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Question

There is a massless pulley which is going upward with an acceleration a=5tm/s2. A string is passing over the pulley as shown in the figure. At one end of the string a plank of mass 2m kg is attached and at the other end a small ball of mass m kg is attached. It is given that after 1 sec it just passes the plank then if length of plank is x + 0.8 . Find x. ___


Solution

For the rod
2mg+2maT=2ma(1)
Tmgma0=ma(2)
2mg+2maT=2ma(1)
Tmgma0=ma(2)

Equation (1) + (2)
mg+ma0=3ma
a=g+a03
aRball=23(g+5t)
dvreldt=23(g+5t)
dvrel=23(g+5t)dt
at t=0, vrms=0
vrel=23[gt+5t22]
dxreldt=23[gt+5t22]
dxrel=23[gt+5t22]dt
xrel0dxrel23[gt22+5t36+c]
xrel=gt23+5t29 in sec
xrel=g3+59=9.83+59=3.8 m

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