Chapter 6, Problem 1CQ

Equal forces are used to move blocks A and B across the floor. Block A has twice the mass of block B, but block B moves twice the distance moved by block A. Which block, if either, has the greater amount of work done on it? Explain.

To determine

Which among the given blocks has greater amount of work done on it.

Answer to Problem 1CQ

The block B has greater amount of work done on it.

Explanation of Solution

Given info: Mass of block A is twice that of block B and the block B moves twice the distance moved by the block A.

The general expression for the work done on a block for moving it in the horizontal plane is,

$W=Fd$

Here,

$W$ is the work done

$F$ is the magnitude of the horizontally applied force

$d$ is the distance moved by the block

It is clear that the work done is a function of force and distance moved. It is not a function of the mass of the object on which the work is done.

Here, same force is acting on the bocks A and B but the block B moves more distance than A. Hence, even though the mass of block A is larger, the block B has the greater amount of work done on it because it is moved more distance as compared to A, when the force is applied.

Conclusion:

Therefore, the block B has greater amount of work done on it.