For each situation listed in the center column below, identify the forms of mechanical energy that exist at the start of the problem and the forms of mechanical energy that exist at the end of the problem. Then, confirm the law of conservation of energy for each by solving for the total mechanical energy at both the start and end of the problem to show that they are equal.
(1) Situation A roller coaster cart with a total mass of 1000kg is at the top of a hill moving at 2 m/s. The cart reaches the bottom of the hill 30m below at a speed of 24.6 m/s. Assume no friction and neglect air resistance.
(2) You pull back a slingshot with a spring constant of 75 N/m at a distance of 0.15 m. You place a rock with a mass of 0.685 kg in the slingshot. You hold the slingshot 1.4 meters above the ground and release the rock. The rock is moving at 5.47 m/s when it reaches the ground.
(3) A mass, m, is attached to a pendulum that swings without friction. The pendulum is released from a height of 3.5 meters. The mass is moving at 8.28 m/s when it reaches the bottom of the swing.
(4) A 1 kg ball held 10 m above a spring of spring constant 130 N/m is dropped. The ball lands on the spring and compresses it 1.23 meters before coming to rest.
(5) A car at the top of a 26 meter hill is moving at 10 m/s. Halfway down the hill, it is now moving at 18.84 m/s.
