impact force of the bat against the ball.
The reaction to this force is the
a) air resistance on the ball.
b) weight of the ball.
c) force that the ball exerts on the bat.
d) grip of the player's hand against the ball.
e) weight of the bat.
Explain:
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5. For all the pictures shown below:
a) Select two objects that interact with each other.
b) Draw force diagrams for each object separately, clearly labeling each force with the receiver
and agent’s name.
c) Identify the action reaction pair of forces for the two interacting objects.
Example
Object 1: Cake & Object 2:
Plate
Force Diagram for cake:
Force Diagram for plate:
Applied
Action force: normal force on cake by plate
Reaction force: applied force on plate by cake
A.
_____________
Force Diagram for
Force Diagram for
&
_______________
Action Force:
Reaction Force:
B.
____________ &
Force Diagram for
Force Diagram for
_____________
Action Force:
Reaction Force:
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C.
____________ &
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Force Diagram for
Force Diagram for
_____________
Action Force:
Reaction Force:
D.
______________ &
Force Diagram for
Force Diagram for
________________
Action Force:
Reaction Force:
E.
_______________ &
Force Diagram for
Force Diagram for
_______________
Action Force:
Reaction Force:
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6. Use choices (A – G) for cases 1 and 2 below
for when a large truck and a small car collide.
A) The truck exerts a greater amount of force
on the car than the car exerts on the truck.
B) The car exerts a greater amount of force on the truck than the truck exerts on the car.
C) Neither exerts a force on the other; the car gets smashed simply because it is in the way of
the truck.
D) The truck exerts a force on the car but the car doesn't exert a force on the truck.
E) The truck exerts the same amount of force on the car as the car exerts on the truck.
F) Not enough information is given to pick one of the answers above.
G) None of the answers above describes the situation correctly.
Case 1: Which choice describes the forces when the truck is much heavier than the car.
_______They are both moving at the same speed when they collide.
_______The car is moving much faster than the heavier truck when they collide.
_______The truck is moving much faster than the car when they collide.
_______The car is standing still when the truck hits it.
_______The heavier truck is standing still when the car hits it.
Case 2: Which choice describes the forces when the truck is a small pickup truck and has the same
mass as the car.
_______They are both moving at the same speed when they collide
_______The car is moving much faster than the truck when they collide.
_______The truck is moving much faster than the car when they collide.
_______The car is standing still when the truck hits it.
_______The truck is standing still when the car hits it.
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7. Use choices (A – F) for cases 1 below for when a
large truck breaks down and receives a push back to
town from a small compact car.
A) The force of the car pushing against the truck is equal to that of the truck pushing back
against the car.
B) The force of the car pushing against the truck is less than that of the truck pushing back
against the car.
C) The force of the car pushing against the truck is greater than that of the truck pushing back
against the car.
D) The car's engine is running so it applies a force as it pushes against the truck, but the truck's
engine isn't running so it can't push back with a force against the car.
E) Neither the car nor the truck exerts any force on each other. The truck is pushed forward
simply because it is in the way of the car.
F) None of these descriptions is correct.
Case 1: Which choice describes the forces between the car and the truck.
_______The car is pushing on the truck, but not hard enough to make the truck move.
_______The car, still pushing the truck, is speeding up to get to cruising speed.
_______The car, still pushing the truck, is at cruising speed and continues to travel at the same
speed.
_______The car, still pushing the truck, is at cruising speed when the truck puts on its brakes and
causes the car to slow down.
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8. Farmer Brown hitches Old Dobbin to his wagon one day,
then says, "OK, Old Dobbin, let's go!" Old Dobbin turns
to Farmer Brown and says "Do you remember how
Newton's Third Law says that every action force has an
equal and opposite reaction force?”. Ignoring Farmer
Brown's impatience, he continues, "If the wagon's pull is always equal and opposite of my pull,
then the net force will always be zero, so the wagon can never move! Since it is at rest, it must
always remain at rest, according to Newton’s 1st law! So, get over here and unhitch me! I have
just proven that Newton's Laws say that it is impossible for a horse to pull a wagon!" At this
point, Farmer Brown throws up his hands in dismay and turns to you. "Please help me!" he says,
"I really should have paid more attention in physics class! I know that Newton's Laws are
correct, and I know that horses really can pull wagons.”
Help Farmer Brown by drawing separate force diagrams for the wagon, the horse, and the horse
and the wagon together. Then explain in words the flaw in the horse’s reasoning. (Your answer
should include three force diagrams with an explanation for each.)
