The truck shown in Figure P-1 moves from rest with constant acceleration ~a up an incline of angle θ. Find the greatest speed v that the truck can acquire in a distance d, if the crate C is not to slip on the truck bed. The coefficient of static friction is µ. Figure P-1 Problem 2 In Figure P-2 a horizontal force ~Fa of magnitude 20N is applied on the block as it slides a distance of d = 0.5m up a frictionless ramp. Then,

(a) During the displacement, find the net work done by ~Fa, the gravitational force and the normal force ~N on the block.

(b) If the block has zero kinetic energy at the start, find the speed at the end of the displacement. Figure P-2 Problem 3 Masses m2 and m3 are initially at rest and the spring of length l0 is unstressed. Then mass m1, traveling with velocity v0 in a direction perpendicular to the spring, hits m2 inelastically and sticks to it. In the ensuing motion the spring stretches to a maximum length 3l0 Solve for v0, assuming that the masses are equal and can be considered as particle.