Answer to Question #288697 in Mechanics | Relativity for Sarah

Question

A man with a mass of 80 kg sits in a bosun's chair of mass 10 kg. He pulls on the rope he is holding in order to accelerate himself up. He presses down on the seat with a force of 392 N. Find the acceleration of the man and the tension in the rope supporting the pulley

Answer 1

Given

In this problem:

M is the mass of the ma, 80 kg;

m is the mass of the chair, 10 kg;

N is the normal force, 392 N.

T is the tension, unknown;

a is the acceleration, unknown.

Solution

Apply Newton's second law:

$$T+N-Mg=Ma,\\ T-N-mg=ma,\\\space\\ a=\dfrac{2N-g(M-m)}{M-m}=1.4\text{ m/s}^2.\\\space\\ T=M(a+g)-N=392\text{ N}.$$