Question

Two person A and B of weight 60kg and 40kg respectively stand facing each other, and pull on a light rope streched between them. Find the ratio of distance covered by them when they meet if their intial separation was 5 metre

Answer 1

To be able to successfully pull the rope with balance, the work done by person A should be just equal to the work done by person B.

workA = workB ----> 1

Where: work = force * distance

In this case, force = mass * gravity

So work = mass * gravity * distance

Rewriting equation 1:

massA * gravity * distanceA = massB * gravity * distanceB ---->2

We know that distanceA + distanceB = 5 m, therefore distanceA = 5 – distanceB. Substituting this to equation 2 and cancelling constant g:

massA * distanceA = massB * distanceB

60 kg * (5 – distanceB) = 40 kg * distanceB

distanceB = 3 m

distanceA = 5 – distanceB = 2 m

ratio is: distanceA / distanceB = 2/3 = 0.67