Worksheet: Elastic Potential Energy

In this worksheet, we will practice calculating the elastic potential energy stored in springs that are not at their equilibrium length.


The keys on a computer keyboard contain small springs that compress by 4.8 mm when a key is pressed. On a particular day, 12,500 keystrokes are made on the keyboard. The springs in the keys each have a constant of 2.5 N/m. How much energy was supplied to make all the keystrokes performed that day?


A spring with a constant of 16 N/m has 98 J of energy stored in it when it is extended. How far is the spring extended?


A spring has 50 J of energy stored in it when it is extended by 2.5 m. What is the spring’s constant?


A spring with a constant of 80 N/m is extended by 1.5 m. How much energy is stored in the extended spring?


The quantity 𝐸 is a spring’s elastic potential energy when the spring is extended or compressed. Which of the following formulas correctly shows the relationship between 𝐸, the constant of the spring 𝑘, and the change in the length 𝑥 of the spring from its equilibrium length?

  • A𝐸=12𝑘𝑥
  • B𝐸=12𝑘𝑥
  • C𝐸=12𝑘𝑥
  • D𝐸=𝑘𝑥
  • E𝐸=𝑘𝑥


A man with a weight of 900 N lies down on a spring-loaded mattress. The combined force constant of all the springs in the mattress is 18,000 N/m. How much elastic potential energy is stored in the bed’s springs?


A spring with a force constant of 500 N/m is extended from its equilibrium length by 12 cm. From its extended length, the spring is shortened by 7 cm. The spring is then shortened from this length by 15 cm.

How much does the spring’s elastic potential energy change during the first time it is shortened?

How much does the spring’s elastic potential energy change during the second time it is shortened?


The force used to stretch a spring is shown in the graph. How much work is required to extend the spring by 0.6 m?


Some joke glasses with eyeballs on springs have springs with an equilibrium length of 10 cm and a constant of 25 N/m. A partygoer is wearing the joke glasses and the springs are extended forward to a length of 26 cm. He jerks his head backward and the springs reduce in length to 1.2 cm. By how much is the energy stored in the springs reduced?


When an umbrella is opened, most of the work required to open it is done by the person using the umbrella, but a spring is used to complete the opening process. In the umbrella, a compressed spring with a length of 9.5 cm extends to a length of 10 cm, which does 0.12 J of work expanding the umbrella. What is the constant of the spring?


While exercising, a woman pulls a spring chest expander that has a spring constant of 500 N/m. The woman does 12,100 J of work during her exercise routine and uses the device forty times. How far does the device expand each time? Assume that no work is done while the device contracts.

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