Work-Energy Theorem Examples in Physics

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

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 net work done on an object by all forces acting on it equals the change in its kinetic energy.

The total work done on an object is exactly what changes its kinetic energy.

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: Work-Energy Theorem asks what energy enters, leaves, stays stored, or changes form in the chosen system.

Common stuck point: Students often know a formula related to work-energy theorem 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

4 \text{ kg}

box initially at rest is pushed with a net force of

20 \text{ N}

over

5 \text{ m}

. What is the final speed of the box?

Answer

v_f \approx 7.07 \text{ m/s}

First step

The work-energy theorem states:

W_{\text{net}} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2

Full solution

2
Net work done: $W = Fd = 20 \times 5 = 100 \text{ J}$ .
3
Since $v_i = 0$ : $100 = \frac{1}{2}(4)v_f^2 \implies v_f = \sqrt{\frac{200}{4}} = \sqrt{50} \approx 7.07 \text{ m/s}$

The work-energy theorem directly connects the net work done on an object to its change in kinetic energy. It provides an alternative to using kinematics equations for finding final speeds.

Example 2

medium

1500 \text{ kg}

car traveling at

25 \text{ m/s}

brakes with a friction force of

7500 \text{ N}

. How far does it take to stop?

Example 3

medium

1500\text{ kg}

car accelerates from

10\text{ m/s}

20\text{ m/s}

. How much net work was done?

Example 4

medium

1\text{ kg}

box at

10\text{ m/s}

is slowed by friction to

4\text{ m/s}

over

7\text{ m}

. Find the friction force.

Example 5

hard

2\text{ kg}

block at

6\text{ m/s}

slides up a rough incline (

\mu_k = 0.3

, angle

25°

). Find the distance it travels before stopping (use

g = 9.8

\sin 25° \approx 0.423

\cos 25° \approx 0.906

Practice Problems

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

Example 1

medium

0.5 \text{ kg}

ball moving at

8 \text{ m/s}

is hit by a bat that does

25 \text{ J}

of work on it. What is the ball's final speed?

Example 2

hard

2 \text{ kg}

block slides down a rough incline (

\mu_k = 0.2

) of height

5 \text{ m}

and length

10 \text{ m}

, starting from rest. What is its speed at the bottom? Use

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

Example 3

easy

A net force does 30 J of work on a resting object. What is its final kinetic energy?

Example 4

easy

An object's KE goes from 10 J to 25 J. What net work was done?

Example 5

easy

Friction does -20 J of net work on a sliding block. What happens to its KE?

Example 6

easy

A 2 kg object speeds up from 0 to 3 m/s. What net work was done?

Example 7

easy

Does the work-energy theorem use net work or the work of a single force?

Example 8

easy

An object moves at constant speed. What is the net work done on it?

Example 9

easy

A 1 kg object slows from 4 m/s to 2 m/s. What is the net work?

Example 10

easy

A 3 kg cart gains 24 J of KE. What is the change in its kinetic energy by the theorem?

Example 11

medium

A 5 N net force acts over 4 m on a 2 kg object from rest. Find its final speed.

Example 12

medium

A 1000 kg car at 15 m/s brakes to a stop. What net work did the brakes do?

Example 13

medium

A 2 kg block at 5 m/s is pushed with 8 N over 3 m in its direction of motion. Find its final speed.

Example 14

medium

A 0.5 kg ball at 6 m/s is stopped by friction over 1.5 m. Find the friction force.

Example 15

medium

A 4 kg object moving at 3 m/s has 18 J of net work done on it (in its direction). Find its final speed.

Example 16

medium

A 1500 kg car needs to go from 10 m/s to 30 m/s. What net work is required?

Example 17

medium

A 2 kg block is pushed 4 m by 12 N while friction of 4 N opposes it. Find the final speed from rest.

Example 18

challenge

A 0.145 kg baseball leaves a bat at 45 m/s after entering at 40 m/s (opposite direction). The bat acts over 0.7 m. Find the average force (use change in KE magnitude).

