PRACTICE TEST I
1. Below is a speed-time graph showing a cart speeding up over a certain period
of time, and then slowing down.
a) On the graph above, carefully sketch the speed-time graph for another
cart that would speed up at a higher rate than the one shown above, reach
the same maximum speed, and then slow down at a lower rate than the
one shown above.
b) Briefly explain why you sketched your graph the way you did.
A higher rate of speeding up is shown by making the graph have a steeper upward
slope, so it reaches the same height (maximum speed) in less time.
A lower rate of slowing down is shown by making the graph have a less steep
downward slope, so it takes a longer time to go from its maximum speed to being
stopped.
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2. A ball sits on a carpeted floor. A child kicks the ball and it starts to roll. While
rolling across the carpet, the ball slows down and eventually stops on the
other side of the room.
Sketch a speed-time graph for the entire motion, including the interval during
which the child kicks the ball and the interval during which the ball slows down
when rolling along the carpet and comes to a stop. On your graph mark with an
X the moment that the boy’s foot looses contact with the ball. Below the graph
explain your reasoning for choosing that particular moment.
X
The moment the foot loses contact with the ball is also the moment the speed stops
increasing rapidly. This is because the speed only increases while the interaction
between the foot and the ball is actually in progress. As soon as the interaction stops,
the effect it has on the balls speed also stops. (The ball starts to slow down at this
point because another interaction, friction, is affecting it.) We saw this in a video of a
hand pushing a cart. As soon as the hand lost contact the speed of the cart stopped
increasing.
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3. Below is a speed-time graph showing a cart speeding up over a certain period
of time, and then slowing down.
Energy source
Shade and label all the portion(s) of the graph where the cart was an energy source
during an interaction. Briefly explain how you reached that conclusion from the
graph. If you think the car was never an energy source during the entire motion, then
explain how you reached that conclusion from the graph.
The cart was definitely an energy source during the period while it was slowing down. It
was decreasing in kinetic energy, which means it was losing energy in some sort of
interaction. The only way for this to happen is if the cart is the energy source in that
interaction and the energy is being transferred to another object (or transformed to
thermal energy).
(If friction is present then it also possible the cart was an energy source in a frictiontype interaction even while it was speeding up, though this cannot be determined from
the graph.)
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4. A soccer player kicks a soccer ball into a
net. As the ball comes in contact with the
net, the net stretches and the ball stops
moving. Consider the time interval when
the soccer ball is in contact with the net.
Complete the following S/R energy
diagram to describe the interaction for this
time interval.
_______________________
Interaction
Contact
Energy Receiver
Energy Source
Ball
Decrease in
kinetic
energy
Mechanical
Energy
Net
Increase in
elastic
potential
energy
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5. A block sits on a carpeted floor. A child kicks the block and it starts to slide.
While sliding across the carpet, the block slows down and eventually stops on
the other side of the room. While sliding across the carpet, both the block and
the carpet warm up.
a) Consider the time interval during which the child’s foot was in contact with
the block. Draw an I/O energy diagram for the block during this time
interval. Make sure you label the appropriate interaction(s), energy change(s)
and energy transfer(s).
Contact Interaction
Contact Interaction
Mechanical
Energy
Mechanical
Energy
Block
Increase in
kinetic energy
Increase in
thermal energy
Heat
Energy
Heat Conduction/IR
Interaction
b) Now consider the time interval after the block leaves the child’s foot and is
slowing down as it slides across the carpet. Draw an I/O energy diagram for
the block as it slides across the carpet. Make sure you label the appropriate
interaction(s), energy change(s) and energy transfer(s).
Contact Interaction
Mechanical
Energy
Block
Decrease in
kinetic energy
Increase in
thermal energy
Heat
Energy
Heat Conduction/IR
Interaction
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6. For the same situation described in the previous question, consider the time
interval when the ball rolls across the carpet after it leaves the child’s foot.
You are to write your own explanation for why the ball slows down and
stops.
Explain: Why does the ball slow down?
