Work Examples in Physics

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

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 transfer of energy that occurs when a force causes an object to move through a distance in the direction of the force, calculated as $W = Fd\cos\theta$ , where $\theta$ is the angle between the force and the displacement. Measured in joules (J).

Energy transferred by pushing something through space — force and displacement must both be present.

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 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 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 person pushes a box with a force of

50 \text{ N}

over a distance of

10 \text{ m}

in the direction of the force. How much work is done?

Answer

W = 500 \text{ J}

First step

Because the force is in the same direction as the displacement, use

W = Fd

Full solution

2
Substitute the values: $W = 50 \times 10$ .
3
$W = 500 \text{ J}$

Work is done when a force causes displacement. When force and displacement are in the same direction, work equals force times distance.

Example 2

medium

A person pulls a sled with

100 \text{ N}

30°

above the horizontal for

20 \text{ m}

. How much work is done?

Example 3

medium

A person pulls a sled with a rope at

60°

above horizontal, applying

40\text{ N}

for

10\text{ m}

. Find the work done.

Example 4

medium

0.4\text{ kg}

ball is thrown up to a height of

5\text{ m}

. How much work does gravity do as it rises (use

g = 9.8

Example 5

hard

A box of

3\text{ kg}

is pushed up a

20°

frictionless incline by a force parallel to the incline. It moves

5\text{ m}

from rest to

4\text{ m/s}

. Find the work done by the applied force (use

g = 9.8

\sin 20° \approx 0.342

Practice Problems

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

Example 1

medium

5 \text{ kg}

box is lifted

3 \text{ m}

vertically at constant speed. How much work is done by the lifting force? Use

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

Example 2

hard

A child pushes a

20 \text{ kg}

crate

8 \text{ m}

across a floor with a

60 \text{ N}

horizontal force. Friction exerts

40 \text{ N}

opposing the motion. What is the net work done on the crate?

Example 3

easy

A 10 N force pushes a box 4 m in the direction of the force. How much work is done?

Example 4

easy

A waiter holds a tray still while standing in place. How much work is done on the tray?

Example 5

easy

A force of 20 N acts at 60 degrees to a 5 m displacement. Find the work done.

Example 6

easy

Friction of 6 N acts opposite to a box moving 3 m. How much work does friction do?

Example 7

easy

How much work lifts a 5 kg mass 2 m at constant speed (g = 9.8)?

Example 8

easy

A 3 N force moves an object 6 m along its line of action. Find the work.

Example 9

easy

Work has the same SI unit as which quantity?

Example 10

easy

A horizontal force does 40 J of work moving a crate 8 m horizontally. What was the force?

Example 11

medium

A 25 N force pulls a sled at 37 degrees to the ground over 10 m (\cos 37 \approx 0.8). How much work does it do?

Example 12

medium

A net force of 12 N acts on a 4 kg cart over 5 m. Using work, what is the cart's final KE if it started from rest?

Example 13

medium

A person pushes with 50 N but also fights 20 N of friction over 4 m. What net work is done on the object?

Example 14

medium

Lifting a 10 kg box up a 4 m vertical wall versus pushing it up a 8 m frictionless ramp to the same 4 m height (g = 9.8). Which path does more work against gravity?

Example 15

medium

A spring with k = 200 N/m is compressed 0.1 m. How much work was done on the spring?

Example 16

medium

A 1500 kg car brakes from 20 m/s to rest. How much work did the brakes do (the work-energy theorem)?

Example 17

medium

A force does 90 J of work over 6 m at 30 degrees to the displacement. What is the magnitude of the force? (\cos 30 \approx 0.866)

Example 18

challenge

A 2 kg block is pushed 5 m across a floor by a constant 15 N horizontal force against friction of 5 N. Find the block's final speed from rest using work.

Example 19

challenge

A variable force on a graph is constant 4 N for the first 3 m, then drops to 2 N for the next 2 m, all along the motion. Find the total work.

