# 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).