Students should be able to calculate relevant values of stored energy and…

The idea

You may be asked to find the energy stored when a spring is stretched, the spring constant when energy and extension are known, or the extension when energy and k are known. Rearranging is often needed: k = 2Eₑ ÷ e² and e = √(2Eₑ ÷ k). For example, if 0.50 J is stored in a spring with k = 100 N/m, then e = √(2 × 0.50 ÷ 100) = 0.10 m. When the spring is released, the elastic potential energy store decreases and equal energy is transferred to kinetic, gravitational potential or thermal energy stores, depending on the situation.

What earns the marks

• Select the equation Eₑ = ½ke² and rearrange it correctly for the quantity required.
• Calculate stored elastic potential energy from a given spring constant and extension.
• Calculate the spring constant from a given stored energy and extension.
• Calculate the extension from a given stored energy and spring constant, taking the positive square root.
• Describe energy transfers between elastic potential, kinetic, gravitational potential and thermal stores when a spring is stretched or released.
• Check that the spring remains within its limit of proportionality when applying the equation.

Common mistakes and how to put them right

• Rearranging incorrectly, for example writing k = Eₑ ÷ e² instead of k = 2Eₑ ÷ e².

  Put it right: Multiply both sides by 2 before dividing by e².

• Forgetting the square root when finding extension.

  Put it right: Take the square root of 2Eₑ ÷ k.

• Assuming all stored energy becomes useful kinetic energy.

  Put it right: State that some energy may be transferred to the thermal store of the surroundings.

Exam tips

• Show each rearrangement step so that method marks can be awarded even if the final value is wrong.
• Give the final answer with the correct unit and a sensible number of significant figures.
• When describing transfers, name the store that decreases and the store that increases, and mention any thermal transfer to the surroundings.