Example 20

challenge

A 0.5 kg ball is thrown straight up and gravity does -12 J of work as it rises (g = 9.8). What height did it reach, and what was its launch speed?

Example 21

medium

A 6 kg box is dragged 5 m by a 30 N force at 0 degrees, then friction of 12 N opposes over the same 5 m. Find the total work done on the box.

Example 22

medium

How much work does gravity do on a 2 kg object that falls 4 m (g = 9.8)?

Example 23

easy

15\text{ N}

force pushes a box

6\text{ m}

in the direction of the force. Find the work done.

Example 24

easy

A force of

25\text{ N}

acts perpendicular to the motion of an object moving

4\text{ m}

. Find the work done.

Example 25

easy

A boy pushes a wall with

80\text{ N}

for

30\text{ s}

, but the wall does not move. How much work does he do on the wall?

Example 26

easy

Gravity pulls a

2\text{ kg}

rock down

3\text{ m}

. How much work does gravity do (use

g = 9.8

Example 27

easy

200\text{ J}

of work moves a box

50\text{ m}

horizontally. What was the force?

Example 28

medium

Lifting a

25\text{ kg}

box

1.5\text{ m}

at constant speed. Find the work done by the lifter (use

g = 9.8

Example 29

medium

5\text{ kg}

cart is pushed

6\text{ m}

across a floor by

30\text{ N}

, with friction of

10\text{ N}

opposing. What is the net work done on the cart?

Example 30

medium

A horizontal force does

500\text{ J}

of work over

25\text{ m}

. Find the magnitude of the force.

Example 31

medium

10\text{ N}

horizontal force pushes a

4\text{ kg}

block

5\text{ m}

up a smooth

30°

incline. Find the work done by this horizontal force.

Example 32

medium

30\text{ N}

force pulls a sled

12\text{ m}

45°

above horizontal. Find the work done by the force (use

\cos 45° \approx 0.707

Example 33

medium

A horizontal

50\text{ N}

force pushes a

20\text{ kg}

crate at constant velocity for

8\text{ m}

. How much work does friction do?

Example 34

medium

A spring with constant

k = 400\text{ N/m}

is stretched

0.2\text{ m}

. How much work was done on the spring?

Example 35

hard

10\text{ kg}

box slides

4\text{ m}

down a

37°

incline with

\mu_k = 0.25

. Find the work done by friction (use

g = 9.8

\cos 37° \approx 0.8

Example 36

hard

A variable force

F(x) = 5x

(N, with

x

in m) acts on an object moving from

x = 0

x = 4\text{ m}

. Find the work done.

Example 37

hard

80\text{ kg}

person climbs stairs

10\text{ m}

tall and

20\text{ m}

along the slope. How much work do they do against gravity (use

g = 9.8

Example 38

hard

1500\text{ kg}

elevator accelerates from rest to

3\text{ m/s}

over

4\text{ m}

vertically. Find the work done by the cable (use

g = 9.8

Example 39

hard

A force-vs-position graph shows

F = 8\text{ N}

from

x = 0

x = 3\text{ m}

, then linearly decreases to

0\text{ N}

x = 6\text{ m}

. Find the total work.

Example 40

challenge

2\text{ kg}

block is pulled along a rough horizontal floor by a rope at

30°

above horizontal with

20\text{ N}

for

6\text{ m}

\mu_k = 0.2

. Find the work done by friction (use

g = 9.8

Example 41

challenge

A spring is compressed

0.3\text{ m}

from natural length and then further to

0.5\text{ m}

. With

k = 200\text{ N/m}

, how much extra work is needed for that additional compression?

Example 42

challenge

4\text{ kg}

block rests on a horizontal surface. A force vector

\vec{F} = (12, 5)

N is applied while the block moves through displacement

\vec{d} = (3, 0)

m. Find the work done.

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Related Concepts

Force Energy Kinetic Energy Power

Background Knowledge

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

forceenergy