Friction Examples: 47 Problems with Answers

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

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A contact force that opposes the relative motion or tendency of motion between two surfaces in contact.

The resistance you feel when sliding something across a rough surface — it always acts opposite to motion.

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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: Friction asks students to choose the object, list external interactions, and reason from the resulting force or torque pattern.

Common stuck point: Students often know a formula related to friction but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Have I isolated one system and listed the external forces or torques acting on it before applying a law?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Free Body Diagrams Mistakes

Worked Examples

Example 1

medium

20 \text{ kg}

box sits on a surface with a coefficient of kinetic friction

\mu_k = 0.3

. What force is needed to pull it at constant velocity?

Answer

F_{applied} = 58.8 N

First step

Calculate the normal force:

N = m g = 20 \times 9.8 = 196 N

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Example 2

hard

15 \text{ kg}

block on a surface (

\mu_k = 0.25

) is pushed with

80 \text{ N}

. What is the acceleration?

Example 3

medium

6 \text{ kg}

block is pushed with a horizontal force

F

and starts to slide when

F

exceeds

24 \text{ N}

. Find

\mu_s

. Use

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

Example 4

hard

50 \text{ kg}

crate is pushed up a

30^\circ

incline at constant speed by a force parallel to the slope.

\mu_k = 0.2

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

. Find the applied force.

Practice Problems

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

Example 1

medium

The coefficient of static friction between a box and the floor is

\mu_s = 0.4

. If the box weighs

98 \text{ N}

, what is the maximum static friction force?

Example 2

medium

12 \text{ kg}

crate is pulled across a level floor at constant speed by a horizontal

29.4 \text{ N}

force. What is the coefficient of kinetic friction?

Example 3

easy

A surface has

\mu=0.4

and a normal force of

50\text{ N}

. Find the friction force.

Example 4

easy

In which direction does kinetic friction act?

Example 5

easy

10\text{ kg}

box on a flat floor (

g=10

) has

\mu=0.3

. Find the friction force when sliding.

Example 6

easy

Does friction depend on the contact area for solid surfaces (standard model)?

Example 7

easy

Which is usually larger: maximum static friction or kinetic friction?

Example 8

easy

A box needs

25\text{ N}

to start sliding and only

18\text{ N}

to keep moving. Which value is kinetic friction?

Example 9

easy

The coefficient of friction

\mu

has what units?

Example 10

easy

5\text{ kg}

box (

g=10

) slides on a floor with friction

f=20\text{ N}

. Find

\mu

Example 11

medium

4\text{ kg}

box (

g=10

\mu=0.25

) is pushed with

20\text{ N}

on a flat floor. Find its acceleration.

Example 12

medium

2\text{ kg}

block on a

30^\circ

incline (

g=10

\cos 30^\circ\approx 0.87

). Find the normal force and the friction with

\mu=0.2

Example 13

medium

50\text{ N}

horizontal push just fails to move a

20\text{ kg}

box (

g=10

). What is the minimum coefficient of static friction?

Example 14

medium

A car skids to a stop from

20\text{ m/s}

with

\mu=0.5

(

g=10

). Find its deceleration.

Example 15

medium

3\text{ kg}

box (

g=10

\mu_k=0.3

) is given a push and slides freely (push removed). Find its deceleration.

Example 16

medium

Why does friction not depend on whether you stack a book flat or on its edge (same book, same floor)?

Example 17

challenge

4\text{ kg}

block on a

37^\circ

incline (

g=10

\sin 37^\circ=0.6

\cos 37^\circ=0.8

\mu_k=0.25

) slides down. Find its acceleration.

Example 18

challenge

10\text{ kg}

box (

g=10

\mu_k=0.2

) is pulled by a rope at

30^\circ

above horizontal with

40\text{ N}

(

\cos 30^\circ\approx 0.87

\sin 30^\circ=0.5

). Find the friction force.

Example 19

challenge

A car rounds a flat curve of radius

50\text{ m}

relying on friction (

\mu=0.8

g=10

). Find the maximum safe speed.

Example 20

medium

2\text{ kg}

box (

g=10

\mu_k=0.5

) slides freely after a push. Find its deceleration.

