Kreutter/Costello: Linear Dynamics 3
Relating Motion Diagrams and Force Diagrams
3.1 Observe and Represent
a) Use a bowling ball and a board (or anything that rolls easily, a billiard
ball or a low friction cart on a
track). Set the ball on the floor at rest and then continually push it
with the board for a while. Try to push
the same way (don’t change the strength of your push!) and keep the
ball moving along a straight line.
Observe the motion of the ball. What kind of motion is it? How do
you know?
b) After you agree on how the ball is moving, fill in the table below.
List all of the objects that
interact with the bowling ball
while it is being pushed.
Describe these interactions
n words.
Draw 3 force diagrams for Nhat forces “cancel” or
he ball that correspond to 3 ‘balance” each other?
different instances on your Explain how you know.
motion diagram.
Nas there an unbalanced
orce exerted on the ball?
Explain how you know.
If there is an unbalanced
Force, indicate the direction
of the unbalanced force.
Draw a motion diagram for the ball.
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C) Compare the direction of the iSv arrow on the motion diagram
to the direction of the unbalanced force
on the force diagram. What do you notice about these arrows?
Kreutter/Costello: Linear Dynamics 3
3.2 Observe and Represent
the ball in motion by pushing it once. After it is already
a) Use a bowling ball and a board. This time, set
direction to the ball’s motion. Try to push the
moving, push with the board very lightly in the opposite
t kind of motion is it? How do you know?
same way each time. Observe the motion of the ball. Wha
B
in the table below.
b) After you agree on how the ball is moving, fill
List all of the objects that
interact with the bowling ball
Nhile it is being pushed.
Describe these interactions
in words.
Draw 3 force diagrams for Nhat forces “cancel” or
each other?
he ball that correspond to 3 ‘balance”
Explain how you know.
instances on your motion
iiagram.
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Nas there an unbalanced
orce exerted on the ball?
Explain how you know.
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If there is an unbalanced
rorce, indicate the direction
of the unbalanced force.
Draw a motion diagram for the ball.
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KreutterfCostello: Linear Dynamics 3
c) Compare the direction of the zv arrow on the moti
on diagram to the direction of the unbalanced force
on the force diagram.
3.3 Find a Relationship
a) Use your findings in activities 3.1 and 3.2 to form
ulate how a motion diagram and a force diagram
for
the same object are related.
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b) Now predict what will happen if you set the bow
ling ball in motion and do not touch it after that.
Explain
how your prediction is based on the relationship
you just developed.
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c) Perform the experiment and record the outcome
. Did4 match the prediction? What can you say
about
the relationship between unbalanced forces and
changes in motion?
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3.4 Test Your Idea
Hold a bowling ball. Imagine now that your frien
d drops the bowling ball vertically so you have
to catch it before
it touches the ground. Consider the motion of the
ball after it touches your hands.
a) Predict what the motion of the ball will be like
and draw a motion diagram. Explain why you drew
it the
way you di
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b) Now use the relationship you developed in 3.3
to draw a force diagram for the ball at an instant
after it
touches your
What can you say about the length of the force
arrows?
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Kreutter/Costello: Linear Dynamics 3
You can check your ideas by actually performing the experiment as it is described and noting how it feels to
you. However to check the force diagram and the lengths of the force arrows, you can drop the heavy ball on a
bathroom scale and observe the reading on the scale. View the following videos (the second one should be
viewed frame by frame):
http://paer. rutqers.edu/pt3/movies/medballdropl mov
jp//paer. rutqers.edu/pt3/movieslmedballdrop2.mov
.
c) How is dropping the medicine ball on the bathroom scale like dropping the bowling ball into your
hands?
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d) Now perform the experiment by letting your friend drop the bowling ball into your hands. What did you
do to catch it before it touched the ground? What happened to the ball after it touched your hands?
e) What judgment can you make about your relationship between the motion diagram and force diagram
for the same object
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In the activities above, you determined that an unbalanced force exerted on an object points in the same
direction as the delta v arrow on a motion diagram for that object. We can also say that when all the forces
exerted on that object are balanced, the delta v arrow is zero. This is a part of the idea behind Newton’s
first law.
Newton’s first law of motion: We choose a particular object as the object of interest—the system. If no other
objects interact with the system object or if the sum of all the external forces exerted on the system object
is zero (forces in the y direction are balanced and forces in the x direction are balanced), then the system
object continues moving at constant velocity (including remaining at rest) as seen by certain observers.
In other words, an object keeps on doing whatever it was doing until it experiences an interaction
that results in an unbalanced force.
3.5 Observe and Find a Pattern
Imagine that you performed the following experiments, and then fill in the table that follows.
Kreutter/Costello: Linear Dynamics 3
Experiment
Sketch a motion diagram Draw a force diagram
for the cart.
for the cart.
.
(a) You steadily push
he back of a cart
along a smooth
surface sothat it
moves faster and
aster.
(c)Youpushgentlyon
he front of the moving
cart so that it moves
slower and slower and
eventually stops.
values and indicate
which direction is
positive)
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(b) You stop pushing
he cart and let it
oast. The cart does
not slow down.
Number description
(make up numerical
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d) Examine the direction of the unbalanced force
in each scenario and compare it to the direc
tion of the Ev
arrow. Do you see a pattern? Explain.
e) How does your answer to d telate to the rule
you developed and tested in 3.3 and 3.4?
f)
How do you understand the difference between
the words “motion” and “change in motion”?
Give an
example. Do you think an unbalanced force
exerted on an object causes motion or a chan
ge in motion?
Kreutter/Costello: Linear Dynamics 3
3.6 Reason
You throw a ball upward.
but before it reaches the top
a) Draw a motion diagram for the motion of the ball after it leaves your hand
of its flight. Remember the stomp rockets!
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when it is almost at the
b) Draw a force diagram for two instances: right after the ball left your hand and
top of the flight.
n.
C) Is the motion diagram consistent with each force diagram? Explai