(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An object of mass 3m is connected by means of a light, inextensible string to a scale pan of mass m. The object rests on the ground. The string passes over a smooth pulley and the scale pan hangs suspended. An object of mass m, falling from rest a distance h above the scale pan, lands on it and does not bounce. Show that the mass of 3m will rise to a height h/5.

Sorry but there's no diagram given! The answer I got was 4h/5 instead! :(

2. Relevant equations

3. The attempt at a solution

To find the speed of the scale pan before the string becomes taut:

mgh=0.5u^2

u=√(2gh)

To find the speed of the scale pan/speed at which the 3m object jerks in motion:

Take upwards direction as negative:

-I = 2mv-2m√(2gh) (this is the change in momentum of the scale pan)

-I = -3mv

Equate both to get:

-3mv=2mv-2m√(2gh)

-5mv=-2m√(2gh)

v=2√(2gh)/5

This speed, v is the initial speed of the upward motion of the 3m mass.

u=2√(2gh)/5

v=0 (mass of 3m rise to a height of h/5 and stop)

To find acceleration, a:

For the 3m mass (it's going upwards):

T-3mg=3ma

For the scale pan+object of mass m (going downwards):

2mg-T=2ma

Equate both equations:

T=3ma+3mg

T=2mg-2ma

3ma+3mg=2mg-2ma

5ma=-mg

5a=-g

a=-g/5

Using an equation of linear motion:

v^2=u^2+2as

0=(2√(2gh)/5)^2 + 2(-g/5)s

s=4h/5

Did I do something wrong in the middle? Was I on the right track in the first place? Thanks!! :D

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