Kinetic and gravitational potential energyIB MYP Physics: Revision notes
Section 1
Energy and its two mechanical stores
Energy is measured in joules (J). Two stores matter in this topic. Kinetic energy is the energy an object has because it is moving. Gravitational potential energy is the energy stored in an object because of its height above the ground in a gravitational field.
Energy is never created or destroyed, it is only transferred from one store to another.
Section 2
Kinetic energy
The kinetic energy of an object depends on its mass and its speed:
Ek = ½ × m × v²
where Ek is in joules (J), m is in kilograms (kg) and v is in metres per second (m/s).
Worked example: a 1500 kg car travels at 20 m/s. Ek = ½ × 1500 × 20² = ½ × 1500 × 400 = 300 000 J.
Because speed is squared, doubling the speed makes the kinetic energy four times bigger.
Do not forget to square the speed and do not leave out the ½. Square v first, then multiply by m, then halve.
Section 3
Gravitational potential energy
When an object is lifted, work is done against gravity and its gravitational potential energy increases:
ΔEp = m × g × h
where ΔEp is the change in gravitational potential energy (J), m is the mass (kg), g is the gravitational field strength (N/kg) and h is the change in height (m). On Earth g is about 10 N/kg (more exactly 9.8 N/kg).
Worked example: a 60 kg climber goes up 50 m. ΔEp = 60 × 10 × 50 = 30 000 J.
Always convert to kilograms and metres before using the equations. A mass of 500 g is 0.50 kg.
Section 4
Energy conversions when friction is ignored
If there is no friction or air resistance, the total of kinetic and gravitational potential energy stays constant; energy just changes between the two stores.
- Ball thrown upwards: Ek is transferred to Ep as it rises. At the top Ek is zero and Ep is greatest. Falling reverses this.
- Pendulum: at the highest point of the swing Ep is greatest and Ek is zero; at the lowest point Ek is greatest and Ep is smallest.
- Roller-coaster: Ep at the top of a hill is transferred to Ek going down, and back to Ep going up the next hill.
In real life, friction and air resistance transfer some energy to thermal energy in the surroundings, so the object does not quite reach the predicted speed or height.
Section 5
Solving for speed or height
With no friction, gravitational potential energy lost = kinetic energy gained:
m × g × h = ½ × m × v²
The mass appears on both sides and cancels, so v = √(2 × g × h) and h = v² ÷ (2 × g).
Speed example: a child slides down a 20 m high water slide from rest. v = √(2 × 10 × 20) = √400 = 20 m/s.
Height example: a ball leaves the ground at 15 m/s. h = 15² ÷ (2 × 10) = 225 ÷ 20 = 11 m (to 2 s.f.).
Write the energy equation first, then substitute. If you want a speed, remember to take the square root as your last step.
Must know
- Ek = ½mv² (J, kg, m/s) and ΔEp = mgh (J, kg, N/kg, m)
- Doubling speed makes Ek four times bigger
- Without friction, Ep lost = Ek gained, and mass cancels
- Falling and roller-coasters: Ep to Ek; rising: Ek to Ep
- With friction, some energy becomes thermal energy and the final speed is lower
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Kinetic and gravitational potential energy
- A student in Nairobi throws a 0.50 kg ball straight up into the air from ground level with an initial speed of 12 m/s. Take g = 10 N/kg.Describe the energy transfers that happen as the ball rises to its highest point and then falls back to the ground.2 marks
- A roller-coaster car and its passengers have a total mass of 400 kg. The car is released from rest at the top of a hill that is 25 m above the lowest point of the track at a theme park in Dubai. Take g = 10 N/kg.In reality the car reaches the lowest point moving more slowly than the speed predicted when friction is ignored. Explain why.2 marks
- A class investigates how the height from which a steel ball is dropped affects its speed just before it hits the ground. The ball has a mass of 0.050 kg and light gates measure its speed just before impact. The measured speeds were 1.9 m/s from a height of 0.20 m, 2.8 m/s from 0.40 m, 3.4 m/s from 0.60 m, 3.9 m/s from 0.80 m and 4.4 m/s from 1.00 m. Take g = 10 N/kg.Identify the independent variable, the dependent variable and one control variable in this investigation.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).