Kinetic and potential energy Cambridge International AS & A Level Physics revision
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In plain words
A ball at the top of a hill has energy because of where it is; a ball rolling along has energy because it is moving. As it rolls down, one turns into the other. Following that swap is often the fastest way to find a speed or a height, with no need for forces or times at all.
Three things to know
- Kinetic energy E = ½mv². Doubling the speed gives four times the kinetic energy.
- Change in gravitational potential energy ΔE = mgΔh, in a uniform field such as near the Earth's surface.
- With no friction or air resistance, the potential energy lost equals the kinetic energy gained: mgΔh = ½mv². With resistive forces, the difference is the work done against them.
Worked example
A 60 kg skier starts from rest and drops through a vertical height of 50 m, reaching a speed of 25 m/s. Find the work done against friction and air resistance.
- Potential energy lost = mgΔh = 60 × 9.81 × 50 = 29 400 J.
- Kinetic energy gained = ½ × 60 × 25² = 18 750 J.
- Work done against resistive forces = 29 400 − 18 750 ≈ 1.1 × 10⁴ J.
Tips and tricks
- For a drop with no resistive forces the mass cancels: v = √(2gh).
- Δh is the change in vertical height, not the distance along the slope.
It lands in your notebook with its questions as flashcards.
Kinetic and potential energy: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the kinetic energy of a 2.0 kg mass moving at 3.0 m/s?
½ × 2.0 × 3.0².
The speed of a car doubles. What happens to its kinetic energy?
Kinetic energy depends on the speed squared.
How much gravitational potential energy does a 5.0 kg mass gain when it is raised 2.0 m?
5.0 × 9.81 × 2.0.
A ball falls from rest with no air resistance. Which is true as it falls?
Energy is conserved, and none is transferred to the air.
A pendulum bob is released from 0.20 m above its lowest point. What is its speed at the lowest point?
√(2 × 9.81 × 0.20).
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 10 marks. Write your answers on paper, then check them.
Kinetic and potential energy
Cambridge International AS & A Level Physics 9702 · 10 marks · papermunch.org
Name ______________________________ Date ______________
A ball is dropped from a height of 5.0 m. Ignoring air resistance, find its speed just before it hits the ground.[2]
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9.9 m/s. √(2 × 9.81 × 5.0).
Find the kinetic energy of a 1200 kg car moving at 20 m/s.[2]
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2.4 × 10⁵ J.
A 0.50 kg ball is thrown vertically upwards at 12 m/s. Ignoring air resistance, find the maximum height it reaches.[3]
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7.3 m. 12² ÷ (2 × 9.81). The mass isn't needed.
Use work done = force × distance and the equations of motion to show that a mass m moving at speed v has kinetic energy ½mv².[3]
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Let a constant force F accelerate the mass from rest over a distance s. Then v² = 2as, so s = v² ÷ 2a. Work done = Fs = ma × v² ÷ 2a = ½mv², and that work becomes the kinetic energy of the mass.
Answers: Kinetic and potential energy
- 1. 9.9 m/s. √(2 × 9.81 × 5.0).
- 2. 2.4 × 10⁵ J.
- 3. 7.3 m. 12² ÷ (2 × 9.81). The mass isn't needed.
- 4. Let a constant force F accelerate the mass from rest over a distance s. Then v² = 2as, so s = v² ÷ 2a. Work done = Fs = ma × v² ÷ 2a = ½mv², and that work becomes the kinetic energy of the mass.