# A2L Item 141

Goal: Reasoning with kinetic energy and work

Source: UMPERG-ctqpe58

Two
blocks, M2 > M1, having the same kinetic energy
move from a frictionless surface onto a surface having friction
coefficient μk.

Which goes further before stopping?

1. M1
2. M1
3. Both go the same distance
4. Cannot be determined

### Commentary:

(1) For a given amount of kinetic energy M1 will have a larger
velocity. The penetration distance depends upon the square of the
velocity.

Many students will notice that the relationship equating the kinetic
energy to work by friction has mass as a factor on both sides and will
answer #3. They are assuming that the masses have the same velocity, not
the same kinetic energy.

# 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).