Question

A man sits on a chair supported by a rope passing over a frictionless fixed pulley. The man who weighs $1000N$ exerts a force of $450N$ on the chair downwards while pulling other end of the rope. If the chair weighs $250N$ and $g$ is $10m/s^2$, the acceleration of the chair is

• A. $0.45m/s^2$
• B. $0m/s^2$
• C. $2m/s^2$
• D. $\frac{9}{25}m/s^2$

Answer 1

Answer: (C)

$2m/s^2$

The chair and man are accelerating upwards with acceleration $a$.

Man has mass $=100kg$

For the free body diagram of the man,
Normal is 450N (up), weight is 1000N (down), and tension is T (up).

$\therefore T+450-1000=100a$
Free body diagram of chair,
weight is 250N (down), Normal of man is 450N (down) Tension is T (up), it accelerates with a, and has mass 25kg.
$T-250-450=25a$
Subtracting the 2 equations, we get:
$75a=150$
$\therefore a=2m/s^2$