(Help) How to solve this question with solution?

Question

Sable, Labelle, and Mabel are sisters working on their tailor shop. The three sisters needed to push one box each with identical mass to prepare for their day of work. Sable finished the task relatively well. Labelle had twice the speed and the same time it took Sable to push the box. Mabel took half the time it took Sable to push the box and the same speed Labelle finished the task. Rank the three sisters by highest to lowest in terms of exerted force.

Answer 1

The Impulse-Momentum Theorem says that the change in momentum of an object equals the impulse applied to it. Momentum is mass x velocity so the change in momentum (between times t = 1 to t = 2) is mv₂ - mv₁. The Impulse is the force x time (that the force is applied).

So Ft = mv₂ - mv₁ or, dividing both sides by "t", F = (mv₂ - mv₁)/t BUT, in our case, v₁ = 0 (at least we assume that the object has an initial velocity of zero), therefore F = mv₂/t

Let "t" be the time that Sable takes to do the job and let "v" be the velocity she attains in pushing the mass. Let "m" be the mass of the three identical objects they push. Let F_S be the force that Sable uses, let F_L be the force Labelle uses, and let F_M be the force Mabel uses.

F_S = mv/t

Since "Labelle had twice the speed and the same time it took Sable" then F_L = m(2v)/t = 2mv/t

Since "Mabel took half the time it took Sable and the same speed Labelle" F_M = m(2v)/(1/2t) = 4mv/t

So F_M > F_L > F_S