Determine weight of body and coefficient of the friction:
Force of 200N is needed just to move a certain body up an inclined plane of angle 15°, the force is parallel to the plane. If the angle of indication is 20º the effort again required parallel to the plane is found 250N. Determine weight of body and coefficient of the friction.
Sol.:
Case-1
Consider When slope of the plane is 15º Sum of forces parallel to the plane = 0
P - µR - Wsin15° = 0 ...(i)
Sum of forces perpendicular to the plane = 0
R = Wcos15° ...(ii)
By putting the value of equation (ii) in (i), We get
P = µWcos15° + Wsin15° = 0
200 = 0.96µW + 0.25W ...(iii)
Case-2
Consider When slope of plane be 20º
The Sum of forces parallel to the plane = 0
P - µR - Wsin20° = 0 ...(iv)
The Sum of forces perpendicular to plane = 0
R = Wcos20° ...(v)
By putting the value of equation(v) in (iv), We get
P = µWcos20° + Wsin20° = 0
250 = 0.939µW + 0.34W ...(vi)
Solved equation (iii) and (vi) we get
W = 623.6N and µ = 0.06 .......ANS