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4.10. Practice: Identifying Pairs of Forces II
For each of the following problems, draw a physical diagram; construct a separate force diagram for
each object, labeling each force with its type, agent and receiver. Circle any Newton’s 3rd law pairs
that occur in your force diagrams.
1. One book lies on top of another book, which rests on a table. System: the two books.
Physical Diagram
Force Diagram: top book Force Diagram: bottom book
Fon book A by book B
Fon book B by table
book A
book B
Fon book A by Earth
Fon book B by book A
Fon book B by Earth
2. A person exerts an upward force to hold a bag of groceries. System: person’s hand and bag of
groceries.
Physical Diagram
Force Diagram: hand
Force Diagram: bag of
groceries
3. A broom is pushing against a bowling ball and makes it move. System: broom and bowling ball
Physical Diagram
Force Diagram: broom
Force Diagram: bowling ball
4. You are pushing a box across a very rough floor. System: you and the box.
Physical Diagram
Force Diagram: you
Force Diagram: box
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5. (a) Eric holds a ball in his hand, and is in the process of throwing the ball upward. System: hand
and ball.
Physical Diagram
Force Diagram: hand
Force Diagram: ball
(b) The ball just left Eric’s hand. System: ball and hand.
Physical Diagram
Force Diagram: hand
Force Diagram: ball
(c) The ball is on its way down. System: ball and hand.
Physical Diagram
Force Diagram: hand
Force Diagram: ball
(d) The ball has just hit the ground, and is slowing down. System: ball and ground.
Physical Diagram
Force Diagram: hand
Force Diagram: ball
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4.11. Practice: Newton’s Third Law Problems
1. While driving down the road, an unfortunate butterfly strikes the windshield of your car. You
are thinking: this is a case of Newton's third law of motion! The butterfly hit the car windshield
and the car windshield hit the butterfly. Which of the two forces is greater: the force on the
butterfly or the force on the car’s windshield? Explain.
2. Andy goes hunting for the first time. He has just learned Newton’s Third Law and is now ready
to explain to his dad why the gun recoils when it is fired. He tells his dad that the recoil is the
result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the
gun pushes the bullet forwards and the bullet pushes the gun backwards. His dad has a question
for Andy (and you must answer it): How are the forces that act on the gun and on the bullet
related and why?
3. A karate chop delivers a blow of 3000 N to a board that breaks. The force that acts on the hand
during this event is
a) zero.
b) 1500 N.
c) 3000 N.
d) 6000 N.
Explain:
4. Arnold Strongman and Suzie Small each pull very hard on opposite ends of a rope in a tug-ofwar. The greater force on the rope is exerted by
a) Arnold, of course.
b) Suzie, surprisingly.
c) both exert the same force.
Explain:
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5. A big truck and a small car traveling at the same speed have a head-on collision. The impact
force is
a) greater on the small car.
b) greater on the big truck.
c) the same for both.
Explain:
6. A 10.0 N force is pulling vertically up on the ring of spring scale that weighs 2.0 N. If an 8.0 N
mass is attached to the bottom hook of the scale, the scale reading would be
a) 0 N.
b) 2.0 N.
c) 8.0 N.
d) 10.0 N
e) 12.0 N
Explain:
7. A horse pulling a wagon forward exerts 500 N of force on the heavy wagon. The wagon pulls
back on the horse with an equal force.
a) The wagon moves forward because these forces are not an action-reaction pair.
b) The wagon moves forward because there is an unbalanced force on the wagon.
c) The wagon moves forward because the horse pulls on the wagon a brief time before the
wagon reacts.
d) The wagon cannot move because these forces are equal and opposite.
Explain:
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Reading Page: Newton’s Second Law
Newton’s first law told us what happens when no net external force acts:
a) Things that are sitting still will not move on their own, they need an outside force to make
them move.
b) Things that are moving in a straight line will not stop, slow down or speed up on their own,
they need an external force to change their motion.
c) Things that are moving in a straight line will not change direction unless a force makes them
do so.
So it is pretty clear that if a net external force does act,
a) Things that are sitting still can begin to move.
b) Things that are moving can be made to slow down, speed up or even stop.
c) Things that are moving in one direction can be made to change direction.
In the previous activity we saw that a net external force changes the motion of an object by making
it accelerate. How does that go along with the statements above?
