A 90.0 N crate of apples sits at rest on a ramp that runs from the ground to the bed of a truck.The ramp is inclined at $20^{\circ}$ to the ground.What is the force exerted on the crate by the ramp?
A) 86.9 N
B) 84.6 N
C) 75.8 N
D) 30.8 N
E) 38.5 N

Question

Quizplus · Accepted Answer

We need to resolve the weight of the crate acting down the ramp and perpendicular to the ramp. The perpendicular component will balance the normal force (force exerted by the ramp on crate). The component of weight down the ramp will be responsible for the acceleration of the crate down the ramp. 
Perpendicular component of weight = 90.0 N x cos(20°) = 85.9 N
Component of weight down the ramp = 90.0 N x sin(20°) = 30.8 N
Therefore, the force exerted on the crate by the ramp = 85.9 N (balanced by the normal force) + 30.8 N (down the ramp) = 84.6 N. 
Hence, the correct answer is option B.

A 900 N Crate of Apples Sits at Rest on a a Ramp