Calculating the energy of springs (E = 1/2 kx²) | Exit Quiz | Oak National Academy

Which of the following words means ‘make something smaller using forces’?

• deform

• expand

• extend

• compress

• compound

Answer explanation

Making an object smaller, such as a spring or a sponge, using forces is compressing the object. ‘Com’ means together’ (as in community and committee) and the second part of the word is ‘press’.

A spring has a length of 10 cm. Starting with the least energy transferred to the elastic store, sort the following deformations into order of increasing energy.

• The spring is stretched from 10 cm to 12 cm long.

• The spring is stretched from 15 cm to 17 cm long.

• The spring is stretched from 15 cm to 18 cm long.

• The spring is stretched from 10 cm to 18 cm long.

Answer explanation

For extensions of 10 to 12 cm and 15 to 17 cm, the force acts over the same distance, but more work is required when the extension is greater. Extending from 15 to 18 cm needs more work than 15 to 17 cm, and most work is done from 10 to 18 cm.

A pupil stretches a spring. The work done by the pupil is equal to …

• extension × average force.

• extension × force at the start.

• extension × force at the end.

Answer explanation

During the stretch, force increases from 0 N to a maximum. If we calculate work using initial force, it will be less than the actual work; if we calculate it using maximum force, it will be greater. Using average force gives the correct value.

A spring of length 6.0 cm has spring constant 960 N/m. How much energy does it gain if it is stretched to 8.0 cm?

• 0.19 J

• 3.1 J

• 92 J

• 180 J

A spring is stretched by 4.0 cm, transferring 96 J of energy to the elastic store. What is the spring constant of the spring?

• 490 N/m

• 4800 N/m

• 30 000 N/m

• 120 000 N/m

A spring has spring constant 2000 N/m. The spring is stretched, transferring 250 J of energy to the elastic store. What is the extension of the spring?

• 0.13 m

• 0.25 m

• 0.35 m

• 0.50 m