**Goal:** Hone the scalar nature of work and distinguish work from impulse.

**Source:** UMPERG-ctqpe74

A block having mass M travels along a horizontal frictionless surface

with speed v. What is the LEAST amount of work that must be done on

the mass to reverse its direction?

- -mv
^{2} - -mv
^{2}/2 - 0
- mv
^{2}/2 - mv
^{2} - None of the above
- Cannot be determined

## Commentary:

## Answer

(3) Zero work must be done. Students will likely become entangled in

the sign of the work as well as the interpretation of the requirement to

“reverse its direction”. The most defensible answer after (3) is (2).

Some students may confuse the sign of the work, Students who choose (2)

or (4) have career potential as a lawyer.

## Background

This is an excellent problem for engaging students in a discussion of

work and energy. A mass traveling in the opposite direction with the

same speed would have the same kinetic energy. The work-kinetic energy

theorem then states that no net work need be done on the mass. The

work-kinetic energy theorem also resolves any ambiguity in the sign of

the work if the mass is just brought to rest.

## Questions to Reveal Student Reasoning

Draw a diagram indicating the direction of motion and the direction of

the force acting on the mass. What is the direction of the

displacement?

If the surface had friction and the mass just slid until it stopped, how

much work would the friction force do?

## Suggestions

It is easy to demonstrate several situations for which an object

reverses its direction and no new work is done. All it requires is a

conservative force. For example, let a ball roll up an incline and then

back down. Or, allow a mass to encounter a spring. Or, have a marble

roll around a semicircular track. This latter case is interesting

because the force acting on the mass (Normal) does no work.