Example 19

challenge

A 3 kg block slides down a frictionless ramp from 2 m, then a 5 N friction force acts over 4 m on flat ground (g = 9.8). Find its final KE.

Example 20

challenge

A 1200 kg car's engine and friction together do net work of 240000 J accelerating it from rest. Find the final speed.

Example 21

medium

A 2 kg object at 8 m/s has -48 J of net work done on it. Find its final speed.

Example 22

medium

A 10 N net force acts on a 5 kg object over 2 m from rest. Find the final KE and speed.

Example 23

easy

2\text{ kg}

cart at rest has

16\text{ J}

of net work done on it. Find its final speed.

Example 24

easy

0.2\text{ kg}

puck slides at

5\text{ m/s}

and comes to rest. How much net work was done on it?

Example 25

easy

0.5\text{ kg}

ball's kinetic energy increases from

4\text{ J}

9\text{ J}

. What net work was done?

Example 26

easy

1\text{ kg}

object's speed doubles from

2\text{ m/s}

4\text{ m/s}

. How much net work was done?

Example 27

easy

4\text{ kg}

block starts from rest. A net force of

10\text{ N}

pushes it

5\text{ m}

. Find its final speed.

Example 28

medium

3\text{ kg}

block at

4\text{ m/s}

is pushed by a net force of

6\text{ N}

over

5\text{ m}

in its direction of motion. Find its final speed.

Example 29

medium

0.4\text{ kg}

arrow leaves a bow at

50\text{ m/s}

. The bowstring acts over

0.6\text{ m}

. What average net force did the string exert?

Example 30

medium

1200\text{ kg}

car needs to slow from

25\text{ m/s}

15\text{ m/s}

. How much net work must the brakes do?

Example 31

medium

0.05\text{ kg}

bullet enters a wood block at

400\text{ m/s}

and embeds

0.1\text{ m}

deep before stopping. What average force did the wood exert on it?

Example 32

medium

2\text{ kg}

block at rest is pulled by

15\text{ N}

forward and resisted by

5\text{ N}

friction over

4\text{ m}

. Find the final speed.

Example 33

medium

A skier of mass

60\text{ kg}

moves down a

10\text{ m}

vertical drop on a frictionless slope, starting from rest. Find her speed at the bottom (use

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

Example 34

medium

0.3\text{ kg}

ball is dropped from rest and hits the ground at

6\text{ m/s}

. How much net work did gravity do on it?

Example 35

hard

5\text{ kg}

block at

8\text{ m/s}

slides up a frictionless

30°

incline. How far along the incline does it travel before stopping (use

g = 9.8

Example 36

hard

0.1\text{ kg}

puck on frictionless ice is hit briefly so it then coasts

20\text{ m}

4\text{ s}

. What net work did the hit do on the puck?

Example 37

hard

1500\text{ kg}

car traveling at

20\text{ m/s}

skids to a stop in

25\text{ m}

. Find the coefficient of kinetic friction (use

g = 9.8

Example 38

hard

0.5\text{ kg}

ball is dropped from

5\text{ m}

onto a spring, compressing it

0.1\text{ m}

before stopping. Find the average spring force (use

g = 9.8

Example 39

hard

1\text{ kg}

box is pulled by a horizontal

20\text{ N}

force across a

5\text{ m}

rough floor (

\mu_k = 0.4

). Find its final speed from rest (use

g = 9.8

Example 40

challenge

0.2\text{ kg}

ball on a

1\text{ m}

string is released from rest at horizontal. Using the work-energy theorem, find its speed at the lowest point of the swing (use

g = 9.8

Example 41

challenge

0.05\text{ kg}

dart at

30\text{ m/s}

is brought to rest by a foam block over

0.02\text{ m}

. Find the average force the foam exerts.

Example 42

challenge

A loaded

40\text{ kg}

cart at

3\text{ m/s}

is pushed up a

4\text{ m}

-long ramp with

200\text{ N}

along the slope. Friction does

-100\text{ J}

on the trip. Gravity component along slope removes

300\text{ J}

. Find its speed at the top.

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Related Concepts

Work Kinetic Energy Power

Background Knowledge

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

workkinetic energy