Draw the energy diagram
_______________________
Interaction
Contact
Energy Receiver
Energy Source
Ball
Decrease in
kinetic energy
Increase in
thermal energy
Mechanical
Energy
Floor
Increase in
thermal
energy
Write the explanation
There is a friction-type contact interaction between the ball and the
carpeted floor. During this interaction there is a transfer of mechanical
energy from the ball to the carpet and at the same time the thermal
energy of the ball increases. The Law of Conservation of Energy tell us
that in order for there to be an increase in thermal energy of the ball
and an energy output from the ball there must be either an energy input
to the ball or a decrease in some other form of energy associated with
it. Thus, since there is no energy input to the ball (the kick is over)
there must be a decrease in kinetic energy of the ball. Because the ball
is losing kinetic energy it slows down as it rolls across the carpet.
7.
Shown below are eight different force diagrams (labeled A to H), taken from
simulator set-ups of a cart on a track.
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A
B
C
D
E
F
G
H
Which situations, represented by these force diagrams, would lead to speed-time
graphs for the motion of the cart like those shown below. In each case you may
choose as few, or as many, force diagrams as you think appropriate. You should
also briefly explain your reasoning in each case.
a)
b)
c)
Set-ups E and H would produce a graph like
this. The graph shows the cart speeding up.
In order for this to happen either a single
force must act on the cart in the direction
of motion (set-up E), or an unbalanced
combination of forces, with the strongest
force in the direction of motion must act on
the cart (set-up H).
Set-ups C and G would produce a graph like
this. The graph shows the cart slowing down.
In order for this to happen either a single
force must act on the cart opposite to its
direction of motion (set-up G), or an
unbalanced combination of forces, with the
strongest force opposite the direction of
motion must act on the cart (set-up C).
Set-ups B and D would produce a graph like
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this. The graph shows the cart moving at a
constant speed. In order for this to happen
the cart must already be in motion and
either no forces must act on the cart (setup D), or a balanced combination of forces,
must act on the cart (set-up B).
d)
Set-ups A and F would produce a graph like
this. The graph shows the cart remainingat
rest, with a constant speed of zero. In order
for this to happen the cart must not be in
motion and either no forces must act on the
cart (set-up A), or aa balanced combination
of forces, must act on the cart (set-up F).
8. A student gives a low-friction cart a quick push
with her hand and the cart starts to move along
the track. After her push the cart moves along the
track, slowing down very gradually as it moves.
The student then used ideas about forces to give
the following explanation for why the cart
slowed down very gradually after it was pushed.
Explanation: Why did the cart slow down very gradually after it was pushed?
Draw the Force Diagram
Direction o f motion
Gradua lly d ecreasing
forc e of hand on ca rt
Write the explanation:
The force of the hand acts on the cart, which is at rest. When a force acts
on an object at rest, the object begins to move in the direction of the force,
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and so the cart begins to move in the direction of the push. After the push,
the force continues with the cart, and gradually runs out. As it does so, the
cart gradually slows down.
Evaluate this Explanation:
Evaluate this explanation by considering each of the following four criteria.
If the written explanation is good, state why. If it is poor, state what is wrong
with it and correct it.
Present
YES/NO
YES/NO
YES/NO
YES/NO
Criterion
Complete: All ideas needed are included
Accurate: All included ideas included correspond to established
ideas
Logical Reasoning: Narrative connects ideas to the phenomenon
Clear: Narrative is well written
This explanation is ______POOR_____ (good, poor) because:
First it is not well written because it starts by giving details about why the cart
started moving in the first place. This is not necessarily wrong but is not necessary to
answer the question being asked, which is why it slowed down after the push.
Second, it uses incorrect ideas to explain why the cart does slow down. The force
from the hand is not transferred to the cart and does not continue with it. The cart
slows down because a force (probably a frictional force exerted on it by the track)
acted on the cart in the opposite direction to its motion.
A better explanation would be:
Direction of motion
Frictional force exerted
on cart by track
When an unbalanced force acts on a moving object in the opposite direction to its
motion it will slow down. As the cart rolls along the track, the track exerts a
frictional force on it in the opposite direction to its motion, so the cart slows down as
it rolls.
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