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jiayingsim123
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Homework Statement
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! :(
Homework Equations
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