Example 21

medium

20\text{ kg}

crate (

g=10

) needs

80\text{ N}

to start sliding. Find the coefficient of static friction.

Example 22

medium

A hockey puck slides

45\text{ m}

before stopping from

30\text{ m/s}

(

g=10

). Find

\mu_k

(use

v^2=2ad

Example 23

easy

A box on the floor has weight

200 \text{ N}

and

\mu_k = 0.2

. Find the kinetic friction force when sliding.

Example 24

easy

15 \text{ kg}

crate on a horizontal floor experiences

\mu_s = 0.5

. Find the maximum static friction. Use

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

Example 25

easy

10 \text{ kg}

box on a flat floor has

\mu_s = 0.3

. A horizontal push of

20 \text{ N}

is applied. Does it slide? Use

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

Example 26

easy

4 \text{ kg}

block slides on a floor with

\mu_k = 0.25

(

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

). Find the friction force on it.

Example 27

medium

5 \text{ kg}

block is pushed with

30 \text{ N}

horizontally;

\mu_k = 0.4

(

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

). Find its acceleration.

Example 28

medium

20 \text{ kg}

box on a horizontal floor needs

60 \text{ N}

to start moving. Find

\mu_s

. Use

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

Example 29

medium

2 \text{ kg}

block slides at

10 \text{ m/s}

on a floor;

\mu_k = 0.5

(

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

). How far does it travel before stopping?

Example 30

medium

A block on a

30^\circ

incline (

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

) needs

\mu_s \ge \tan 30^\circ

to remain stationary. Find

\mu_s

Example 31

medium

3 \text{ kg}

block pushed with

25 \text{ N}

horizontally has

\mu_s = 0.4

\mu_k = 0.3

(

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

). Find the friction force.

Example 32

medium

1 \text{ kg}

block slides on a horizontal floor and decelerates at

4 \text{ m/s}^2

. Find

\mu_k

(

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

Example 33

medium

50 \text{ kg}

sled on snow has

\mu_k = 0.05

(

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

). What horizontal force keeps it moving at constant velocity?

Example 34

hard

4 \text{ kg}

block on a horizontal floor (

\mu_k = 0.3

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

) is pulled by a rope at

37^\circ

above horizontal with

30 \text{ N}

(

\sin37^\circ = 0.6

\cos 37^\circ = 0.8

). Find its acceleration.

Example 35

hard

5 \text{ kg}

block slides down a

37^\circ

incline (

\mu_k = 0.2

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

\sin 37^\circ = 0.6

\cos 37^\circ = 0.8

). Find its acceleration.

Example 36

hard

A car traveling at

20 \text{ m/s}

skids to a stop in

40 \text{ m}

. Find

\mu_k

between tires and road. Use

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

Example 37

hard

10 \text{ kg}

box is on a

20^\circ

incline. The coefficient of static friction is

\mu_s = 0.5

. Will it slide? Use

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

Example 38

hard

2 \text{ kg}

block sits on a

3 \text{ kg}

board on a frictionless floor. The coefficient of static friction between block and board is

0.3

. What's the maximum acceleration the system can have without the block slipping? Use

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

Example 39

hard

A car rounds a banked curve of radius

50 \text{ m}

20 \text{ m/s}

on an icy (frictionless) road. What banking angle is required? Use

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

Example 40

hard

1 \text{ kg}

puck slides off a horizontal table at

4 \text{ m/s}

after being pushed across

2 \text{ m}

of rough surface (

\mu_k = 0.2

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

). What was its initial speed?

Example 41

hard

4 \text{ kg}

block on a horizontal surface is pulled by a

30 \text{ N}

horizontal force;

\mu_k = 0.25

(

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

). How much work does friction do in

5 \text{ m}

Example 42

challenge

A block on a rough incline of angle

\theta

is at rest. The angle is slowly increased until the block just begins to slide at

\theta = 25^\circ

. Find

\mu_s

Example 43

challenge

2 \text{ kg}

block on a

30^\circ

rough incline (

\mu_k = 0.1

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

) is given a push up the slope at

6 \text{ m/s}

. How far up the slope does it travel before stopping?

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Related Concepts

Force Normal Force Kinetic Friction Static Friction

Background Knowledge

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

forcenormal force