Elastic Potential Energy (AQA GCSE Combined Science: Trilogy: Physics): Revision Note

A mass is attached to the bottom of a hanging spring with a spring constant of 250 N/m. It stretches from 10.0 cm to 11.4 cm.

Calculate the elastic energy stored by the stretched spring.

Answer:

Step 1: Determine the extension of the spring

• The extension is how much longer the spring is than its original length:

$\text{extension}=\text{stretched length}-\text{original length}$

$e=11.4-10.0=1.4\text{ cm}$

Step 2: List the known quantities

• Spring constant, k = 250 N/m

• Extension, e = 1.4 cm

Step 3: Convert the extension into metres

• The spring constant is in N/m, so the extension must be in metres. There are 100 cm in 1 m:

$e=\frac{1.4}{100}=0.014\text{ m}$

Step 4: Write down the elastic potential energy equation

• This equation is given on the Physics Equations Sheet

$E_e=\frac{1}{2}\times k\times e^2$

Step 5: Substitute the known values and calculate the elastic potential energy

• Square the extension first, then multiply by the spring constant and by ½

$E_e=\frac{1}{2}\times 250\times 0.{014}^2$

$E_e=0.0245\text{ J}$

Step 6: Round the answer to 2 significant figures

• The extension is given to 2 significant figures, so the answer is given to the same degree of accuracy

$E_e=0.025\text{ J}$

Look out for units. If the question gives the extension in cm, you must convert it into metres for the calculation to be correct.

Remember to square the extension before multiplying by the spring constant. Only e is squared, not k or ½. Forgetting to square e is the most common mistake in this calculation. If you substitute the values first and then work out the answer, you still gain the substitution mark even if the final answer is wrong

To change the shape of an object, two contact forces must be acting on the object in different directions. In this case, the spring is attached to the arm of the clamp providing a contact force, and the mass is attached to the spring providing a contact force. These forces pull the spring in opposite directions and this is the reason that the spring stretches. The forces and energy topics are linked by the concept of work done which is a force acting over a distance, and also the energy transferred. Making links between concepts is an important way to fast-track your understanding.