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songoku
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Homework Statement
A metal platform of mass M and length L is placed on a frictionless floor. A man of mass m walks on the platform from the left end to the right end of the platform. Let left end of platform denoted as point O. How much does the platform move on the floor with respect to O?
Homework Equations
conservation of momentum
d = v.t
The Attempt at a Solution
Using conservation of momentum:
total momentum of system before the man walks = total momentum of system after the man walks
0 = m.v1 + M.v2
v2 = m.v1 / M
When the person walks to the right, the platform will move to the left so the time needed for the man to reach the right end:
t = d / v = L / (v1 + v2)
Distance moved by the platform with respect to O
= v2 . t
= m.v1 / M . L / (v1 + v2)
= m.v1 / M . L / (v1 + m.v1 / M)
= m/(m + M) . L
Is this correct? Thanks