A man of mass 60 kg is standing on a massless plank and holding a string passing over a system of ideal pulleys. A mass of 20 kg hanging over a light pulley such that the system is in equilibrium. The force exerted by the plank on the man is (g=acceleration due to gravity).

Calculation of Tension and Reaction Forces

This example demonstrates the relationship between tension (T), reaction (R), and gravitational force (g) in a simple pulley system supporting a 20 kg mass and a man.

Step 1: Establish the Equation for the Man

For the man, the net force equation is:
2T + R = 60g ...(1)

Step 2: Calculate Tension for the 20 kg Mass

For the 20 kg mass, tension is equal to its weight:
T = 20g ...(2)

Step 3: Find the Reaction Force (R)

Substituting equation (2) into equation (1):
R = 60g - 2 × 20g = 20g

Hence, the reaction force (R) equals 20g.

In this example of a pulley system, the man and a 20 kg mass are analyzed using Newton’s laws. The calculated tension is 20g and the reaction force is also 20g, confirming equilibrium.