TYPES OF ENERGY STORE  examples explained
(b) Elastic potential energy stores and calculations
Doc Brown's GCSE 91 Physics Revision
Notes
Suitable for GCSE/IGCSE Physics/Science courses or
their equivalent
This page will help you with ...
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:

(assuming the limit of proportionality has not been
exceeded)

elastic potential energy,
E_{e}, 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,} E_{e} = ^{1}/_{2}
k e^{2}
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.
E_{epe} = ^{1}/_{2}
k e^{2}, 10.0 cm ≡
10.0 / 100 = 0.10 m
E_{epe} = 0.5 x 5.0 x 0.10^{2}
E_{epe} =
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?
E_{epe} = ^{1}/_{2}
k e^{2}, rearranging gives e^{2} = 2E_{epe} / k,
e = √(2E_{epe} / k) and e = the compression
e = √(2E_{epe} / 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
E_{epe} = ^{1}/_{2}
k e^{2}, rearranging gives k = 2E_{epe} / e^{2}
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.
E_{epe} = ^{1}/_{2}
k e^{2} = 0.5 x 250 x 0.40^{2} =
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.
E_{epe} = ^{1}/_{2}
k e^{2}, rearranging:
k = E_{epe} x 2 / e^{2}
= 20 x 2 / 0.40^{2} =
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?
E_{epe} = ^{1}/_{2}
k e^{2}, rearranging and 60 cm = 0.60 m
e = √(2E_{epe} / 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
See more on
Elasticity and energy stored in a spring 
more on experiments and calculations
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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 *
Electrical
& electrostatic
*
Gravitational potential
energy
Kinetic
energy store *
Nuclear
energy store *
Thermal
energy stores *
Light energy *
Sound energy
Conservation of energy,
energy transfersconversions, efficiency  calculations and
Sankey diagrams
Energy resources: uses, general survey & trends,
comparing renewables, nonrenewables, generating electricity
Renewable energy (1) Wind power and
solar power, advantages and disadvantages gcse physics revision
notes
Renewable energy (2) Hydroelectric power and
geothermal power,
advantages and disadvantages
gcse physics
Renewable energy (3) Wave power and tidal barrage power,
advantages and disadvantages
gcse physics
See also
Renewable energy  biofuels & alternative fuels,
hydrogen, biogas, biodiesel
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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