A 55 kg child is swinging on a swing with length 4.0 m. When the child stops at the top of its motion, the swing makes an angle of 60.° from vertical. Calculate the speed of the child at the bottom of the swing. Assume no thermal energy is created.

When jogging at 13 km/h on a level surface, a 70-kg man uses energy at a rate of approximately 850 W. Using the facts that the “human engine” is approximately 25 efficient, determine the rate at which this man uses energy when jogging up a 5.0 slope at this same speed. Assume that the frictional retarding force is the same in both cases.

The Flybar high-tech pogo stick is advertised as being capable of launching jumpers up to 6 ft. The ad says that the minimum weight of a jumper is 120 lb and the maximum weight is 250 lb. It also says that the pogo stick uses a patented system of elastometric rubber springs that provides up to 1200 lbs of thrust, something common helical spring sticks simply cannot achieve (rubber has 10 times the energy storing capability of steel). a. Use Figure P8.32 to estimate the maximum compression of the pogo sticks spring. Include the uncertainty in your estimate. b. What is the effective spring constant of the elastometric rubber springs? Comment on the claim that rubber has 10 times the energy-storing capability of steel. c. Check the ads claim that the maximum height a jumper can achieve is 6 ft.

A roller-coaster car of mass 1.50 103 kg is initially at the top of a rise at point . It then moves 35.0 m at an angle of 50.0 below the horizontal to a lower point . (a) Find both the potential energy of the system when the car is at points and and the change in potential energy as the car moves from point to point , assuming y = 0 at point . (b) Repeat part (a), this time choosing y = 0 at point , which is another 15.0 m down the same slope from point .