Answer to Question #174790 in Physics for Nicole

Question

Two students push two identical shopping carts along a rough level surface at constant velocities and argue about who is doing more work. The first student pushes on a cart (with mass m) over a distance d using a horizontal force F. The second student pushes a cart (also mass m) a distance 2d with the same size force F, but this force is directed at an angle of 60° below the horizontal. Which of the following is true?

(A) Both students do the same amount of work on their respective carts.

(B) The first student is doing twice as much work as the second.

(C) The second student is doing twice as much work as the first.

(D) The second student is doing four times as much work as the first

Answer 1

The work done by the first student can be written as follows:

$$W_1=Fd.$$

The work done by the second student can be found as follows:

$$W_2=F2dcos60^{\circ}=Fd.$$

As we can see from the calculations, $W_1=W_2$, therefore, both students do the same amount of work on their respective carts.

Answer:

(A) Both students do the same amount of work on their respective carts.