What is the maximum acceleration the belt can have without the crate slipping? express your answer using two significant figures?

To prevent the crate from slipping, the maximum force that the belt can exert on the crate must be equal to the static friction force.

Ff = 0.5 * 16 * 9.8 = 78.4 N

a = 4.9 m/s^2

If acceleration of the belt exceeds the value determined in the previous question, what is the acceleration of the crate?

In this situation, the kinetic friction force is causing the crate to decelerate. So the net force on the crate is 78.4 N minus the kinetic friction force.

Ff = 0.28 * 16 * 9.8 = 43.904 N

Net force = 78.4 – 43.904 = 34.496 N

To determine the acceleration, divide by the mass of the crate.

a = 34.496 ÷ 16 = 2.156 m/s^2

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).