Author Archives: Automated Transfer Script

A2L Item 036

Goal: Translate between representations of motion

Source: UMPERG

The strobe diagram below shows the position of an object at successive
equal time intervals. The object moves from left to right.

Consider the following situations:

A. A book slides down an incline, moving from a rough region onto a
smooth region.

B. A cart is connected to a compressed spring and released.

C. A ball is dropped, hits the ground and rebounds to its initial
position.

D. A runner runs a race.

Which of these situations could be roughly described by the strobe
diagram?

  1. A
  2. B
  3. C
  4. D
  5. A & B
  6. C & D
  7. B & D
  8. A, B, C & D
  9. None of the above

Commentary:

Answer

(2),(4) or (7); Depending upon assumptions (B) or (D) are possible. The cart leaving the spring would speed up then eventually slow down due to friction. Also, the runner will speed up and eventually slow down.

A2L Item 034

Goal: Comparing the relative size of forces from changes in position.

Source: UMPERG

Below is shown a strobe diagram indicating the position of four objects
at successive time intervals. The objects move from left to right.

During the intervals shown, which of the objects experiences the largest
net force?

  1. Object A only
  2. Object B only
  3. Object C only
  4. Object D only
  5. Objects A and B
  6. Objects B and C
  7. Objects A and C
  8. None of the above
  9. Cannot be determined

Commentary:

Answer

(9); It is not possible to determine the size of the net forces without
knowledge of the masses of the objects. Because the horizontal force in
(A) points initially to the left, then to the right, students may say
that the net force is zero, which is true only for a time average.

A2L Item 033

Goal: Perceiving the presence of forces from changes in position.

Source: UMPERG

Below is shown a strobe diagram indicating the position of four objects
at successive time intervals. The objects move from left to right.

During the intervals shown, which of the objects experience no net force
in the horizontal direction?

  1. Object A only
  2. Object B only
  3. Object C only
  4. Object D only
  5. Objects A and B
  6. Objects B and C
  7. Objects A and C
  8. None of the above
  9. Cannot be determined

Commentary:

Answer

(8); Objects with no net horizontal force will move with constant velocity. The objects moving with constant velocity are B and D. This question helps to reinforce the idea that it is change in motion, not motion itself, that requires a force.

A2L Item 032

Goal: Hone the vector nature of force and how the net force can be determined from the 2nd law.

Source: UMPERG

A soccer ball rolls across the road and down a hill as shown below.

Which of the following sketches of Fy vs. t represents the net vertical
force on the ball as a function of time?

Commentary:

Answer

(4); on the horizontal partion there is no net force, and therefore no Fy. On the slope the net force in the y direction is due to gravity and a component of the normal force. Alternatively, since the ball accelerates along the slope, the net force must be parallel to the slope and have a component in the vertical direction.

A2L Item 030

Goal: Reasoning with 2nd law and honing of the concept of tension.

Source: UMPERG

Consider the three cases presented below. Assume the friction force
between the table and block in situations (B) and (C) can be ignored.

Which of the following statements about the tensions in the strings is
true?

  1. TA = TB = TC
  2. TB = TC < TA
  3. TA < TB < TC
  4. TB < TC < TA
  5. TA = TC < TB
  6. None of the above
  7. The relationship of the tensions cannot be determined

Commentary:

Answer

(4) By applying Newton’s second law to the hanging block one obtains a
relationship between the tension in the string and the acceleration of
the hanging block: The larger the acceleration the smaller the tension
force. The acceleration is determined by the total mass of the system.

Background

This is a good problem for challenging students to reason without
resorting to writing down a lot of equations. As one of the procedure
forces (tension, normal, static friction), the value of tension requires
application of the 2nd law.

Questions to Reveal Student Reasoning

What is the tension in situation (A)? Explain. Is the tension equal to
the weight in situation (B)? (If some students think so explore what
the net force is on the hanging mass, which will lead to a net force of
O, and a contradiction since this implies O acceleration.) Of systems
(A) and (B), which has the larger acceleration?

Suggestions

Ask students to consider limiting cases. What if the string was not
attached to a block on the table (or if the block had almost no mass)?
What would happen if the block on the table had a very large mass ?

A2L Item 031

Goal: Hone the vector nature of force and interrelate model and procedure forces.

Source: UMPERG

A marble rolls on to a piece of felt and slows down.

Indicate the direction that most nearly corresponds to the direction of
the force that the marble exerts on the felt. If none of the directions
are appropriate, or if the answer cannot be determined, respond (9).

Commentary:

Answer

(3) The force the felt exerts on the marble is up (normal force) and to
the left (friction force). Newton’s third law tells us that the force
the marble exerts on the felt must be down and to the right. Students
may focus on the normal force alone (4) or the friction force alone (2).
These are not two forces, but the components of a single force.
Students also find it difficult to extract some information from the
dynamical statement “slows down” and integrate this with the familiar
normal force.

