A \(10 \mathrm{~kg}\) crate is placed on a horizontal conveyor belt. The materials are such that \(\mu_{\mathrm{s}}=0.50\) and \(\mu_{\mathrm{k}}=0.30\).

a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed.

b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.

c. What is the maximum acceleration the belt can have without the crate slipping?

d. If the acceleration of the belt exceeds the value determined in part \(\mathrm{c}\), what is the acceleration of the crate?