Question 7.7: An increasing force P N is applied to a block, as shown in f...
An increasing force P N is applied to a block, as shown in figure 7.39, until the block moves. The coefficient of friction between the block and the plane is 0.4. Does it slide or topple?
The forces acting are shown in figure 7.40. The normal reaction may be thought of as a single force acting somewhere within the area of contact. When toppling occurs (or is about to occur) the line of action is through the edge about which it topples.
Until the block moves, it is in equilibrium.
Horizontally P = F ①
Vertically R = 2g ②
If sliding is about to occur F = μR
From ① P = μR = 0.4 × 2g
= 7.84
If the block is about to topple, then A is the pivot point and the reaction of the plane on the block acts at A. Taking moments about A gives
\begin{matrix}(\curvearrowleft ) 2g × 0.25 – P × 0.2 = 0 & \boxed{\text{ R acts through A}}\end{matrix}P = 24.5
So to slide P needs to exceed 7.84 N but to topple it needs to exceed 24.5N: the block will slide before it topples.