 Things that are sitting still can begin to move: the object had a velocity of zero to begin with,
and after a force is applied, it accelerates to a higher velocity.
 Things that are moving can be made to slow down (force is applied to change a high velocity
to low velocity) speed up or even stop.
 Things that are moving in one direction can be made to change direction – this is also a
change in velocity, namely, the amount of velocity may not have changed, but the direction
has, so there is a net acceleration.
We also saw in the previous activity that the amount of mass affects the force applied. In other
words, for two masses to have the same acceleration, the larger mass needs a larger force. In
equation form,
Force = (mass) x (acceleration) or in equation form F  ma
A lot of the applications of Newton’s second law deal with the fact that several forces can act on an
object, but if the forces don’t all balance out then there is a net external force. This net force causes
acceleration – and the acceleration will be along the direction of that net force. If all forces balance
out, the object will either be at rest (or in equilibrium) or move with a constant velocity. In the
examples below all forces are drawn and a motion diagram is associated to each example.
Example 1: A Teddy Bear sits on
a table.
Unit 4: Forces
The weight acts downward, and the normal force acts upward.
They balance each other out; the bear does not move. We
know the two forces are equal because;
a) if FG > FN the bear would fall downward
b) if FN > FG the bear would fly upward
c) since it stays put, FN = FG
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Example 2: A bear sitting on a table is
pushed gently to the right but does not
move.
In the vertical direction:
The weight acts downward, the normal force upward.
They balance each other out; bear does not move in
the vertical direction.
In the horizontal direction:
The pushing force Fpush to the right is opposed by the
force of friction, Ff; Since there is no motion along
the horizontal direction, the pushing force must
balance the force of friction: Fpush = Ff.
Example 3: The bear is being pulled
on a table and moves to the right with
constant speed.
Vertical:
The weight acts downward, the normal force upward.
They balance each other out; bear does not move along
the vertical direction.
Horizontal:
Since the bear moves to the right, the force of friction acts
toward the left since friction always opposes motion.
Constant velocity means that there are no net forces acting
in the horizontal direction. Therefore the pulling force and
the force of friction balance each other:
F(pull) = Ff
Example 4: The bear is being pulled on a Vertical:
table and moves to the right with
The weight acts downward, the normal force upward.
constant acceleration.
They balance each other out; bear does not move along
the vertical direction.
Horizontal:
Since the bear accelerates to the right, the force of
friction acts toward the left since friction always
opposes motion. Acceleration to the right means that
the net force acting in the horizontal direction is to the
right. Therefore the pulling force must be stronger than
the force of friction for the bear to accelerate to the
right.
FN
a
Ff
F(pull)
Fnet = ma where Fnet = Fpull - Ff
Fg
Unit 4: Forces
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4.12. Practice: Newton’s Second Law Problems
1. A 10-kg brick and a 1-kg book are dropped in a vacuum. The force of gravity on the 10-kg brick
a) is the same as the force on the 1-kg book.
c) is one-tenth as much.
b) is 10 times as much
d) is zero.
Explain your answer:
2. If an object's mass is decreasing while a constant force is applied to the object, would its
acceleration decrease, increase, or remain the same? Explain.
3. An object is propelled along a straight-line path in space by a force. If the object sweeps up
extra particles and its mass becomes twice as much, its acceleration
a) quadruples.
d) halves.
b) doubles.
e) none of these
c) stays the same.
Explain your answer:
4. The force of friction on a sliding object is 10 newtons. Would the applied force needed to
maintain a constant velocity be more than 10 N, less than 10 N or 10 N? Explain.
5. A 10-N falling object encounters 4 N of air resistance. The net force on the object is
a) 6 N upwards.
d) 10 N downwards.
b) 4 N upwards.
e) none of these.
c) 6 N downwards.
Explain your answer:
6. A 10-N falling object encounters 10 N of air resistance. The net force on the object is
a) 0 N.
d) 10 N.
b) 4 N.
e) none of these
c) 6 N.
Explain your answer:
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7. An apple weighs 1 N. When held at rest above your head, what is the net force on the apple?
8. An apple at rest weighs 1 N. Tammy throws it up in the air.
a) What is the net force on the apple on its way up? What is the direction of the acceleration?
b) What is the net force on the apple during the time is falling? What is the direction of the
acceleration?
