A 450 kg block is pressed against a vertical wall by a force

A 4.50 kg block is pressed against a vertical wall by a force (F), as shown in the figure below. The coefficient of static friction between the block and the wall is 0.30 and the directional angle for the force is 32.0°. Determine the magnitude of the force (F) when the block is about to slide down the wall.

Solution

here,

mass , m =4.5 kg

us = 0.3

theta = 32 degree

the normal reaction force , N = F * sin(theta)

for the block to just slide down the ramp

m* g = us * N + F * cos(theta)

4.5 * 9.81 = 0.3 * F * sin(32) + F * cos(32)

solving for F

F = 43.8 N

the magnitude of the force when the block is about to slide down the wall is 43.8 N