A force of magnitude $F_{1}$ $F_1$ accelerates a body of mass $m$ $m$ from rest to speed $v$ $v$ . Another force $F_{2}$ $F_2$ accelerates a body of mass $2 m$ $2m$ from rest to a speed $2 m$ $2m$ . What is the ratio of the work done by $F_{2}$ $F_2$ to that of $F_{1}$ $F_1$ ?

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A force of magnitude $F_{1}$ $F_1$ accelerates a body of mass $m$ $m$ from rest to speed $v$ $v$ . Another force $F_{2}$ $F_2$ accelerates a body of mass $2 m$ $2m$ from rest to a speed $2 m$ $2m$ . What is the ratio of the work done by $F_{2}$ $F_2$ to that of $F_{1}$ $F_1$ ?

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Answer 1 · 2016-11-24T13:12:31

$\frac{W_{2}}{W_{1}} = 8$ $W_2 / W_1 = 8$

Explanation:

We assume that the statement contains an error: where it says that the force $F_{2}$ $F_2$ accelerates a body of mass $2 m$ $2 m$ from rest to a speed $2 m$ $2m$ , we understand that it should say that $F_{2}$ $F_2$ accelerates said body to a speed $2 v$ $2 v$ . 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:

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

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A force of magnitude $F_{1}$ $F_1$ accelerates a body of mass $m$ $m$ from rest to speed $v$ $v$ . Another force $F_{2}$ $F_2$ accelerates a body of mass $2 m$ $2m$ from rest to a speed $2 m$ $2m$ . What is the ratio of the work done by $F_{2}$ $F_2$ to that of $F_{1}$ $F_1$ ?

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A force of magnitude F_1F1F_1 accelerates a body of mass mmm from rest to speed vvv. Another force F_2F2F_2 accelerates a body of mass 2m2m2m from rest to a speed 2m2m2m. What is the ratio of the work done by F_2F2F_2 to that of F_1F1F_1?

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A force of magnitude $F_{1}$ $F_1$ accelerates a body of mass $m$ $m$ from rest to speed $v$ $v$ . Another force $F_{2}$ $F_2$ accelerates a body of mass $2 m$ $2m$ from rest to a speed $2 m$ $2m$ . What is the ratio of the work done by $F_{2}$ $F_2$ to that of $F_{1}$ $F_1$ ?