Why is there a factor of ½ in E = ½ F ΔL?

The force rises from zero to F during the extension, so the average force is F / 2.

By what factor does the energy stored change if the extension of a Hooke's law spring is tripled?

It increases by a factor of 9, since E is proportional to ΔL².

A spring launches a ball horizontally. Which energy transfer occurs?

Elastic strain energy is transferred to the kinetic energy of the ball.

A spring launches a ball vertically. What does the elastic strain energy become?

Kinetic energy and gravitational potential energy (with some thermal energy lost to air resistance).

What happens to a metal wire beyond its elastic limit?

Layers of atoms slip past each other, giving permanent (plastic) extension that remains when the load is removed.

Why does a wire warm up after being stretched beyond its elastic limit and unloaded?

The work done in plastic deformation is not recovered and is transferred to internal (thermal) energy.

What does the area between the loading and unloading lines represent?

The energy transferred to the material as thermal energy and not recovered.

Give one advantage of regenerative braking.

Energy that would be wasted as thermal energy in the brakes is stored and reused, reducing fuel use and emissions.

Give one disadvantage of adding a spring energy store to a vehicle.

The extra mass means more energy is needed to accelerate, and making the spring uses energy and resources.

Elastic strain energyAQA A-Level Physics: Flashcards

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What does the area under a force–extension graph represent?

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What does the area under a force–extension graph represent?: The work done in stretching the material; for elastic behaviour this is the elastic strain energy stored.
State the equation for elastic strain energy in terms of force and extension.: $E = \frac{1}{2} F \Delta L$
Write the elastic strain energy in terms of the spring constant.: $E = \frac{1}{2} k \Delta L^2$
Why is there a factor of ½ in E = ½ F ΔL?: The force rises from zero to F during the extension, so the average force is F / 2.
By what factor does the energy stored change if the extension of a Hooke's law spring is tripled?: It increases by a factor of 9, since E is proportional to ΔL².
A spring launches a ball horizontally. Which energy transfer occurs?: Elastic strain energy is transferred to the kinetic energy of the ball.
A spring launches a ball vertically. What does the elastic strain energy become?: Kinetic energy and gravitational potential energy (with some thermal energy lost to air resistance).
What happens to a metal wire beyond its elastic limit?: Layers of atoms slip past each other, giving permanent (plastic) extension that remains when the load is removed.
Why does a wire warm up after being stretched beyond its elastic limit and unloaded?: The work done in plastic deformation is not recovered and is transferred to internal (thermal) energy.
What does the area between the loading and unloading lines represent?: The energy transferred to the material as thermal energy and not recovered.
Give one advantage of regenerative braking.: Energy that would be wasted as thermal energy in the brakes is stored and reused, reducing fuel use and emissions.
Give one disadvantage of adding a spring energy store to a vehicle.: The extra mass means more energy is needed to accelerate, and making the spring uses energy and resources.

Exam questions on Elastic strain energy

A spring obeys Hooke's law within its limit of proportionality. A force of 8.0 N extends the spring by 0.040 m.
Calculate the additional energy that must be transferred to the spring to increase its extension from 0.040 m to 0.080 m.2 marks
A technician loads a steel wire with increasing weights until it has been stretched beyond its elastic limit, and then removes the weights one by one. After unloading, the wire is found to be permanently longer than at the start and feels slightly warm.
Explain, in terms of energy, why the wire is slightly warm after it has been unloaded.2 marks
A pinball machine launches a steel ball of mass 0.080 kg using a spring of spring constant 320 N m⁻¹. The spring is compressed by 0.045 m and then released. The ball leaves the spring when the spring reaches its natural length. Take g = 9.81 m s⁻².
Calculate the speed of the ball as it leaves the spring, assuming the spring energy is transferred entirely to the kinetic energy of the ball.3 marks

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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).