# A2L Item 183

Goal: Reason with impulse and energy

Source: CT151.2S02-46 Two
blocks are connected to the ends of a spring as shown. Assume that the
mass is proportional to the size of the block. The spring is compressed
(same amount) and released suddenly. In which orientation will the
system achieve the largest height?

1. A
2. B
3. both go to the same height
4. cannot be determined

### Commentary:

(2) This is a very rich problem for reasoning. It IS possible for
students to reason to the correct solution if they consider appropriate
concepts. To help them along suggest the following: Draw free body
diagrams for each of the masses separately. Combine them to get a valid
free body diagram for the system. Such a process reveals that the normal
force is responsible for the impulse causing the system to jump. The
spring force is internal to the system and does not appear on the
system’s free body diagram.

Students can deduce the answer using analogy or experience. Pogo sticks
or even the human body are analogous systems.

# A2L Item 157

Goal: Hone the concept of impulse

Source: UMPERG-ctqpe86 The
two blocks shown below are identical. In case A the block sits on a
horizontal surface and in case B the block is in free fall. Which
statement is correct regarding the impulse delivered to the block by the
gravitational force during a time interval Δt?

1. In case A the impulse is zero.
2. In case B the impulse depends upon v.
3. The impulse is larger in case B than A.
4. None of the above
5. Cannot be determined

### Commentary:

(4) Even students who understand forces and would respond
correctly to this question if asked in terms of forces have difficulty
with this question. Many think that motion matters, or answer the
question as if it was about the net impulse.

# A2L Item 155

Goal: Problem solving

Source: UMPERG-ctqpe84

A mass of 0.5 kg moving along a horizontal frictionless surface
encounters a spring having k = 200 N/m. The mass compresses the spring
by 0.1 meters before reversing its direction. Consider the total time
the mass is in contact with the spring. What is the total impulse
delivered to the mass by the spring?

1. -4 N-s
2. -2 N-s
3. 0 N-s
4. 2 N-s
5. 4 N-s
6. none of the above
7. cannot be determined.

### Commentary:

(2) This problem requires students to put together the concepts
of kinetic and potential energy, and change of momentum. Some may be
tempted to resort to the definition of impulse and try to determine the
force due to the spring.

# A2L Item 153

Goal: Hone the concept of impulse

Source: UMPERG-ctqpe80

A MOVING car collides with a STATIONARY truck. Which of the following
statements is true about the magnitudes of the impulse on each due to
the other?

1. The impulse on the car is larger than the impulse on the truck.
2. The impulse on the truck is larger than the impulse on the car.
3. The magnitudes of the two impulses are equal.
4. Answer depends upon circumstances of the collision.

### Commentary:

(3) The 3rd law requires that the impulses be equal. Even
students who understand the 3rd law have difficulty realizing that the
magnitude of the impulse on two interacting bodies is the same. Many
students, however, do not understand impulse enough to recognize the
with regard to ALL the forces, not just the one due to the other
vehicle.

# A2L Item 076

Goal: Interrelate and contrast the concepts of work, kinetic energy and impulse.

Source: UMPERG-ctqpe96 Compare two collisions that are perfectly inelastic. In case (A) a car
traveling with velocity V collides head-on with a sports car having half
the mass and traveling in the opposite direction with twice the speed.
In case (B) a car traveling with velocity V collides head-on with a
light truck having twice the mass and traveling in the opposite
direction with half the speed. In which case is the work done on the
car during the collision the greatest?

1. A
2. B
3. Both the same
4. Cannot be determined

### Commentary:

(4) The total momentum of both systems is zero, so after the collision
there is no KE in either system. System (A) has more kinetic energy
initially. There is no way, however, to determine how much of the
kinetic energy in the combined system of the two vehicles is dissipated
in the automobile as opposed to the other vehicle.

#### Background

This question serves only to provoke a discussion of the dissipation of
energy in a collision. Students are tempted to assume that each
vehicle must absorb its own initial KE.

#### Questions to Reveal Student Reasoning

How do the forces acting on the car in the two cases compare?

Which collision takes longer?

Which vehicle do you think will suffer the greatest damage?

#### Suggestions

Promote a discussion of auto safety.

# A2L Item 077

Goal: Contrast the concepts of impulse and work.

Source: UMPERG-ctqpe127

Consider the following statements:

A. If an object receives an impulse, its kinetic energy must change.

B. An object’s kinetic energy can change without it receiving any impulse.

C. An object can receive a net impulse without any work being done on it.

D. A force may do work on an object without delivering any impulse.

Which of the following responses is most appropriate?

1. None of the statements are true.
2. Only statement A is true.
3. Only statement B is true.
4. Only statement C is true.
5. Only statement D is true.
6. Two of the statements are true.
7. Three of the statements are true.
8. All of the statements are true.
9. Cannot be determined.

### Commentary:

(4) We consider only a simple object with no internal structure. A mass
traveling in a circle with constant speed (mass on a string, satellite
in circular orbit or marble rolling around a hoop on a horizontal
surface) receives a net impulse, say, every quarter circle without any
work being done because the force is perpendicular to the motion.

#### Background

Students need to sort out the difference between impulse (integral of
force over time) and work (integral of force over displacement). This
question is most easily answered considering the impulse-momentum
theorem and the work-kinetic energy theorem. The example mentioned in
the answer to demonstrate the truth of statement C also serves to
demonstrate the falseness of statement A. As for statement B, if an
object’s KE changes its momentum must change so it must have received an
impulse. Statement D is also false because if a force does work on the
object it must have acted over time.

#### Questions to Reveal Student Reasoning

A book sits at rest on a table. Does gravity do work on the book? Does
gravity provide an impulse?

Compare a satellite in circular orbit around the Earth with a simple
pendulum. Does gravity deliver an impulse over a quarter cycle? a half
cycle? a whole cycle? Does gravity do work on the object over a quarter
cycle? a half cycle? a whole cycle?

#### Suggestions

Ask students to create physical situations meeting certain
specifications. E.g. A situation for which a force acts over a
particular time causing a change of momentum but no change in kinetic
energy (mass on a spring).

# A2L Item 073

Goal: Hone the vector nature of impulse and contrast impulse to kinetic energy.

Source: UMPERG-ctqpe82

A block having mass M travels along a horizontal frictionless surface
with speed vx. What impulse must be delivered to the mass
to reverse its direction?

1. -mvx
2. -2mvx
3. 0
4. 2mvx
5. mvx
6. None of the above
7. Cannot be determined

### Commentary:

(1) or (2) or (6) are all defensible answers depending upon how students
interpret the question. This is a good question for stressing to
students that it is their reasoning not their answer that is important.

#### Background

Impulse is a vector. Using the impulse-momentum relation, the change in
momentum must be at least mvx in the direction opposite to
the motion to reverse direction.

#### Questions to Reveal Student Reasoning

What impulse would be needed to make the mass travel parallel to the
y-axis?

Suppose a constant force Fx acts for 4 seconds causing the
mass to stop. What force would be needed to stop the mass in 2 seconds.

#### Suggestions

Have students make a concept map showing the relationships among the
quantities mass, velocity, momentum, impulse, time, force, and average
force.

Does it bother students that, in 10 seconds gravitation provides an
impulse of 10mg to a book whether it is dropped or sitting on a table?