Energy Examples: 44 Problems with Answers

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

The capacity to do work or cause change in a physical system, measured in joules (J).

The 'currency' that makes things happen. It's what you need to move, heat, or change anything.

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: 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 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

2 \text{ kg}

ball is held

10 \text{ m}

above the ground and then dropped. What is its total mechanical energy at the top? Use

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

Answer

E = 196 J

First step

At the top, the ball is at rest, so kinetic energy is zero:

KE = 0

Full solution

2
Potential energy: $P E = m g h = 2 \times 9.8 \times 10 = 196 J$
3
Total mechanical energy: $E = K E + P E = 0 + 196 = 196 J$

Energy is the capacity to do work. Mechanical energy is the sum of kinetic and potential energy. At the top, all energy is stored as gravitational potential energy.

Example 2

medium

1000 \text{ kg}

car traveling at

20 \text{ m/s}

brakes to a stop. How much energy is dissipated as heat?

Example 3

medium

A pendulum bob of

0.2\,\text{kg}

rises to

0.5\,\text{m}

above its lowest point (

g = 9.8

). Find its maximum KE during the swing.

Example 4

hard

0.2\,\text{kg}

mass on a spring (

k = 50\,\text{N/m}

) is pulled

0.1\,\text{m}

from equilibrium and released. Find the maximum speed.

Practice Problems

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

Example 1

easy

Name the energy transformations when a ball is thrown upward and comes back down.

Example 2

medium

3 \text{ kg}

rock at

15 \text{ m}

above the ground is moving at

4 \text{ m/s}

. What is its total mechanical energy? Use

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

Example 3

easy

What is the SI unit of energy?

Example 4

easy

A 2 kg book sits on a shelf 3 m high (g = 9.8 m/s^2). How much gravitational energy is stored relative to the floor?

Example 5

easy

Name the form of energy an object has purely because it is moving.

Example 6

easy

A 100 W bulb runs for 10 s. How much energy does it use?

Example 7

easy

True or false: energy can be destroyed.

Example 8

easy

A 1 kg ball moves at 4 m/s. What is its kinetic energy?

Example 9

easy

Which has units of joules: force, power, or energy?

Example 10

easy

A stretched spring is released and launches a ball. What energy was stored in the spring?

Example 11

medium

A 0.5 kg ball is dropped from 8 m (g = 9.8 m/s^2). Find its kinetic energy just before hitting the ground, ignoring air resistance.

Example 12

medium

A 3 kg cart at 2 m/s on the floor, plus the same cart held 1 m high at rest (g = 9.8). Which configuration stores more energy relative to the floor, and by how much?

Example 13

medium

An engine transfers 6000 J of energy in 30 s. What is its power output?

Example 14

medium

A 1200 kg car speeds up from 10 m/s to 20 m/s. How much energy was added (its KE change)?

Example 15

medium

A pendulum swings from its highest point (at rest, 0.2 m above the bottom) to the lowest point. For a 0.5 kg bob (g = 9.8), find its speed at the bottom.

Example 16

medium

A 2 kg object slides down a frictionless ramp from 5 m height (g = 9.8). What fraction of its initial PE is kinetic at a height of 2 m?

Example 17

medium

A motor uses 500 J to lift a load but only 400 J becomes gravitational PE. Where did the rest go, and how much?

Example 18

medium

A 0.1 kg arrow leaves a bow at 30 m/s. The bow stored elastic PE that became the arrow's KE. How much energy did the bow store (ignore losses)?

Example 19

challenge

A 4 kg block slides 3 m down a 30 degree frictionless incline (g = 9.8). Using energy ideas, find its speed at the bottom if it started at rest.

Example 20

challenge

A 0.05 kg ball is thrown up at 10 m/s (g = 9.8). At the moment its KE has dropped to one-quarter of its initial value, what height has it reached?

Example 21

challenge

A roller coaster car (500 kg) at the top of a 20 m hill moving 5 m/s reaches a second hill. Ignoring friction (g = 9.8), what is the maximum height of a hill it can just crest with zero speed?

Example 22

medium

A 0.2 kg ball rolls off a table 1 m high at 3 m/s (g = 9.8). Find its total mechanical energy relative to the floor.

Example 23

easy

2\,\text{kg}

object moves at

5\,\text{m/s}

. Find its kinetic energy.

Example 24

easy

4\,\text{kg}

rock is at height

5\,\text{m}

(

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

). Find its gravitational PE.

Example 25

easy

A motor delivers

1200\,\text{J}

of energy in

4\,\text{s}

. Find the power.

Example 26

easy

50\,\text{W}

light bulb runs for

30\,\text{s}

. How much energy does it use?

Example 27

medium

0.5\,\text{kg}

ball is dropped from

4\,\text{m}

(

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

). Ignore drag. Find its speed just before hitting the ground.

Example 28

medium

1500\,\text{kg}

car accelerates from rest to

30\,\text{m/s}

. Find the change in KE.

Example 29

medium

3\,\text{kg}

block on a frictionless ramp drops

2\,\text{m}

vertically (

g = 9.8

). Find its KE at the bottom from rest.

Example 30

medium

0.1\,\text{kg}

arrow with

30\,\text{m/s}

speed strikes a target and stops. How much energy is dissipated?

Example 31

medium

An athlete lifts a

40\,\text{kg}

barbell

1.5\,\text{m}

1.5\,\text{s}

(

g = 9.8

). Find the average power.

Example 32

medium

2\,\text{kg}

block slides down a frictionless ramp from

h = 3\,\text{m}

. Find its speed at the bottom (

g = 9.8

Example 33

medium

A spring with

k = 200\,\text{N/m}

is compressed

0.2\,\text{m}

. Find the elastic PE stored.

Example 34

medium

0.5\,\text{kg}

projectile leaves a spring-loaded gun whose spring was compressed

0.1\,\text{m}

with

k = 800\,\text{N/m}

. Find the projectile's launch speed.

Example 35

medium

0.5\,\text{kg}

object has

KE = 100\,\text{J}

. Find its speed.

Example 36

hard

1000\,\text{kg}

car drives uphill, gaining

50\,\text{m}

height while increasing speed from

10\,\text{m/s}

20\,\text{m/s}

(

g = 9.8

). Find the total energy delivered by the engine (ignore friction).

Example 37

hard

2\,\text{kg}

block slides

5\,\text{m}

down a

30^\circ

incline with friction force

4\,\text{N}

(

g = 9.8

). Find its KE at the bottom from rest.

Example 38

hard

A pump lifts

200\,\text{kg}

of water

10\,\text{m}

20\,\text{s}

(

g = 9.8

). Find the average power.

Example 39

hard

0.05\,\text{kg}

ball is thrown up at

20\,\text{m/s}

. At its peak (

g = 9.8

), find the maximum height (energy method).

Example 40

challenge

500\,\text{kg}

roller coaster crests hill A (

h = 30\,\text{m}

) at

4\,\text{m/s}

. Friction dissipates

20\,\text{kJ}

between A and hill B. The car barely reaches hill B with zero speed (

g = 9.8

). Find B's height.

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Related Concepts

Kinetic Energy Potential Energy Work