Kinetic and gravitational potential energyIB MYP Sciences: Revision notes
Section 1
Kinetic energy
Kinetic energy (KE) is the energy of anything that is moving. It depends on the mass and the speed:
KE = ½ × m × v²
KE is in joules (J), mass m in kilograms (kg) and speed v in metres per second (m/s).
Worked example: a 1200 kg car travels at 20 m/s. KE = ½ × 1200 × 20² = ½ × 1200 × 400 = 240 000 J.
Because speed is squared, doubling the speed makes the kinetic energy four times bigger.
Square only the speed, not the whole of ½mv. Work out v² first.
Section 2
Gravitational potential energy
Gravitational potential energy (GPE) is the energy stored in an object because of its height above the ground:
GPE = m × g × h
m is the mass in kg, g is the gravitational field strength (10 N/kg on Earth for these questions) and h is the height lifted in metres.
Worked example: a 60 kg climber is lifted 5.0 m. GPE = 60 × 10 × 5.0 = 3000 J.
Only the change in height matters, so measure h from the lowest point you choose.
Section 3
Energy conversions
Many motions involve a store changing between GPE and KE:
- Falling object: GPE decreases, KE increases
- Rolling down a slope: GPE decreases, KE increases. Going up, KE decreases and GPE increases
- Pendulum: at the top of the swing GPE is highest and KE is zero. At the lowest point KE is highest and GPE is lowest
- Roller coaster: a chain lifts the car (GPE increases), then it runs down (KE increases)
In real life friction and air resistance transfer some energy to the thermal store of the surroundings, so the car or bob never quite returns to its starting height.
Section 4
Using conservation of energy
If we ignore friction, energy is conserved, so the GPE lost equals the KE gained:
m × g × h = ½ × m × v²
The mass appears on both sides and cancels, so v² = 2 × g × h.
Worked example: a ball is dropped from 5.0 m. v² = 2 × 10 × 5.0 = 100, so v = 10 m/s.
To find a height instead, rearrange: h = v² / (2 × g). For example, a ball thrown up at 10 m/s reaches h = 100 / 20 = 5.0 m.
State the idea first: 'GPE lost = KE gained'. Then substitute the numbers. The method marks are for this step.
Must know
- KE = ½ × m × v² and GPE = m × g × h, both in joules
- Doubling speed makes KE four times bigger
- Falling or rolling down: GPE decreases and KE increases
- A pendulum swaps GPE and KE as it swings
- Ignoring friction, GPE lost = KE gained, so v² = 2gh
- In practice some energy is wasted as thermal energy
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Kinetic and gravitational potential energy
- A roller coaster car at a theme park in Orlando is pulled slowly to the top of the first hill by a chain. It is then released and runs down the track.Describe the energy changes as the car runs down the hill, and explain why in practice it cannot climb a second hill as high as the first.2 marks
- A pendulum clock in a museum in Prague has a brass bob of mass 0.50 kg that swings back and forth. Use a gravitational field strength of 10 N/kg.The bob is released from a height of 0.40 m above its lowest point. Use conservation of energy to calculate its speed at the lowest point, ignoring air resistance.2 marks
- Students in Mexico City investigate how the release height of a 0.20 kg toy car on a ramp affects its speed at the bottom. A light gate measures the speed. The mean speeds were 1.3 m/s from a height of 0.10 m, 1.8 m/s from 0.20 m, 2.2 m/s from 0.30 m and 2.5 m/s from 0.40 m.Outline two ways the students should make their data reliable and one safety precaution they should take.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).