Townsend-PAP Physics
Gravitational Potential Energy
· Gravitational Potential energy (PE) is the energy an object has by virtue of its position
(Its height above the ground).
· The potential energy gained when an object is lifted up is equal to the work done against gravity.
Ex. 1: How much work do you do when you lift a 10kg boulder 2m?
Ex. 2: How much potential energy does the 10 kg boulder have 2m above the ground?
Notice that the work done to lift the boulder is equal to the potential energy it gained.
Ex. 3: A 20 N box sits on a platform that is 0.5 m high. How much potential energy does the box have?
Ex.4: A 10 kg monkey is hanging from a tree and has 294 J of energy.
a) How high up in the air is the monkey?
b) The monkey climbs down the tree. Calculate his potential energy:
- 2.0 m from the ground
- 1.5 m from the ground
- 1.0 m from the ground
- on the ground
Law of Conservation of Energy (LOCOE)
· The law of conservation of energy says that in the absence of outside forces, the total amount of energy for a system remains the same.
o Energy can change forms, but the total amount of all of the different types of energy added together remains the same!
EOC Formula Sheet: Law of Conservation of Energy = PEi + KEi = PEf + KEf
Recall what happened when we dropped objects of different masses:
When an object is above the ground it has ______energy.
As it falls, its ______energy is converted to ______energy.
So by the time it reaches the ground the ______energy is zero and the ______energy at the bottom equals the ______energy at the top.
Ex. 5: A car is sitting on top of a 30 m tall hill. How fast is the car going when it reaches the bottom of the hill?
Ex. 6: A 8.0 x104 kg airplane is cruising at 165 m/s at an altitude of 3,000 m. What is the plane’s total energy?
Ex. 7: If the engine were to fail and the plane fell to the ground, how fast would it be going right before it crashed?
Ex. 8: The Pendulum
Where will the pendulum have maximum potential energy?
Where will the pendulum have the minimum potential energy?
Where will the pendulum have maximum kinetic energy?
Where will the pendulum have the minimum kinetic energy?
Where will the pendulum have its maximum speed?
Where will the pendulum’s speed equal zero?
Ex. 9: A pendulum is released from a height of 1.2 m. How fast will the pendulum be traveling at the bottom of its swing?
Ex. 10: A pendulum is released and is going 2 m/s at the bottom of its swing. How high was it released from?
Practice Problems
1. A ball is dropped from a height of 5 m. How fast is the ball traveling right before it strikes the ground?
2. A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9m/s. What is the initial height of the bob?
3. The frictionless rollercoaster
4. A frictionless ramp
10 m vf = ?
A) The block starts from rest and slides to the bottom of the ramp. What is its final speed?
B) If the ramp had friction how would your answer change?
5. A 1 kg ball rolls off the edge of a 4 m platform with a speed of 5 m/s.
a. How much potential energy does the ball have while on the platform?
b. How much kinetic energy does it have as it rolls off the edge?
c. How much kinetic energy will it have right before it strikes the ground?