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.

Q1:

The keys on a computer keyboard contain small springs that compress by 4.8 mm when a key is pressed. On a particular day, 12โ€‰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?

Q2:

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?

Q3:

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

Q4:

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

Q5:

The quantity ๐ธ is a springโ€™s elastic potential energy when the spring is extended or compressed. Which of the following formulas correctly shows the relationship between ๐ธ, the constant of the spring ๐‘˜, and the change in the length ๐‘ฅ of the spring from its equilibrium length?

  • A ๐ธ = 1 2 ๐‘˜ ๐‘ฅ ๏Šจ
  • B ๐ธ = 1 2 ๐‘˜ ๐‘ฅ ๏Šจ ๏Šจ
  • C ๐ธ = 1 2 ๐‘˜ ๐‘ฅ ๏Šจ
  • D ๐ธ = ๐‘˜ ๐‘ฅ ๏Šจ
  • E ๐ธ = ๐‘˜ ๐‘ฅ

Q6:

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 bedโ€™s springs?

Q7:

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 springโ€™s elastic potential energy change during the first time it is shortened?

How much does the springโ€™s elastic potential energy change during the second time it is shortened?

Q8:

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?

Q9:

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?

Q10:

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?

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