9. A 1-kg rock that weighs 9.8 N is thrown straight upward at 20 m/s. Neglecting air resistance,
would the net force that acts on it when it is half way to the top of its path be less than 9.8 N,
9.8 N, or more than 9.8 N?
10. Which case has zero acceleration?
a) A car stopped in front of your house.
b) A child biking past your house at
constant velocity.
c) Sledding down a very steep hill.
d) B and C only
e) A and B only
Explain your answer:
11. Whenever the net force on an object is zero, would its acceleration be less than zero, zero, or
more than zero? Explain.
12. Your car is coasting on level ground at 60 km/h and you apply the brakes until the car slows to
40 km/h. If you suddenly release the brakes now, would the car tend to momentarily regain its
higher initial speed, continue moving at 40 km/h, or decrease in speed if no other forces act?
Explain.
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13. When you hang from a pair of gym rings, the upward support forces of the rings will always
a) each be half your weight.
c) add up to equal your weight.
b) each be equal to your weight.
Explain your answer:
14. A car has a mass of 2000 kg and accelerates at 2 meters per second per second. What is the
magnitude of the net force exerted on the car?
15. A tow truck exerts a force of 3000 N on a car, accelerating it at 2 meters per second per second.
What is the mass of the car?
16. A girl pulls on a 10-kg wagon with a constant horizontal force of 30 N. If there are no other
horizontal forces, what is the wagon's acceleration in meters per second per second?
17. A force of 1 N accelerates a mass of 1 kg at the rate of 1 m/s2. The acceleration of a mass of 2
kg acted upon by a net force of 2 N is
a) half as much.
c) the same.
b) twice as much.
d) none of these
Explain your answer:
18. An object following a straight-line path at constant speed
a) has a net force acting upon it in the
c) has no forces acting on it
direction of motion.
d) none of these
b) has zero acceleration.
Explain your answer:
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19. A man weighing 800 N stands at rest on two bathroom scales so that his weight is distributed
evenly over both scales. The reading on each scale is
a) 200 N.
d) 1600 N.
b) 400 N.
e) none of these
c) 800 N.
Explain your answer:
20. When a woman stands at rest with both feet on a scale, it reads 500 N. When she gently lifts one
foot, the scale reads
a) less than 500 N.
c) 500 N.
b) more than 500 N.
Explain your answer:
21. A 10-N block and a 1-N block lie on a horizontal frictionless table. To provide them with equal
horizontal acceleration, we would have to push with
a) equal forces on each block.
b) 10 times as much force on the heavier block.
c) 10 squared or 100 times as much force on the heavier block.
d) 1/10 as much force on the heavier block.
e) none of these
Explain your answer:
22. A block is dragged without acceleration in a straight-line path across a level surface by a force of
6 N. What is the force of friction between the block and the surface?
a) less than 6 N
c) 6 N
b) more than 6 N
d) need more information to say
23. Suppose a particle is being accelerated through space by a 10-N constant force. Suddenly the
particle encounters a second force of 10 N in the opposite direction from the first force. The
particle with both forces acting on it
a) is brought to a rapid halt.
b) decelerates gradually to a halt.
c) continues at the speed it had when it encountered the second force.
d) theoretically tends to accelerate toward the speed of light.
e) none of these
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4.13. Practice: Newton’s Third and Second Laws with Blocks
For each of the situations below compare the forces exerted by the blocks on each other as they
move on a table with some friction. Note: the 100 g block experiences twice as much frictional
force as the 50 g block.
For each of the problems A through F, select from the following choices:
a) block A exerts a greater force
b) block B exerts a greater force
c) the forces are equal
Also draw separate force diagrams for block A, for block B, and for a system that includes both
blocks.
Block A
Block B
Block A+B together
1. Both blocks move with
constant speed to the left
2. Both blocks move with
constant speed to the left
3. Both blocks move with
constant speed to the left.
4. Both blocks move with
constant acceleration to the
left.
5. Both blocks move with
constant acceleration to the
right.
Unit 4: Forces
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4.14. Practice: Balanced Forces
1. Draw force diagrams for the following situations:
An object lies motionless on a flat,
horizontal surface.
Two equal forces in opposite directions
along the horizontal act on an object that
lies motionless on a flat surface.
2. A swing is suspended by two ropes. Amy and Ryan sit together on the swing. The swing’s
weight is 60 N. Amy’s weight is 520 N and Ryan’s is 640 N. Draw a diagram indicating all forces
acting on your system (Amy, Ryan, swing). If the tension in the two support ropes are equal,
calculate those tensions.
