This question had appeared in the Osmania University exams in the year 1973.
Problem: A force of 40 kg pulls a body of weight 60 kg up an inclined plane; the force being applied parallel to the plane. The inclination of the plane, to the horizontal, is 30 degree. Calculate the coefficient of friction.
Given = Weight, W = 60 kg
Force = P = 40 kg,
Inclination, theta = 30 degrees.
Let R = Normal reaction,
mu = Coefficient of friction.
Resolving the forces along the inclined plane, we get
F = 40 – 60 sin 30 degree
R = 60 cos 30 degree = 51.26 kg,
Using the relation F = mu * R, we get,
Mu = F / R = 10 / 51.96 = 0.193, is the answer.
Note – While solving problems related to friction and coefficient of friction we follow the standard procedure where the forces are resolved along a surface or plane which may be perpendicular or at right angles to the surface and subsequently by using the formula, F = mu * R,
Where, F = Force of friction, mu = Coefficient of friction and R = Normal reaction between the involved planes or surfaces which are in contact with each other.