A 5-kg block is sent sliding up an inclined plane with initial speed 2 m s (at the bottom of the incline). The coefficient of kinetic friction between the block and the plane is 0.3. The angle of the incline is θ = 36.87? , which means you have a 3-4-5 right triangle (sin θ = 3 5 , cos θ = 4 5 ).

(a) Draw a free-body diagram for the block as it slides up along the incline. Try to get all the forces approximately to scale. (The following questions may be helpful.)

(b) What is the magnitude of the normal force?

(c) What is the magnitude of the force of kinetic friction?

(d) What is the acceleration (magnitude and direction)?

(e) How far along the incline does the block travel before coming to a stop?

(f) Considering the block alone as the system, at the time it stops, how much of its initial kinetic energy was dissipated by friction, and how much was lost because of the work done on it by gravity?

(g) How large would the coefficient of static friction have to be (at a minimum) to prevent the block from sliding back down after it comes to a stop?