Potential Energy Examples in Physics

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 N/mk = 200 \text{ N/m} is compressed by 0.1 m0.1 \text{ m}. What is the elastic potential energy stored?

Answer

PE=1 JPE = 1 \text{ J}

First step

1
Use the elastic PE formula: PE=12kx2PE = \frac{1}{2}kx^2.

Full solution

  1. 2
    Square the compression distance: (0.1)2=0.01(0.1)^2 = 0.01.
  2. 3
    PE=12(200)(0.01)=1 JPE = \frac{1}{2}(200)(0.01) = 1 \text{ 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
A 0.3 kg0.3 \text{ kg} ball on a compressed spring (k=800 N/mk = 800 \text{ N/m}, compressed 0.15 m0.15 \text{ m}) is released. What speed does the ball reach?

Example 3

medium
A 0.4 kg0.4 \text{ kg} ball is at the top of a 1.25 m1.25 \text{ m} frictionless ramp (g=9.8g = 9.8). All PE converts to KE at the bottom. Find the speed there.

Example 4

medium
A spring (k=250 N/mk = 250 \text{ N/m}) is stretched from 0.10 m0.10 \text{ m} to 0.20 m0.20 \text{ m} from its natural length. Find the change in its elastic PE.

Example 5

medium
Two springs in parallel (k1=150 N/mk_1 = 150 \text{ N/m}, k2=250 N/mk_2 = 250 \text{ N/m}) are each compressed 0.10 m0.10 \text{ m} together. Find the total stored elastic PE.

Example 6

hard
A 0.6 kg0.6 \text{ kg} block on a frictionless surface is pushed into a spring (k=500 N/mk = 500 \text{ N/m}) by 0.20 m0.20 \text{ m}, then released. Find the speed of the block when the spring has returned to its natural length.

Example 7

hard
A 4 kg4 \text{ kg} mass at height hh 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 m/s5 \text{ m/s}. Find hh (g=9.8g = 9.8).

Example 8

challenge
A roller-coaster car (m=500 kgm = 500 \text{ kg}) starts at rest at 40 m40 \text{ m}, then crests a second hill at 15 m15 \text{ m}. Friction dissipates 30000 J30000 \text{ J} over the run (g=9.8g = 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 N/mk = 500 \text{ N/m}) is stretched 0.2 m0.2 \text{ m}. How much work was done to stretch it?

Example 2

easy
A bungee cord has an effective spring constant k=100 N/mk = 100 \text{ N/m}. If it stretches 3 m3 \text{ m} beyond its natural length, how much elastic potential energy is stored?

Example 3

easy
What kind of energy is stored due to an object's position or configuration?

Example 4

easy
A 1 kg object sits 5 m above the floor (g = 9.8). What is its gravitational PE relative to the floor?

Example 5

easy
A spring with k = 100 N/m is stretched 0.2 m. Find its elastic PE.

Example 6

easy
Does potential energy depend on a chosen reference point?

Example 7

easy
Can gravitational potential energy be negative?

Example 8

easy
A 2 kg object is raised from the floor to a 3 m shelf (g = 9.8). What is its change in PE?

Example 9

easy
Potential energy is measured in what unit?

Example 10

easy
A stretched bow and a raised hammer: which kind of PE does each store?

Example 11

medium
A 0.3 kg ball at the top of a 2 m ramp rolls down (g = 9.8). How much PE converts to KE at the bottom (frictionless)?

Example 12

medium
A spring stores 8 J of elastic PE at x = 0.4 m. Find its spring constant k.

Example 13

medium
An object's PE is 120 J at 4 m and 30 J at 1 m above the floor. Is the mass consistent (g = 9.8)?

Example 14

medium
A 2 kg mass hangs from a spring (k = 50 N/m) stretched 0.4 m (g = 9.8). Compare its elastic PE to the gravitational PE relative to the unstretched position.

Example 15

medium
A 5 kg box is moved up a frictionless 10 m ramp inclined so its top is 3 m high (g = 9.8). What is its PE change?

