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GCSE Physics notes: (b) Elastic potential energy stores and calculations

TYPES OF ENERGY STORE - examples explained

(b) Elastic potential energy stores and calculations

Doc Brown's GCSE 9-1 Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

How solve numerical problems involving elastic potential energy?

How to explain examples of elastic potential energy

How to use the formula and do calculations involving elastic potential energy

Elastic potential energy and elastic potential energy stores

• This is energy stored when some material is stretched or compressed and the energy released when the constriction is released - usually as kinetic energy.

• eg the wound up compressed spring of a clockwork clock - provides the energy store to drive the mechanical motor,

• a pulled elastic rubber band - a stretched catapult stores elastic potential energy, on release the projectile is fired forward as its kinetic energy store is increased,

• stretched coiled metal spring,

• the compressed spring in a an animal trap - the springs on a car suspension absorb the impact energy of the wheels on the road to give a smoother ride,

• stretched bow before the arrow is released - the 'twang' increases the kinetic energy store of the arrow..

• Since elastic potential energy is a form of stored energy, it does nothing until it is released and converted into another form of energy - often converting to kinetic energy.

• When the forces causing the stretching is removed, the spring or elastic returns to its original length (shape)

• The more an elastic material is stretched, the greater the elastic potential energy store.

• The amount of elastic potential energy stored in a stretched spring can be calculated using the equation:

• elastic potential energy = 0.5 × spring constant × (extension)2,    Ee = 1/2 k e2

• (assuming the limit of proportionality has not been exceeded)

• elastic potential energy, Ee, in joules, J

• spring constant, k, in newtons per metre, N/m

• extension or compression, e, in metres, m

How to solve elastic potential energy store problems

elastic potential energy = 0.5 × spring constant × (extension)2,    Ee = 1/2 k e2

Q1 A spring with spring constant of 5.00 N/m is stretched for an extra 10.0 cm.

How much extra energy is stored in the elastic potential energy store of the spring by this extension.

Eepe = 1/2 k e2,  10.0 cm ≡ 10.0 / 100 = 0.10 m

Eepe = 0.5 x 5.0 x 0.102

Eepe = 0.025 J

Q2 A car suspension spring has a spring constant of 2000 N/m.

If the elastic potential energy store of the spring is 50 J, how far is the spring compressed?

Eepe = 1/2 k e2,  rearranging gives e2 = 2Eepe / k,  e = √(2Eepe / k)  and  e = the compression

e = √(2Eepe / k) = √(2 x 50 / 2000) = √0.063 = 0.224 m  (22.4 cm, 3 s.f.)

Q3 It takes 5.0 J of work to stretch a spring 20 cm.

How much extra work must be done to stretch it another 20 cm?

(i) You need to work out the spring constant.  20 cm ≡ 20 / 100 = 0.20 m

Eepe = 1/2 k e2,  rearranging gives k = 2Eepe / e2

k = (2 x 5.0) / (0.20 x 0.20) = 250 N/m

(ii) Then work out the total work to stretch the spring a total of 40 cm.

The total work done on the spring equals its elastic potential energy store when fully stretched 40 cm (which is 0.40 m). Since you now know the spring constant, you use the same equation again, but solving for the total elastic potential energy.

Eepe = 1/2 k e2 = 0.5 x 250 x 0.402 = 20 J

(iii) You then subtract (i) from (ii) to get the extra work done.

Therefore the extra work done = 20 - 5 = 15 J

Q4 A spring stores an extra 20 J of elastic potential energy when stretched an extra 40 cm.

Calculate the spring constant.

40 cm = 0.40 m.

Eepe = 1/2 k e2, rearranging:

k = Eepe x 2 / e2 = 20 x 2 / 0.402 = 250 N/m

Q5 A stretched string has a total length of 60 cm and a spring constant of 240 N/m.

If the stretched spring is storing 20 J of energy, what is the length of the unstretched spring to the nearest cm?

Eepe = 1/2 k e2, rearranging and 60 cm = 0.60 m

e = √(2Eepe / k) = √(2 x 20 / 240) = √(1/6) = 0.408 m

0.408 m = 40.8 cm, ~41 cm = extra length added to the stretched string

Therefore original length of spring = 60 - 41 = ~19 cm

Q6

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Energy resources, and transfers, work done and electrical power supply revision notes index

Types of energy & stores - examples compared/explained, calculations of mechanical work done and power

Chemical  * Elastic potential energy  * Gravitational potential energy

Kinetic energy store  *  Nuclear energy store  *  Thermal energy stores  * Light energy  * Sound energy

Renewable energy (1) Wind power and solar power, advantages and disadvantages gcse physics revision notes

Greenhouse effect, global warming, climate change, carbon footprint from fossil fuel burning gcse physics

The Usefulness of Electricity gcse physics electricity revision notes

and The 'National Grid' power supply, mention of small scale supplies, transformers gcse physics notes

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