Question

A force of magnitude `F_1` accelerates a body of mass `m` from rest to speed `v`. Another force `F_2` accelerates a body of mass `2m` from rest to a speed `2m`. What is the ratio of the work done by `F_2` to that of `F_1`?

Answer 1

`W_2 / W_1 = 8`

Explanation:

We assume that the statement contains an error: where it says that the force `F_2` accelerates a body of mass `2 m` from rest to a speed `2m`, we understand that it should say that `F_2` accelerates said body to a speed `2 v`. In another case, the statement would not make much sense.

That said, we will solve the problem.

The work done by force on the body will be equal to the variation of the kinetic energy that it experiences:

`W = Delta K = 1/2 m (v^2 - cancel {v_0^2}) = 1/2 m v^2`

As both bodies start from rest, their initial velocities are two equal to zero.

The work done by the first force will be:

`W_1 = 1/2 m v^2`

and the one done by the second is:

`W_2 = 1/2 (2 m) cdot (2 v)^2 = 4 m v^2`

Then, the ratio between `W_2` and `W_1` is:

`W_2 / W_1 = {4 m v^2}/{1/2 m v^2} = 8`