Download Force as an Interaction

Sierzega: Dynamics 1
Force as an Interaction
1.1 Observe and Represent
a) Pick up a small object, like a tennis ball, and hold it in your hand. Now pick up a larger object,
like a bowling ball, and hold it. Do you feel the difference? How can you describe what you feel
in simple words?
b) What do you have to do to hold the ball? Does this have a direction?
c) Think of how we represented objects and motion in the last module. What are some possible
ways of representing the magnitude and direction of the interaction between your hand and the
tennis ball?
d) Let’s choose the tennis ball as our object of interest. Represent the tennis ball with a dot and
label the dot with “tennis ball.” Draw an arrow to show how your hand pushes the ball. Connect
the tail of the arrow to the dot. This arrow represents the force that your hand exerts on the
tennis ball.
e) Repeat part d) for the bowling ball. How is this arrow similar to the one you drew in part d)?
How is it different?
Did You Know?
The word “force” is used in physics for a physical quantity that characterizes the interaction of two
objects. A single object does not have a force by default, as the force is defined through the interaction
of two objects.
Remember that all physical quantities are measured in units. The unit of force is called the newton (N),
where 1 N = (1 kg)(1 m/s2 ).
f) How could you label each force arrow to show that they are different forces that your hand exerts
on different objects? Add this label to your representations.
Here’s An Idea!
To show that the force arrow represents the push that the hand exerts on the ball, we can use a symbol F
with subscripts.
For example: If we look at the interaction of a golf ball and a golf club while the club is hitting the ball.
Then if we choose the golf ball as the object of interest, the golf club exerts a force on the golf ball. As a
label for an arrow on a force diagram, this would be written as F club on ball.
g) What do you think would happen to a ball if your hand were the only object interacting with it?
Why doesn’t this happen?
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h) What other objects are interacting with the ball? List each object and the direction of the push or
pull that it exerts.
i) Some people think that only live (animate) objects can exert forces. How can a non-living thing
push or pull an object?
1.2 Test Your Reasoning
a) In the previous activity, did you say that air interacts with the ball for part f? How do you think
air interacts with the ball?
b) What experiment can you perform to test your idea about whether the air pushes up or down on
the ball? One experiment could be to hang an object by a spring inside a container and pump the
air out of the container. Write a prediction of what should happen to the bottle based on your
hypothesis of how air interacts with the ball.
c) Watch the video of this experiment at http://paer.rutgers.edu/pt3/movies/bottle_in_vacuum.mov
then summarize what effect the air has on the ball.
1.3 Represent and Reason
a) In activity 1.1, did you say that gravity interacts with the ball? Gravity is not an object; you
cannot hold or touch it. Gravity, or gravitational force, is the force that an object exerts on
another object without touching it. So when we use the word gravity to note the pull down on all
objects on Earth, what is the object that exerts this downward pull?
b) Add another arrow on each of your diagrams from 1.1. Label the arrow with the appropriate
subscripts.
c) What do you notice about the length of the two arrows in each diagram? What do you think
would happen if the arrow representing the interaction with your hand were longer than the
arrow representing the interaction with Earth? If it were the other way around?
d) How are the arrows for the bowling ball different from the arrows on the diagram for the tennis
ball?
Did You Know?
The two diagrams you created in activity 1.1 through 1.3 are called force diagrams. Force diagrams are
used to represent the forces exerted on an object of interest (or system) by other objects.
A system is an object or group of objects that we are interested in analyzing. Everything outside the
system is called the environment and consists of objects that might interact with and affect the system
object’s motion. Interactions between the system object and an object in the environment are external
interactions. When we draw force diagrams, we only consider the external forces exerted on the system
object(s) by objects in the environment.
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1.4 Represent and Reason
a) Consider the force diagram you created for the bowling ball. How would you describe how the
lengths of the force arrows compare to each other?
Did You Know?
When the sum of all the forces exerted on an object of interest is equal to zero, we say that the object is
in equilibrium.
b) How might we represent our force diagrams with a mathematical representation or math
statement in order to show that an object is in equilibrium? Write a math statement for the
bowling ball.
Need Some Help?
Imagine putting an axis next to the force diagram with the origin at the dot. You can use + for the up
direction and – for the downward direction.
For example: Let’s take the situation of a puppy curled up in your lap. Then we can write the total force
exerted on the puppy by your legs and Earth as: Flegs on dog + FEarth on dog = 0.
c) For your math statement, does it matter whether you chose up as positive or down as positive?
How would this affect the math statement you wrote? What happens to the total force exerted on
the ball if we switched the axis?
