1. A particle of mass m = 5.00 kg is released from point A and slides on the frictionless track shown in Figure P8.24. Determine (a) the particle's speed at points B and C and (b) the net work done by the gravitational force in moving the particle from A to C.

Figure P8.242. A bead slides without friction around a loop-the-loop (Fig. P8.5). The bead is released from a height h = 3.50R. (a) What is its speed at point A? (b) How large is the normal force on it if its mass is 5.00 g?

Figure P8.53. A simple, 2.00-m-long pendulum is released from rest when the support string is at an angle of 25.0° from the vertical. What is the speed of the suspended mass at the bottom of the swing?

4. A 120-g mass is attached to the bottom end of an unstressed spring. The spring is hanging vertically and has a spring constant of 40.0 N/m. The mass is dropped. (a) What is its maximum speed? (b) How far does it drop before coming to rest momentarily?

5. The coefficient of friction between the 3.00-kg block and the surface in Figure P8.31 is 0.400. The system starts from rest. What is the speed of the 5.00-kg ball when it has fallen 1.50 m?

6. A parachutist of mass 50.0 kg jumps out of a balloon at a height of 1 000 m and lands on the ground with a speed of 5.00 m/s. How much energy was lost to air friction during this jump?

7. A child slides without friction from a height h along a curved water slide (Fig. P8.66). She is launched from a height h/5 into the pool. Determine her maximum airborne height y in terms of h and θ.