The problem had appeared in the Allahabad Untiversity examination, in the year 1972
Problem: A body resting on a rough horizontal plane, required a pull of 18 kg inclined at 30 degrees to the plane just to remove it. It was found that a push of 22 kg inclined at 30 degrees to the plane just removed the body. Determine and find the weight of the body and the coefficient of friction.
Given - Angle of pull theta = 30 degree
Let W = weights of the body in kg.
mu = coefficient of friction,
F = Force of friction.
Case #1: Given pull, P =18 kg,
Resolving the forces horzontally,
F = 18 cos 30 degree = 10 * 0.5 = 15.6 kg.
Now resolving the forcesvertically,
R = W - 18 sin 30 degree = W - 18 * 0.5 = W - 9 kg
Using the relation,
F = mu * R, with normal notations.
Therefore 15.6 = mu(W - 9)
Case #2: Given Push, P = 22 kg
Resolving the forces horizontally,
F= 22 cos 30 degree = 22 * 0.866 kg = 19.04 kg,
Now resolving the forces vertically,
R = W + 22 sin 30 degree = W + 22 * 0.5 = W + 11 kg,
Again using the standard notations,
F = mu * R,
19.04 = mu(W + 11)'
Solving equations in the first case and the second case, we get,
W = 99 kg and mu = 0.1732.