Question

A slippery plastic block is resting on a ramp that makes an angle of 20° with the horizontal. The coefficient of static friction between the block and the ramp is 0.2. The coefficient of kinetic friction is 0.15. Will the block start sliding on its own?

a) Yes
b) No

Answer 1

The block will not start sliding on its own because the force due to gravity down the slope is less than the maximum force of static friction.

Step-by-step explanation:

To determine if the plastic block will start sliding on its own, we should compare the force of gravity pulling the block down the slope to the maximum force of static friction holding it in place. The force of gravity down the slope is calculated by mg sin(θ), where m is the mass of the block, g is the acceleration due to gravity, and θ is the slope angle. The maximum static friction force is given by μ_s N, where μ_s is the coefficient of static friction and N is the normal force, which is mg cos(θ).

If the force of gravity down the slope exceeds the maximum static friction force, the block will start to slide. In mathematical terms, this is expressed as mg sin(θ) > μ_s mg cos(θ). Plugging in the values, we get:

μ_s = 0.2
θ = 20°
g = 9.8 m/s² (standard gravitational acceleration)

sin(20°) is approximately 0.342, and cos(20°) is approximately 0.940. This means that the force of gravity pulling the block down is 0.342mg, and the maximum static friction force is 0.2 × 0.940mg. Therefore, 0.342mg < 0.188mg, which shows that the gravitational force does not exceed the maximum force of static friction. As a result, the block will not start sliding on its own, so the answer is (b) No.