Chapter 8 : Principles of Friction 133
Example 8.5. A body of weight 500 N is lying on a rough plane inclined at an angle of
25 ° with the horizontal. It is supported by an effort (P) parallel to the plane as shown in Fig. 8.9.
Fig. 8.9.
Determine the minimum and maximum values of P, for which the equilibrium can exist, if
the angle of friction is 20 °.
Solution. Given: Weight of the body (W) = 500 N ; Angle at which plane is inclined (α)
= 25° and angle of friction (φ) = 20°.
Minimum value of P
We know that for the minimum value of P, the body is at the point of sliding downwards.
We also know that when the body is at the point of sliding downwards, then the force
1sin ( – ) sin (25 – 20 )
500 N
cos cos 20PW
αφ ° °
=× = ×
φ°
sin 5 0.0872
500 500 46.4 N
cos 20 0.9397°
=× =× =
°Ans.Maximum value of P
We know that for the maximum value of P, the body is at the point of sliding upwards. We
also know that when the body is at the point of sliding upwards, then the force
2sin ( ) sin (25 20 )
500 N
cos cos 20PW
α+φ °+ °
=× = ×
φ°sin 45 0.7071
500 500 376.2 N
cos 20 0.9397°
=× =× =
°Ans.Example 8.6. An inclined plane as shown in Fig. 8.10. is used to unload slowly a body
weighing 400 N from a truck 1.2 m high into the ground.
Fig. 8.10.
The coefficient of friction between the underside of the body and the plank is 0.3. State
whether it is necessary to push the body down the plane or hold it back from sliding down. What
minimum force is required parallel to the plane for this purpose?