OCR · GCSE · Physics
Course version: J249 · Version from Sept 2018
Calculate the amounts of energy associated with a moving body, a stretched…
Full specification wording
Work done: calculate the amounts of energy associated with a moving body, a stretched spring and an object raised above ground level
Three stored-energy equations are needed here.
Checked against the OCR J249 specification (opens in a new tab) on .
- Point 5 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Three stored-energy equations are needed here. A moving body has kinetic energy E_k = ½ × m × v², with mass in kilograms and speed in metres per second, giving joules; note that doubling the speed quadruples the energy because speed is squared. A stretched spring has elastic potential energy E_e = ½ × k × x², where k is the spring constant in N/m and x the extension in metres. An object raised above ground level has gravitational potential energy E_p = m × g × h, with g taken as 9.8 N/kg and h the height in metres.
For example: A 2 kg mass moving at 3 m/s has E_k = ½ × 2 × 3² = 9 J; a spring with k = 200 N/m stretched 0.1 m has E_e = ½ × 200 × 0.1² = 1 J; and a 2 kg mass raised 5 m has E_p = 2 × 9.8 × 5 = 98 J. Square the speed or extension before multiplying by the other factors.
What earns the marks
- Applies E_k = ½ × m × v² with mass in kilograms and speed in metres per second to find the energy of a moving body.
- Squares the speed before multiplying by ½ and the mass when calculating kinetic energy.
- Applies E_e = ½ × k × x² with the spring constant in N/m and the extension in metres for a stretched spring.
- Applies E_p = m × g × h with g = 9.8 N/kg and height in metres for an object raised above ground level.
- Gives each calculated energy in joules and checks that the magnitude is reasonable.
Common mistakes and how to put them right
Multiplies mass by speed without squaring the speed.
Put it right: Square the speed first in E_k = ½ × m × v².
Uses the total length of the spring instead of its extension.
Put it right: Use only the change in length in E_e = ½ × k × x².
Omits the factor of ½ in the kinetic or elastic equation.
Put it right: Include ½ in both.
Uses height in centimetres in E_p = m × g × h.
Put it right: Convert the height to metres first.
Exam tips
- Write the equation, then square the speed or extension before doing any other multiplication.
- Convert centimetres to metres and grams to kilograms before substituting.
- Check the units of the spring constant; it must be in N/m for the answer to come out in joules.
Try the lesson
The start of the Work done: calculate the amounts of energy associated with a moving body, a stretched spring and an object raised above ground level lesson, made from checked teaching notes for this specification point.
Have a go first
A 0.5 kg ball is lifted 2 m above the ground. Taking g = 10 N/kg, how much gravitational potential energy does it gain?
Listen
Three stored-energy equations are needed here. A moving body has kinetic energy E_k = ½ × m × v², with mass in kilograms and speed in metres per second, giving joules; note that doubling the speed quadruples the energy because speed is squared. A stretched spring has elastic potential energy E_e = ½ × k × x², where k is the spring constant in N/m and x the extension in metres. An object raised above ground level has gravitational potential energy E_p = m × g × h, with g taken as 9.8 N/kg and h the height in metres. For example, a 2 kg mass moving at 3 m/s has E_k = ½ × 2 × 3² = 9 J; a spring with k = 200 N/m stretched 0.1 m has E_e = ½ × 200 × 0.1² = 1 J; and a 2 kg mass raised 5 m has E_p = 2 × 9.8 × 5 = 98 J. Square the speed or extension before multiplying by the other factors. A strong answer earns marks for these points. Applies E_k = ½ × m × v² with mass in kilograms and speed in metres per second to find the energy of a moving body. Squares the speed before multiplying by ½ and the mass when calculating kinetic energy. Applies E_e = ½ × k × x² with the spring constant in N/m and the extension in metres for a stretched spring. Applies E_p = m × g × h with g = 9.8 N/kg and height in metres for an object raised above ground level. Exam tip: Write the equation, then square the speed or extension before doing any other multiplication.
See it
Key words
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Kinetic energy
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Elastic potential energy
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Gravitational potential energy
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Spring constant
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See every definition
- Kinetic energy
- The energy associated with a moving body, given by E_k = ½ × m × v², with mass in kilograms and speed in metres per second, giving joules.
- Elastic potential energy
- The energy associated with a stretched spring, given by E_e = ½ × k × x², where k is the spring constant in N/m and x the extension in metres.
- Gravitational potential energy
- The energy associated with an object raised above ground level, given by E_p = m × g × h, with g taken as 9.8 N/kg and h the height in metres.
- Spring constant
- The quantity k in the elastic potential energy equation, measured in N/m.
Label the diagram
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