Example 16

medium
How much elastic PE is stored if a spring's deformation triples from x to 3x (k fixed)?

Example 17

medium
A 4 kg object at 6 m has PE = 235.2 J relative to the floor. What value of g was used?

Example 18

challenge
A 2 kg pendulum bob is raised so its PE increases by 9.8 J (g = 9.8). It is released; ignoring friction, find its speed at the lowest point.

Example 19

challenge
A spring (k = 800 N/m) is compressed 0.05 m and pushes a 0.2 kg block on a frictionless surface. Find the block's launch speed.

Example 20

challenge
A 3 kg object is dropped from a height where its PE is 176.4 J (g = 9.8). After falling halfway, what are its KE and remaining PE?

Example 21

medium
A 1 kg object is raised 3 m and a spring (k = 200 N/m) is stretched 0.2 m (g = 9.8). Find the total stored potential energy.

Example 22

medium
A 4 kg object's gravitational PE doubles from 78.4 J as it is raised higher (g = 9.8). Find the new height.

Example 23

easy
A 0.5 kg0.5 \text{ kg} apple sits on a shelf 2 m2 \text{ m} above the floor. Using g=9.8 m/s2g = 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 N/mk = 100 \text{ N/m}) compressed 0.1 m0.1 \text{ m} or one (k=50 N/mk = 50 \text{ N/m}) compressed 0.2 m0.2 \text{ m}?

Example 26

easy
A 2 kg2 \text{ kg} rock is held 1 m1 \text{ m} below a tabletop chosen as the zero level (g=9.8g = 9.8). Find the rock's gravitational PE.

Example 27

medium
A spring stores 18 J18 \text{ J} of elastic PE when stretched 0.30 m0.30 \text{ m}. Find its spring constant.

Example 28

medium
A 5 kg5 \text{ kg} box on a frictionless 30°30° ramp is held 3 m3 \text{ m} up the slope from the bottom (g=9.8g = 9.8). Find its gravitational PE relative to the bottom.

Example 29

medium
A pendulum bob of mass 0.25 kg0.25 \text{ kg} is pulled aside so it is 0.40 m0.40 \text{ m} higher than at the lowest point (g=9.8g = 9.8). Find its KE at the lowest point (frictionless, started from rest).

Example 30

medium
A 0.50 kg0.50 \text{ kg} mass dropped from 2 m2 \text{ m} lands on a spring (k=200 N/mk = 200 \text{ N/m}) and compresses it by xx. Ignoring spring height vs. drop, find xx at the instant of maximum compression. Use g=9.8g = 9.8.

Example 31

medium
Two ramps end at the same height hh above the floor. Ramp A is twice as long as ramp B. A block of mass mm rests at the top of each. Compare their gravitational PE values relative to the floor.

Example 32

medium
A 0.8 kg0.8 \text{ kg} ball at 5 m5 \text{ m} is released and lands on the floor (g=9.8g = 9.8). How much PE was converted to KE just before impact (frictionless)?

Example 33

medium
Increase a spring's deformation from xx to 4x4x. By what factor does the stored elastic PE change?

Example 34

medium
A pendulum's PE relative to its lowest point is 00 at the bottom and 3 J3 \text{ J} at the highest point. By energy conservation (no friction), find the KE at the bottom.

Example 35

hard
A 3 kg3 \text{ kg} object slides down a 4 m4 \text{ m} ramp inclined 30°30° (g=9.8g = 9.8). Friction does 20 J20 \text{ J} of negative work. Find the object's KE at the bottom.

Example 36

hard
A 0.10 kg0.10 \text{ kg} dart is fired vertically by a spring gun. The spring (k=800 N/mk = 800 \text{ N/m}) was compressed 0.05 m0.05 \text{ m}. Ignoring spring length and using g=9.8g = 9.8, find the dart's maximum height above the release point.

Example 37

challenge
A 0.20 kg0.20 \text{ kg} mass on a vertical spring (k=50 N/mk = 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=9.8g = 9.8).
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Background Knowledge

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

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