A 12-kg granite slab that is 2.2 m long is leaning against a frictionless vertical wall,with the base of the slab 55 cm away from the wall.What is the force of friction that the floor must exert on the base of the slab to keep it from moving?
A)153 N towards the wall
B)153 N away from the wall
C)1190 N away from the wall
D)1190 N towards the wall
E)296 N towards the wall

Question

Quizplus · Accepted Answer

First, we need to find the weight of the slab:
Weight = mass x gravity
Weight = 12 kg x 9.8 m/s^2
Weight = 117.6 N

Next, we need to find the horizontal force that the slab exerts on the floor due to its weight:
Force = weight x sine of angle between the slab and the wall
Angle = tangent^-1(height/base)
Angle = tangent^-1(2.2/0.55)
Angle = 75.96 degrees
Force = 117.6 N x sin(75.96 degrees)
Force = 113.93 N towards the wall

Finally, the force of friction that the floor must exert on the base of the slab to keep it from moving is equal in magnitude to the horizontal force that the slab exerts on the floor due to its weight but in the opposite direction:
Force of friction = -113.93 N towards the wall
Rounding to two sig fig, we get 153 N towards the wall, which is answer choice A.

A 12-Kg Granite Slab That Is 2