Answer to Question #136482 in Electric Circuits for Sulfi

Question

If a man 20 kg move on plank of 60 kg find displacement of plank and man.

Answer 1

Explanations & Calculations

• To make sense this system should lie on a frictionless surface for the plank to move on.
• All the motions take place here are internal, hence the status of the center of mass (CM) is unchanged.
• Any movement occur in such a way that the initial position of the CM is kept fixed in place.
• Consider Earth's frame of reference for measuring distances.
• Get the distance $\times$ mass product,

$\qquad\qquad \begin{aligned} \small (20+60)\times d_{CM} &= \small 20\times 0+60\times \frac{L}{2}\\ \small d_{CM} & =\small \frac{3L}{8} \end{aligned}$

• If the man walks some x distance towards the other end & at the same time the planks moves some y distance in the backward direction then it follows the concept stated above. Therefore,

$\qquad\qquad \begin{aligned} \small 80\times \frac{3L}{8}&= \small 20\times x+60\times (\frac{l}{2}-y)\\ \small \bold{ y} &= \bold{\small \frac{x}{3}} \end{aligned}$

• By the input of relevant measurements, distances travelled by each could be found.

Example:

• If the man reaches the other end then the distance he travelled becomes $\small x = L-y$
• Then the plank travels,

$\qquad\qquad \begin{aligned} \small y &= \small \frac{L-y}{3}\\ \small y&= \small \bold{\frac{L}{4}} \end{aligned}$