Potential Energy Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Potential Energy.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Energy stored in a system due to the position or configuration of its parts, ready to be converted into kinetic or other forms of energy.

Energy waiting to be released—like a stretched rubber band or a ball held high.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Potential Energy asks what energy enters, leaves, stays stored, or changes form in the chosen system.

Common stuck point: Students often know a formula related to potential energy but skip the recognition step: Can I define the system and track energy before and after the interaction or process? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Can I define the system and track energy before and after the interaction or process?

Worked Examples

Example 1

easy

A spring with spring constant

k = 200 \text{ N/m}

is compressed by

0.1 \text{ m}

. What is the elastic potential energy stored?

Answer

P E = 1 J

First step

Use the elastic PE formula:

PE = \frac{1}{2}kx^2

Full solution

2
Square the compression distance: $(0.1)^2 = 0.01$ .
3
$P E = \frac{1}{2} (200) (0.01) = 1 J$

Elastic potential energy is stored in deformed elastic objects like springs. It depends on the spring constant and the square of the deformation.

Example 2

medium

0.3 \text{ kg}

ball on a compressed spring (

k = 800 \text{ N/m}

, compressed

0.15 \text{ m}

) is released. What speed does the ball reach?

Example 3

medium

0.4 \text{ kg}

ball is at the top of a

1.25 \text{ m}

frictionless ramp (

g = 9.8

). All PE converts to KE at the bottom. Find the speed there.

Example 4

medium

A spring (

k = 250 \text{ N/m}

) is stretched from

0.10 \text{ m}

0.20 \text{ m}

from its natural length. Find the change in its elastic PE.

Example 5

medium

Two springs in parallel (

k_1 = 150 \text{ N/m}

k_2 = 250 \text{ N/m}

) are each compressed

0.10 \text{ m}

together. Find the total stored elastic PE.

Example 6

hard

0.6 \text{ kg}

block on a frictionless surface is pushed into a spring (

k = 500 \text{ N/m}

) by

0.20 \text{ m}

, then released. Find the speed of the block when the spring has returned to its natural length.

Example 7

hard

4 \text{ kg}

mass at height

h

is released. After falling, half its PE has converted to KE; the rest was lost to air drag. The mass is then moving at

5 \text{ m/s}

. Find

h

(

g = 9.8

Example 8

challenge

A roller-coaster car (

m = 500 \text{ kg}

) starts at rest at

40 \text{ m}

, then crests a second hill at

15 \text{ m}

. Friction dissipates

30000 \text{ J}

over the run (

g = 9.8

). Find the car's speed at the top of the second hill.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

A spring (

k = 500 \text{ N/m}

) is stretched

0.2 \text{ m}

. How much work was done to stretch it?

Example 2

easy

A bungee cord has an effective spring constant

k = 100 \text{ N/m}

. If it stretches

easy

0.5 \text{ kg}

apple sits on a shelf

2 \text{ m}

above the floor. Using

g = 9.8 \text{ m/s}^2

and the floor as the zero level, find its gravitational PE.

Example 24

easy

True or false: changing the reference height changes the value of gravitational PE.

Example 25

easy

Which has more elastic PE: a spring (

k = 100 \text{ N/m}

) compressed

0.1 \text{ m}

or one (

k = 50 \text{ N/m}

) compressed

0.2 \text{ m}

Example 26

easy

2 \text{ kg}

rock is held

1 \text{ m}

below a tabletop chosen as the zero level (

g = 9.8

). Find the rock's gravitational PE.

Example 27

medium

A spring stores

18 \text{ J}

of elastic PE when stretched

0.30 \text{ m}

. Find its spring constant.

Example 28

medium

5 \text{ kg}

box on a frictionless

30°

ramp is held

3 \text{ m}

up the slope from the bottom (

g = 9.8

). Find its gravitational PE relative to the bottom.

Example 29

medium

A pendulum bob of mass

0.25 \text{ kg}

is pulled aside so it is

0.40 \text{ m}

higher than at the lowest point (

g = 9.8

). Find its KE at the lowest point (frictionless, started from rest).

Example 30

medium

0.50 \text{ kg}

mass dropped from

2 \text{ m}

lands on a spring (

k = 200 \text{ N/m}

) and compresses it by

x

. Ignoring spring height vs. drop, find

x

at the instant of maximum compression. Use

g = 9.8

Example 31

medium

Two ramps end at the same height

h

above the floor. Ramp A is twice as long as ramp B. A block of mass

m

rests at the top of each. Compare their gravitational PE values relative to the floor.

Example 32

medium

0.8 \text{ kg}

ball at

5 \text{ m}

is released and lands on the floor (

g = 9.8

). How much PE was converted to KE just before impact (frictionless)?

Example 33

medium

Increase a spring's deformation from

x

4x

. By what factor does the stored elastic PE change?

Example 34

medium

A pendulum's PE relative to its lowest point is

0

at the bottom and

3 \text{ J}

at the highest point. By energy conservation (no friction), find the KE at the bottom.

Example 35

hard

3 \text{ kg}

object slides down a

4 \text{ m}

ramp inclined

30°

(

g = 9.8

). Friction does

20 \text{ J}

of negative work. Find the object's KE at the bottom.

Example 36

hard

0.10 \text{ kg}

dart is fired vertically by a spring gun. The spring (

k = 800 \text{ N/m}

) was compressed

0.05 \text{ m}

. Ignoring spring length and using

g = 9.8

, find the dart's maximum height above the release point.

Example 37

challenge

0.20 \text{ kg}

mass on a vertical spring (

k = 50 \text{ N/m}

) hangs at rest. The natural length is the reference. Find the mass's equilibrium stretch and the elastic PE there (

g = 9.8

← Back to Potential Energy Practice Mode

Related Concepts

Energy Gravitational Potential Energy Elastic Potential Energy Conservation of Energy

Background Knowledge

These ideas may be useful before you work through the harder examples.

energy