Background

This presents an interesting twist to students. The friction force is
usually formulated in terms of a moving object and a fixed surface.
Students may not know for sure whether there is a friction force on the
felt – the felt is not moving. The analysis on the marble is reasonably
straightforward. Newton’s third law can be used to determine the force
on the felt if the force cannot be determined from the situation
directly.

Questions to Reveal Student Reasoning

Question students about how they got their answer. Did they use the
force laws that they learned previously? Did they use Newton’s second
or third laws?

Suggestions

Instead of a marble consider a sliding block and see if students think
differently – some students will have difficulty thinking about friction
with a rolling object.

A2L Item 029

Goal: Analyze the role of internal and external forces and the difference between static and kinetic friction.

Source: UMPERG

A person sits in an office chair with small wheels that swivel. The
person claims she can move the chair across the room without touching
anything but the chair, simply by kicking her legs outward. This claim:

  1. Is consistent with Newton’s laws and can be done.

  2. Is consistent with Newton’s laws but cannot be done.

  3. Is not consistent with Newton’s laws and, therefore, cannot be done.

  4. Is not consistent with Newton’s laws but nevertheless can be done.

  5. It is not possible to determine the correctness of the claim.

Commentary:

Answer

(1); the process is possible because sudden impulse due to internal
forces can exceed the static friction limit. By rapidly extending legs,
alternated by slow retraction, the chair can be moved. Students are
often aware of this but find it difficult to explain in terms of forces
and dynamics.

A2L Item 028

Goal: Reasoning using the 2nd law.

Source: UMPERG

A tow truck (2,000kg) pushing a car (1000kg) experiences an average
friction force of 13,000N while accelerating from rest to a final
velocity of 36 mi/hr (16 m/s). The air and the road exert an average
resistive force of 1,000N on the car. What force does the car exert on
the tow truck?

  1. 1,000N
  2. 2,000N
  3. 4,000N
  4. 5,000N
  5. 6,000N
  6. 12,000N
  7. 14,000N
  8. None of the above
  9. Cannot be determined

Commentary:

Answer

(4) The net force on the car and tow truck is 12,000N (13,000N –
1,000N). The acceleration is 4m/s2. The magnitude of the force between
the two vehicles is 5,000N.

Background

Answers are not as important as approach. What did students do to
understand the physical situation? Did they draw pictures. Did they
draw a free-body diagram.

Questions to Reveal Student Reasoning

Ask a couple of students to describe how they approached the problem.
Ask them to describe the steps they took without getting into
mathematical details. For example, did they draw a free-body diagram?
What forces did they consider? What system did they analyze?

Suggestions

After a couple of descriptions of how to approach solving the problem,
work through the problem with help from the class.

A2L Item 026

Goal: Reasoning with 2nd law.

Source: UMPERG

Consider the three situations shown below. In each case two small carts
are connected by a spring. A constant force F is applied to the
leftmost cart in each case. In each situation the springs are
compressed so that the distance between the two carts never changes.

Which of the following statements must be true regarding the compression
of the spring in each case? Assume the springs are identical.

  1. Compression A = Compression B = Compression C
  2. B = C < A
  3. A < B = C
  4. A < B < C
  5. B < A < C
  6. C < A < B
  7. A < C < B
  8. None of the above
  9. Cannot be determined

Commentary:

Answer

(5) The total mass is the same so the acceleration of the systems must
be the same. In each case the spring exerts the only horizontal force
on the cart to the right. The spring force must be largest for the 3M
cart and smallest for the M cart: B < A < C.

Background

This item requires students to reason. It is difficult to resort to
equation manipulation to answer this question. One difficulty with the
problem is that it involves a complex system (two carts connected by a
spring).

Questions to Reveal Student Reasoning

Is it really possible to compress the carts so that they stay a fixed
distance apart? What forces act on each cart? Will the carts
accelerate or move with a constant velocity? Compare the carts
acceleration.

Suggestions

Draw a free-body diagram for each cart.

Define a new problem in terms of the carts on the right: Each cart is
given an applied force so that each has the same acceleration. How do
the applied forces compare?

A2L Item 027

Goal: Contrast internal, external forces and net force.

Source: UMPERG

A toy
is made from two blocks and a spring as shown at right. When the spring
is compressed and suddenly released, the toy will jump off the table
surface. Which of the following is true about the net force on the toy
just after it is released?

  1. The net force is zero.
  2. The net force points up.
  3. The net force points down.
  4. The direction of the net force cannot be determined.

Commentary:

Answer

(2); This question seems difficult but it is available
to beginning students. Students can analyze the problem considering the
entire toy as a single system or decompose into the separate masses.
Viewed as a single system, since the center of mass accelerates up, the
net force must point up. Free body diagrams for each mass individually
would show no net force on the bottom mass (because the normal force
assumes a value necessary to balance gravity and spring force) and a
large net force on the upper mass (spring force exceeds gravity). If
sketched to scale, the two can be added showing that the net force
derives from the normal force on the lower block.

Background

This question is intended to have students distinguish between internal
and external forces. The question also can be approached in a variety
of ways.

Questions to Reveal Student Reasoning

Can the toy ever leave the surface? Would there be a net force if it
did leave the surface?