First slide

Motion of centre of mass

Question

A wagon of 200 kg is moving on a smooth track with velocity of 2 m/sec. A man of 80 kg also runs in the wagon with a velocity such that speed of the centre of mass of the system is zero. Find the velocity of man relative to the wagon (in m/s).

Moderate

A

5
B

6
C

7
D

8

Solution

Velocity of centre of mass
$v_{com} = \frac{m_{wagon} \times v_{wagon} + {mass}_{man} \times v_{man}}{(m_{wagon} + m_{man})}$
$v_{com} = \frac{(200) (2) + (80) (V)}{280} = 0 \Rightarrow V = - 5 m / s$
$\vec{v_{man}} = \vec{v}_{man, wagon} + \vec{v_{wagon}}$
$\vec{v_{man, wagon}} = \vec{v_{man}} - \vec{v_{wagon}} = - 5 - 2 = - 7 m / s$ -ve sign indicates opposite direction.

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