Practice Elastic Potential Energy in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Energy stored in an elastic object that has been stretched or compressed from its natural length.

A stretched rubber band 'wants' to snap back—that desire is stored energy.

Showing a random 20 of 50 problems.

Example 1

easy
What is the elastic PE of an unstretched spring at its natural length?

Example 2

medium
A spring is stretched so it stores 50 J at x = 0.5 m. How much does it store at x = 0.1 m (same k)?

Example 3

medium
A spring stores 1616 J at x=0.4x = 0.4 m. Find the stored PE at x=0.1x = 0.1 m (same spring).

Example 4

easy
If a spring's compression triples, by what factor does its stored elastic PE change?

Example 5

medium
Spring A (k = 100, x = 0.4 m) and spring B (k = 400, x = 0.2 m). Which stores more elastic PE?

Example 6

hard
A trampoline can be modeled as k=4000k = 4000 N/m. A 5050 kg child stretches it 0.30.3 m at the bottom of a jump. Find the elastic PE stored.

Example 7

hard
A spring stores 3030 J of elastic PE when stretched 0.20.2 m. A 1.51.5 kg block attached on a frictionless surface is released. Find the block's speed when the stretch is 0.10.1 m.

Example 8

challenge
A 0.50.5 kg block sliding at 66 m/s hits a spring (k=900k = 900 N/m). A constant friction force of 33 N acts during compression. Find the maximum compression.

Example 9

medium
A bow stores 60 J of elastic PE and transfers it to a 0.05 kg arrow (no loss). Find the arrow's launch speed.

Example 10

medium
A spring stores 99 J at x=0.3x = 0.3 m. Find the spring constant and the force needed to hold it there.

Example 11

medium
A 2 kg mass on a spring (k = 800 N/m) is pulled 0.1 m and released on a frictionless surface. Find its max speed.

Example 12

easy
A spring stores 2 J at x = 0.1 m. Find k.

Example 13

medium
A spring stretched xx stores EE. How much is stored when stretched x/2x/2?

Example 14

easy
True or false: doubling the spring constant doubles the elastic PE at the same stretch.

Example 15

easy
In the formula PE=12kx2PE = \tfrac12 k x^2, what does xx represent?

Example 16

easy
A spring (k=600k = 600 N/m) is compressed 0.050.05 m. Find PEPE.

Example 17

medium
A toy gun spring (k=400k = 400 N/m) stores enough energy to give a 0.020.02 kg dart a speed of 1010 m/s. Find the compression xx.

Example 18

easy
A spring with spring constant k=400 N/mk = 400 \text{ N/m} is compressed by 0.05 m0.05 \text{ m}. How much elastic potential energy is stored in the spring?

Example 19

easy
A spring (k = 200 N/m) is stretched 0.3 m. Find its elastic PE.

Example 20

easy
In PE = \frac{1}{2}kx^2, what is x measured from?
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