Gravitational Potential Energy Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Gravitational 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 an object due to its height above a reference point in a gravitational field: $PE = mgh$ .

The higher you lift something, the more energy it stores (ready to fall).

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: Gravitational 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 gravitational 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

What is the gravitational potential energy of a

4 \text{ kg}

book on a shelf

2.5 \text{ m}

above the floor? Use

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

Answer

P E = 98 J

First step

Use the gravitational potential energy formula:

PE = mgh

Full solution

2
Substitute the values: $PE = 4 \times 9.8 \times 2.5$ .
3
$P E = 98 J$

Gravitational potential energy depends on mass, gravitational acceleration, and height above a reference point. It represents stored energy due to an object's position in a gravitational field.

Example 2

medium

50 \text{ kg}

person climbs a

15 \text{ m}

ladder. How much gravitational PE do they gain? Use

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

Example 3

medium

0.8\text{ kg}

ball is thrown upward at

10\text{ m/s}

(

g=9.8

). How high does it rise?

Example 4

medium

A skier (

60\text{ kg}

) starts at rest at the top of a hill and reaches

20\text{ m/s}

at the bottom. Find the height dropped (

g=9.8

, no friction).

Example 5

hard

4\text{ kg}

object is lifted at constant velocity through

3\text{ m}

4\text{ s}

(

g=9.8

). Find (a) the work done against gravity, and (b) the average power.

Practice Problems

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

Example 1

easy

At what height does a

2 \text{ kg}

object have

392 \text{ J}

of gravitational PE? Use

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

Example 2

medium

0.5 \text{ kg}

ball is thrown upward and reaches a maximum height of

12 \text{ m}

. What was the ball's kinetic energy at launch? Use

g = 10 \text{ m/s}^2

Example 3

easy

A 5 kg object is 4 m high (g = 9.8). Find its gravitational PE.

Example 4

easy

A 2 kg object is 10 m up (g = 9.8). What is its gravitational PE?

Example 5

easy

A 10 kg object has gravitational PE = 490 J (g = 9.8). How high is it?

Example 6

easy

In PE = mgh, what does h represent?

Example 7

easy

Two objects at the same height, 3 kg and 7 kg. Which has more gravitational PE?

Example 8

easy

A 4 kg object is lifted from 2 m to 5 m (g = 9.8). Find the change in gravitational PE.

Example 9

easy

If g on the Moon is about 1.6 m/s^2, does a 10 kg object 2 m up have more PE on the Moon or Earth?

Example 10

easy

A 1 kg object rests on the floor chosen as the reference (h = 0). What is its gravitational PE?

Example 11

medium

A 0.5 kg ball is dropped from 6 m (g = 9.8). Find its speed just before landing using PE.

Example 12

medium

A 1200 kg elevator rises 30 m (g = 9.8). How much work is done against gravity?

Example 13

medium

A 3 kg object on a 5 m ramp whose top is at 4 m height (g = 9.8). Find its gravitational PE at the top.

Example 14

medium

A 2 kg object's PE relative to the floor is -39.2 J (g = 9.8). How far below the floor is it?

Example 15

medium

A 0.2 kg ball is thrown up and reaches a point where its gravitational PE is 3.92 J (g = 9.8). What height is that?

Example 16

medium

Object A (2 kg at 6 m) and object B (4 kg at 3 m), g = 9.8. Compare their gravitational PE.

Example 17

medium

A 50 kg climber ascends 200 m (g = 9.8). How much gravitational PE is gained?

Example 18

challenge

A 0.4 kg ball is launched up at 12 m/s (g = 9.8). Using PE and KE, find the maximum height it reaches.

Example 19

challenge

A 3 kg object is lifted from the floor to a 4 m shelf, then a different reference is set at the shelf. What is its PE relative to each reference (g = 9.8)?

Example 20

challenge

A 2 kg block slides down a frictionless 30 degree incline from rest, dropping 1.5 m in height (g = 9.8). Find its speed at the bottom and the PE lost.

Example 21

medium

A 6 kg object is lifted to 5 m and then a 2 kg object to 3 m (g = 9.8). Find the total gravitational PE.

Example 22

medium

How much gravitational PE does a 10 kg object lose falling from 8 m to 2 m (g = 9.8)?

Example 23

easy

3\text{ kg}

book sits on a shelf

1.2\text{ m}

above the floor (reference). Find its gravitational PE (

g=9.8

Example 24

easy

8\text{ kg}

box is lifted

0.5\text{ m}

above the floor (

g=9.8

). Find its gravitational PE relative to the floor.

Example 25

easy

20\text{ kg}

object has

PE = 392\text{ J}

(

g=9.8

). How high is it above the reference?

Example 26

medium

0.6\text{ kg}

ball drops

4\text{ m}

(

g=9.8

). Use energy conservation to find its speed just before hitting the ground (no friction).

Example 27

medium

0.3\text{ kg}

apple has

PE = 5.88\text{ J}

on a branch (

g=9.8

). How high is the branch?

Example 28

medium

2\text{ kg}

block slides up a frictionless ramp from rest until it stops, having risen

0.9\text{ m}

in height (

g=9.8

). Find the initial KE.

Example 29

medium

A roller coaster car (

500\text{ kg}

) sits at the top of a

40\text{ m}

hill (

g=9.8

). Find its gravitational PE relative to the ground.

Example 30

medium

70\text{ kg}

hiker climbs

300\text{ m}

vertically (

g=9.8

). What minimum work was done against gravity?

Example 31

medium

A pendulum bob (

0.25\text{ kg}

) is pulled up by

0.1\text{ m}

above its lowest point (

g=9.8

). Find its maximum speed at the bottom (no friction).

Example 32

hard

2\text{ kg}

block slides down a

5\text{ m}

incline that drops

3\text{ m}

vertically. Friction does

10\text{ J}

of negative work (

g=9.8

). Find the block's speed at the bottom (starting from rest).

Example 33

hard

A reservoir holds

1\times 10^6\text{ kg}

of water

50\text{ m}

above a turbine (

g=9.8

). If the system is

80\%

efficient, how much electrical energy is produced when the reservoir empties?

Example 34

hard

0.05\text{ kg}

ball is dropped from

2\text{ m}

and bounces back to

1.5\text{ m}

(

g=9.8

). Find the energy lost in the bounce.

Example 35

hard

On the Moon (

g=1.6\text{ m/s}^2

), a

3\text{ kg}

rock is lifted

5\text{ m}

. Compare its PE to the same rock at the same height on Earth (

g=9.8

Example 36

challenge

0.5\text{ kg}

ball is dropped from

5\text{ m}

and rebounds elastically off a spring of stiffness

k=200\text{ N/m}

on the floor. Find the maximum spring compression (

g=9.8

Example 37

medium

1\text{ kg}

ball is held at

2\text{ m}

. The reference is then shifted up to

3\text{ m}

. What is the ball's new PE (

g=9.8

Example 38

medium

0.1\text{ kg}

stone is launched at

20\text{ m/s}

upward from the top of a

15\text{ m}

cliff (

g=9.8

). Using energy methods, find its speed when it returns to the cliff height.

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Related Concepts

Potential Energy Gravity Conservation of Energy Work

Background Knowledge

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

potential energygravity