83. **A crate with a mass of 45 kg is suspended from a massless rope that runs vertically upward over a light pulley. The other end of the rope is connected to a 35 kg crate, which lies on a tabletop. The coefficients of the kinetic friction and the static friction between the crate and the surface are 0.3 and 0.5 respectively. An applied force, F, pulls the 35 kg crate to the right.
a. In the first case, the applied force is just sufficient to keep the crates from sliding. Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale.
b. How much force would need to be applied in this first case?
c. In the second case, the 35 kg crate is sliding to the right with a constant velocity. Draw clearly labeled free-body diagrams for each crate including all forces drawn to scale.
d. How much force would need to be applied in this second case?
e. In the third case, the 35 kg crate moves to the right at a constant acceleration of 0.5 m/s2. Draw clearly labeled free-body diagrams for each crates including all forces drawn to scale. In this instance, draw the direction of acceleration next to each diagram.
f. How much force would need to be applied in the third case?