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3. Qi and Jared sit on a board that is suspended by two cables. Qi weighs 590 N and Jared weighs
850 N. The board weighs 180 N. The tension in one of the ropes is 670 N. Draw a diagram for
all forces acting on the system (Qi, Jared, board).
a) Calculate all the downward forces.
b) Calculate all the upward forces.
d) Use the idea that the net force is zero to calculate the tension in the second rope.
4. Draw force diagrams for the following situations:
a) An object is suspended from the ceiling
by a rope.
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b) An object is suspended from the ceiling
by two parallel ropes.
c) The tension in the cable is 100 N. Find
the mass of the tire.
d) The tension in the cable on the left is 30
N. Draw a force diagram and then
calculate the mass of the ball.
Hint: how is the tension in the second cable
compared to the tension in the first one?
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e) Draw the force diagrams and figure out
the tension in each cable for case (a)
and case (b).
(a)
(b)
f) An owl is sitting on a branch in a tree.
The owl’s mass is 1.2 kg. Draw a force
diagram of the owl and calculate the
normal force acting on it.
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g) The force with which the balance beam
pushes up on the gymnast is 450 N.
Knowing that the gymnast is in
equilibrium on the beam (all forces
acting on her are balanced), draw a
force diagram and find the gymnast’s
mass.
5. A block is sitting at rest on a level floor. The normal force on the block is 3.00 N. Draw a
picture, identify the system, define the system with a curve, draw a force diagram and then
calculate the mass of the block.
Unit 4: Forces
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4.15. Practice: Force Diagrams related to Motion
1. Draw a force diagram for each one of the cases shown below: Indicate the direction of the
acceleration for each object.
A. Equilibrium
B. Equilibrium
C. Friction prevents sliding
D. Equilibrium
E. Equilibrium
F. Equilibrium
G. Rock is sliding on a
frictionless incline
H. Rock is falling. No air
resistance.
I. Rock is falling with constant
speed. Air resistance is present.
J. Rock is sliding at constant
speed on a frictionless surface
K. Rock is slowing down
because of friction.
L. Rock pulled by a rope
moves horizontally at constant
velocity. There is friction with
ground.
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M. Rock is rising in a parabolic N. Rock is at the top of a
trajectory.
parabolic trajectory.
O. Rock is tied to a rope and
pulled so that it accelerates
horizontally.
2. For the following problems, draw a picture of the system described and a force diagram.
Picture
A.
Draw the force diagram for:
Book
Verbal description
A book is at rest on a table
top.
B.
Backpack
A student rests a backpack
upon his shoulder. The
pack is suspended
motionless by one strap
from one shoulder.
C.
Book
A rightward force is
applied to a book in order
to move it across a desk at
constant velocity.
D.
Skydiver
A skydiver is descending
with a constant velocity.
Consider air resistance.
Unit 4: Forces
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Picture
E.
Draw the force diagram for:
Person
F.
Bird
G.
Pot
H.
Child
I.
Skier
Unit 4: Forces
Verbal description
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4.16. Practice: Force Diagrams, Motion Diagrams and Newton’s Laws
1. For each of the situations below, draw a picture and then the force diagram.
A. A rightward force is applied to a book in order to move it
across a desk with a rightward acceleration. Consider
frictional forces. Neglect air resistance. Diagram the forces
acting on the book.
B. A force is applied to the right to drag a sled across looselypacked snow with a rightward acceleration. Diagram the
forces acting upon the sled.
C. A football is moving upwards towards its peak after having
been booted by the punter. Diagram the forces acting upon
the football as it rises upward towards its peak.
D. A car is coasting to the right and slowing down. Diagram
the forces acting upon the car.
E. An egg falls from a nest in a tree. Neglect air resistance.
Diagram the forces acting on the egg as it falls.
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2. In the following problems you are given a representation of the motion that occurs. Fill in the
rest of the table.
A. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
B. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
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C. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion:
D. Picture of motion (the points are drawn at equal 1 second time intervals)
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
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E. Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion
F. Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
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G. Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram:
Verbal description of motion and force diagram
H. Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
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I. Picture of motion
Motion diagram (including position, velocity and acceleration)
Position, velocity and acceleration vs time graphs
Force diagram
Verbal description of motion
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3. In the following table you are given either the motion diagram, force diagram, verbal description,
or a graph. Fill in the rest of the table.
