Question

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? Select one:

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.

Answer 1

B) Jane, because work does not depend on mass, only on force times distance.

Step-by-step explanation:

As we know that the force applied on two objects is of same magnitude for same interval of time

So we know that

`F\Delta t = m(v_f - v_i)`

so we have

`v_(f1) = (F\Delta t)/(m)`

for another mass of double magnitude we have

`F\Delta t = (2m)(v_f - v_i)`

`v_(f2) = (F\Delta t)/(2m)`

since the speed of heavy mass is half that of speed of light mass so work done must be different on two masses.

While As per Jane if two forces are same and if the cover equal distance then in that case the work done is given as

`W = F(d)`

so work done would be same and it is independent of the mass of the object