Did You Know?
Notice that depending on the orientation of the axis, either FHand on Ball or FEarth on Ball has a negative value,
thus the sum of a positive and a negative number can be zero. How do we know which force is positive
and which one is negative? If the force arrow points in the positive direction of the chosen axis, we
consider the force positive. If the +y axis points down, for example, then FEarth on Ball > 0 and FHand on Ball < 0.
d) Label the positive direction on each force diagram from 1.1.
e) Is the tennis ball in equilibrium? Explain.
f) Write an expression for the forces exerted on the tennis ball similar to the expression you wrote
for the bowling ball.
Sierzega: Dynamics 1
1.5 Observe and Explain
a) You place an object on a table. Draw a force diagram of the object.
b) What is exerting a force that balances the force that Earth exerts on the object? What is the
direction of that force?
c) Write a mathematical expression for the forces exerted on the object.
d) A book rests on top of a table. Jim says that the force exerted by the table on the book is always
the same in magnitude as the force exerted by Earth on the book. Why would Jim say this? Do
you agree or disagree with Jim? If you disagree, how can you argue your case?
Did You Know?
The diagrams we constructed above are force diagrams. A force diagram is a physical representation
used to analyze and evaluate processes involving forces. In order to create a force diagram, follow the 6
steps below.
SKETCH
FORCE DIAGRAM
1. Sketch the situation
+
2. Circle the object of
interest
r
F S on B

3. Draw a dot
representing the
box
FFloor onSBox
on BF
6. Label the
forces
Check for understanding:
What does the length of
an arrow on the diagram
mean?
4. Identify interactions between
the system and other objects.
Here: Earth, floor, rope and
surface
FEarth on Box
5. Draw forces to
represent
interactions, watch
the length of
arrows
Sierzega: Dynamics 1
Did You Know?
System: A system is the object of interest that we choose to analyze. Make a sketch of the process that
you are analyzing. Then circle the object of interest – your system. Everything outside that system is
called the environment and consists of objects that might interact with and affect the system object’s
motion. These are external interactions.
Force: A force that one object exerts on another characterizes an interaction between the two
objects. Forces are represented by the symbol F and with two subscripts indicating the two objects.
For example, if Earth pulls on a ball, we note the force exerted by Earth on the ball as: FEarth on ball.
Force is a physical quantity that has both magnitude and direction. The symbol also indicates that in
this case our system is the ball and Earth is the external object. If we are interested in the force that
the ball exerts on Earth, we write it as Fball on Earth .
1.6 Represent and Reason
A person pushes a box across a very smooth floor.
a) Examine the force diagram to the right. Is the sum of the forces
in the vertical direction equal to zero? Is the sum of
forces in the horizontal direction equal to zero?
b) Draw an arrow to indicate the direction of the sum of the
forces, if there is one. Discuss whether the result is
reasonable.
1.7 Represent and Reason
Read each of the scenarios and then draw a force diagram for the selected object of interest.
1. You are throwing a tennis ball
upward. Consider the moment right
before the ball leaves your hand. The ball
is the object of interest.
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2. The ball is flying up. The ball is the
object of interest.
3. The ball is at the top of the flight. The
ball is the object of interest
4. The ball is being caught by you.
Consider the moment when your hands
are stopping the ball. The ball is the
object of interest.
Now use the rubric below to self-assess your force diagrams.
Missing
No force diagram
is constructed.
An attempt
Force diagram is constructed but
contains major errors: missing or
extra forces (not matching with the
interacting objects), incorrect
directions of arrows, or incorrect
relative length of force arrows.
Needs improvement
Force diagram contains no
errors in force arrows but
lacks a key feature such as
labels of forces with two
subscripts or forces are not
drawn from single point.
Acceptable
The diagram contains forces for
each interaction and each force
is labeled so that one can clearly
understand what each force
represents. Relative lengths of
force arrows are correct.
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1.8 Represent and Reason
Draw force diagrams and use them to determine the direction of the sum of the forces exerted on the
following objects of interest:
a.
b.
c.
d.
e.
A hockey puck moving on ice slows to a stop. The puck is the object of interest.
You start lifting up a heavy suitcase; the suitcase is the object of interest.
A boat floats in the ocean; the boat is the object of interest.
You are pulling a sled horizontally on fresh snow at constant speed; the sled is the object
of interest.
You are pushing a lawnmower horizontally; the lawnmower is the object of interest.
Reflect: What did you learn about forces in this lesson? You heard the expression “May the force
be with you.” Explain why it is not a possible thing for a force in physics.