A. Motion Diagram
Force Diagram (you must label all
forces)
Verbal Description
Position, velocity and acceleration vs time graphs
B. Motion Diagram
Force Diagram (you must label all
forces)
Verbal Description:
You throw a ball up into the air. Describe what happens
from the instant it leaves your hand up until it reaches its
highest point.
Position, velocity and acceleration vs time graphs
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C. Motion Diagram of an airplane on a runway
Force Diagram (you must label all
forces)
Verbal Description
Position, velocity and acceleration vs time graphs
D. Motion Diagram
Force Diagram (you must label and
draw all forces)
Verbal Description:
A box is pulled up a ramp that has no friction. Continue the
description of its motion:
Position, velocity and acceleration vs time graphs
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E. Motion Diagram
Force Diagram (you must label and
draw all forces)
Verbal Description:
Position, velocity and acceleration vs time graphs
4. The motion of a cart in three different situations is described below .
a) A cart is released from the top of a frictionless ramp. Which of the following best describes
the situation after the cart was released? Explain your reasoning.
b) After the cart reaches the bottom of the ramp, a boy gives it a shove and sends it moving up
the ramp. Which of the following best describes the situation just after the cart was shoved?
Explain your reasoning.
c) After it was shoved upward in the previous problem, the cart reaches the highest point it can
reach on the ramp. Which of the following best describes the situation at the instant when
the cart is at its highest point? Explain your reasoning.
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Unit 4: Forces
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Review:Forces
Name __________________________ Hour______
What is a force?
A force is nothing else than a push or a pull applied by one object to another.
Type of Forces
Symbol
FN or Fn
FG or Fg
Ff
FT
Fe
Name
Normal force
Gravitational force (or weight
force)
Friction force
Tension force
Elastic force
Type of force
Contact force
Non-contact force (field force)
Contact force
Contact force
Contact force
Analyzing forces
Steps to follow when analyzing forces acting on an object:
1. Determine the object that is the receiver (has forces applied to it).
2. Identify the agents (objects that apply forces to the receiver).
3. For each agent, identify the force it applies. (Note: remember that we live on Earth and
therefore Earth (agent) always applies a force (gravity) to every single object (receiver) on its
surface).
4. Represent the direction of the force with an arrow starting on the receiver.
5. Describe the effect of the identified forces on the receiver.
Force Diagrams
Steps to follow when drawing force diagrams:
1. Draw a picture of the problem, showing the object and everything in the environment that
touches the object – ropes, tables, springs are all part of the environment.
2. Identify the system – which is the object or objects of interest – and draw a closed curve
around the system. The object should be inside the curve and everything else outside the
curve.
3. Locate every point in the system at the boundary of the curve where the environment
touches the system. These are the points where the environment exerts contact forces on the
system.
4. Identify by name all the contact forces at each point of contact (there may be more than one
force), then give each one an appropriate symbol.
5. Identify any long-range forces acting on the object. Name the force and write its symbol in
the picture.
6. Indicate the object by a point and draw the force diagram.
Calculating forces
Force of gravity on Earth can be determined from: Fg  mg where g = 9.8 N/kg.
Elastic force can be calculated from: Fe  k x where k = elastic constant and x is the stretch or
compression of the spring.
Netwon’s Laws:
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Newton’s first law tells us what happens when no net external force acts on an object:
a) Things that are sitting still will not move on their own, they need an outside force to make
them move.
b) Things that are moving in a straight line will not stop, slow down or speed up on their own,
they need an external force to change their motion.
c) Things that are moving in a straight line will not change direction unless a force makes them
do so.
Newton’s second law tells us what happens when a net external force does act on an object:
a) Objects that are sitting still can begin to move: the object had a velocity of zero to begin
with, and after a force is applied, it accelerates to a higher velocity.
b) Objects that are moving can be made to slow down (force is applied to change a high
velocity to low velocity), speed up, or stop.
c) Objects that are moving in one direction can be made to change direction – this is also a
change in velocity, namely, the amount of velocity may not have changed, but the direction
has, so there is a net acceleration.
Newton’s second law also gives us the connection between the net force, mass and acceleration:
Force = (mass) x (acceleration) or in equation form F  ma
Newton’s Third Law explains how two objects/systems interact with each other. Every time an
object A pushes or pulls on object B, object B pushes or pulls back on object A. Forces in nature
always act in pairs; one force is called action and the other one reaction. The two forces are always
equal, in opposite directions and act on different objects.
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