The Law of Conservation of Energy Worksheet
1. Mr. James (60 kg) is swinging on a park swing. As he swings
back and forth, he reaches a peak height of 2.0 m above the
lowest point of his swing. Assuming friction and air resistance
do negligible work against him, calculate his speed when he is
at the lowest point.
2. The roller coaster shown on the right has a mass of 1500 kg. It
starts at the top of a 50 m hill at rest and then rolls down to the
bottom where it reaches its maximum speed. Then it goes up
and around a loop that is 30 m high. Assume that friction is
negligible. Use the law of conservation of energy to answer the
following:
a) How much potential energy does the roller coaster start out with?
b) How fast will the roller coaster be going when it reaches the bottom?
c) How fast will the coaster be going when it reaches the top of the loop?
3. Josh is driving his 1200 kg car at a constant 20 m/s. He comes to the top of a hill that is 15.0 m tall.
Then he coasts (move easily without using power) his car down the hill.
(a) How fast is he at the bottom?
(b) How far up the next hill (50.0 m high) could his car go if he continues to coast?
4. You throw a ball directly upward, giving it an initial velocity of 15.0 m/s. Neglect air resistance.
What would be the maximum height of the ball?
5. A 4.0 x 104 kg roller coaster starts from rest at point A.
Neglect friction.
(a) Calculate its total mechanical energy at point A.
(b) Calculate its gravitational potential energy at point B.
(c) What is its total mechanical energy at point C ?
(d) Calculate its speed at point C.
6. An alien with a mass of 180 kg jumps down from its flying craft with an initial velocity of 2.4 m/s.
When it reaches the ground, its velocity is 42 m/s. How much distance does it travel if the
gravitational field strength is 8.7 N/kg?