First slide

Motion of centre of mass

Question

A man of mass 80 kg is riding on a small cart of mass 40 kg which is rolling along a level floor at a speed of 2 m/s. He is running on the cart so that his velocity relative to the cart is 3 m/s in the direction opposite to the motion of cart. What is the speed of the centre of mass of the system

Moderate

A

1.5 m/s
B

1 m/s
C

3 m/s
D

zero

Solution

$v e l o c i t y o f t h e m a n w i t h r e s p e c t t o c a r t v_{m c} = v_{m} - v_{c} - 3 = v_{m} - 2 v_{m} = - 1 m / s v_{c o m} = \frac{- 1 x 80 + 40 x 2}{120} = 0$

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