Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct? A) Jake, because the speed of body 1 is half the speed of body 2, but m₁v₁ = m₂v₂. B) Jane, because work does not depend on mass, only on force times distance. C) Jake, because all bodies travel equal distances when equal forces are applied for equal times. D) Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved. E) Neither, because we can't compare the amounts of work done on bodies of different mass.

Question

Quizplus · Accepted Answer

Jane is correct because work only depends on force times distance, not on the mass of the object being moved. Therefore, if equal forces are applied to both objects and they move equal distances, then they will have done equal amounts of work. Jake's reasoning is incorrect because although the two objects may end up with the same kinetic energy (m₁v₁ = m₂v₂), the work done on them was not necessarily equal since they may have traveled different distances. Choices A, C, and D are incorrect because they either make incorrect assumptions or contradict established principles of work and energy. Choice E is partially correct in that we cannot directly compare the work done on objects of different mass, but it is not the best answer because we can still determine that equal forces applied for equal distances will do equal amounts of work on objects of different mass.

Jane and Jake Are Looking at What Happens to Body