A2L Item 072
- Description: Specify work to reverse the motion of an object.
- Goal: Hone the scalar nature of work and distinguish work from impulse.
- Source: UMPERG-ctqpe74
- Keywords: Energy, Mechanics, Work
The question for students:
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?
- -mv2
- -mv2/2
- 0
- mv2/2
- mv2
- None of the above
- Cannot be determined
Commentary for teachers:
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.