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Question

A man of mass m moves on a plank of mass M with a constant velocity u with respect to the plank. as shown in Fig.
a) If the plank rests on a smooth horizontal surface, determine the velocity of the plank.
b) If the man travels a distance L with respect to the plank, find the distance travelled by the plank with respect to the ground.
984454_5a4e63ffa77141fc9f78201a31afe280.png

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Solution

a) let ν1 and ν2 be the velocities of the man and the plank w.r.t ground. Then we have
[νman]plank=[νman]ground[νman]ground
The, [νman]plank=[νman]ground+[νman]ground
Or ν1=uν2
Initially, the system is at rest. Therefore,
0=mν1Mν2
or 0=m(uν2)Mν2
or ν2=mum+M
b) Let x be the displacement of plank in backward direction, the displacement of mass is Lx in forward direction.
ΔcCM=M(x)+m(Lx)M+m
0=Mx+m(Lx)x=mLM+m
1027481_984454_ans_41ea789f563e463faf7b670aeb208a03.png

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