Gravitational Potential Energy
Gravitational potential energy (GPE) is the energy an object acquires when it changes height. GPE is a form of stored energy, the ‘potential’ will be converted to kinetic energy if the object reduced its height as it is pulled by gravity. The gravity will then be doing work to the object as it falls or is lowered.
The symbol ‘Δ’ (Delta), is used in equations before a quantity to mean ‘a change in’.
So __Δ__h would be pronounced ‘Delta h’ and means a change in height.
__Calculating Gravitational Potential Energy __
Change in GPE = mass x gravity x change in height. Measured in Joules.
Δ_GPE_ = mg_Δ_h (where g = 9.8 N/kg on Earth).
A person with a mass of 50 kg climbs a set of steps to the next floor 4 m above the ground. What was there change in GPE?
Δ_GPE_ = mg_Δ_h = 50 kg x 9.8 N/kg x 4m = 1960 J
If a car of mass 2000 kg gains 300 KJ of GPE as it climbs a hill, what has been the change in height?
Δ_GPE_ = mg_Δ_h so Δ_h = Δ_GPE _÷ (_mg)
Δ_h_ = 300,000 ÷ (2000 x 9.8) = 15.31 m
A cat of 9 kg falls of a fence to the ground 2 m below, landing safely on all fours. What has been the change in GPE of the cat?
Δ_GPE_ = mg_Δ_h = _9 x 9.8 x -2 = -176.4 _J The GPE is negative to indicate that energy has been lost.
Kinetic Energy (KE) is the energy an object has due to its movement. The more massive the object and the faster it is travelling, the more kinetic energy the object has. Kinetic energy of particles is measured by temperature.
Calculating Kinetic Energy
Kinetic Energy = ½ x mass x velocity2
What is the kinetic energy of a girl of mass 55 kg running at 2.2 m/s ?
KE = ½mv2 = ½ x 55 x (2.2)2 = 133.1 J
What is the velocity of a 100 kg mass with 9800 J of kinetic energy?
A roller coaster car of mass 3000 kg is pulled to a height of 30m, then runs down the first drop in the track to 5 m above the ground. How fast was the car going at the bottom of the first drop? (ignore friction and air resistance).
Due to the Law of Conservation of Energy the loss in GPE will equal the gain in Kinetic energy.
So Δ_GPE_ =Δ_KE_ mg_Δ_h = ½mv2
the mass on each side cancel out (mass does not affect how quickly objects fall).
- A 3 kg ball is placed on the top shelf at a height of 2.3.m from the ground. What type of energy does the ball have sitting on the shelf, calculate how much energy it has gained.
- Your answer should include: gravitational potential energy / 67.62J / 67.62
Explanation: The ball has gravitational potential energy due to its gain in height. ΔGPE = mgΔh = 3 x 9.8 x 2.3 = 67.62 J
- A javelin has 75 J of kinetic energy and is travelling at 10 m/s, what is its mass?
- Your answer should include: 1.5kg / 1.5
Explanation: KE = ½mv² so 2 KE =mv² so m =2KE ÷ v²= (2 x 75) ÷ (10)² = 1.5 kg