Static 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 Static 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

The friction force that prevents a stationary object from beginning to slide when an external force is applied, adjusting in magnitude up to a maximum.

It takes more force to get something moving than to keep it moving.

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: Static 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 static 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?

Worked Examples

Example 1

medium

A block on an incline at angle

\theta

has

\mu_s = 0.4

. Find the largest angle at which it remains at rest.

Answer

θ_{\max} \approx {21.8}^{\circ}

First step

At impending slip:

mg\sin\theta = \mu_s mg\cos\theta

See the full worked solution + why-it-works coaching

SetupKey insightWhy it worksCommon pitfallConnection

Unlock answer keys One Family plan — every worked solution, all subjects

Example 2

medium

6

kg block on level ground with

\mu_s = 0.3

g = 10

m/s

^2

. A rope pulls at

\theta = 37^\circ

above horizontal with

F = 25

N. Does the block move? (

\sin 37^\circ = 0.6

\cos 37^\circ = 0.8

Example 3

medium

5

kg block on a

30^\circ

incline,

\mu_s = 0.4

g = 10

m/s

^2

. Find the friction force needed to keep it static, and whether it actually does. (

\sin 30^\circ = 0.5

\cos 30^\circ = 0.866

Example 4

hard

Two blocks

A

(

2

kg, top) and

B

(

3

kg, bottom) sit stacked on a frictionless floor. Between them

\mu_s = 0.4

. A horizontal force

F

is applied to

B

. Find the largest

F

for which

A

does not slide. (

g = 10

m/s

^2

Example 5

hard

20

kg block sits on level ground,

\mu_s = 0.5

g = 10

m/s

^2

. A rope pulls at

\theta

above horizontal. Find the angle that minimizes the pulling force needed to set it in motion.

Example 6

hard

0.5

kg coin sits at radius

0.2

m from the center of a turntable,

\mu_s = 0.4

g = 10

m/s

^2

. Find the maximum angular speed before the coin slips.

Example 7

challenge

A car on a banked curve of radius

80

m, banking angle

20^\circ

\mu_s = 0.3

g = 10

m/s

^2

(

\sin = 0.342

\cos = 0.940

). Find the maximum speed without slipping.

Practice Problems

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

Example 1

easy

A box rests on a level floor. The maximum static friction is

\mu_s N

with

\mu_s = 0.5

and

N = 40\,\text{N}

. Find the maximum static friction force.

Example 2

easy

A 5 kg block sits on level ground,

\mu_s = 0.4

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

. Find the maximum static friction.

Example 3

easy

A 10 N horizontal push is applied to a resting box; maximum static friction is

15\,\text{N}

. Does it move, and what is the actual friction force?

Example 4

easy

Why is it generally harder to start a heavy box moving than to keep it sliding?

Example 5

easy

Maximum static friction is

24\,\text{N}

with normal force

N = 60\,\text{N}

. Find

\mu_s

Example 6

easy

A book on a level desk has

\mu_s = 0.6

. With no horizontal push applied, what is the static friction force on it?

Example 7

easy

A 2 kg block on level ground has

\mu_s = 0.3

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

. What is the minimum horizontal force to start it sliding?

Example 8

easy

A resting crate has maximum static friction

50\,\text{N}

. A worker pushes with

30\,\text{N}

. What friction force acts on the crate?

Example 9

medium

A 4 kg block on level ground,

\mu_s = 0.5

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

, is pushed with

15\,\text{N}

. Does it move? Give the friction force.

Example 10

medium

A 6 kg block on a level surface,

\mu_s = 0.4

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

, is pushed with

30\,\text{N}

. Does it slip?

Example 11

medium

A block sits on an incline at angle

\theta

. As

\theta

increases, it begins to slide at

\theta = 30^\circ

. Find

\mu_s

Example 12

medium

A 10 kg block on a

20^\circ

incline,

\mu_s = 0.5

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

(

\sin 20^\circ = 0.342

\cos 20^\circ = 0.940

). Does it stay at rest?

Example 13

medium

A 3 kg block on level ground has

\mu_s = 0.6

\mu_k = 0.4

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

. A force ramps up slowly. What is the friction force just before it starts to slide?

Example 14

medium

A 2 kg book is pressed against a vertical wall by a horizontal force

N = 50\,\text{N}

. If

\mu_s = 0.5

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

, will it stay (not slide down)?

Example 15

medium

A block needs at least

12\,\text{N}

to start moving and only

8\,\text{N}

to keep moving at constant speed, with

N = 40\,\text{N}

. Find

\mu_s

and

\mu_k

Example 16

medium

On a flat bed of a truck, a

5\,\text{kg}

crate has

\mu_s = 0.4

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

. What maximum acceleration can the truck have without the crate sliding?

Example 17

medium

A 5 kg block on level ground has

\mu_s = 0.6

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

. A

20\,\text{N}

horizontal push is applied. Does it move, and what is the friction force?

Example 18

challenge

A 4 kg block rests on a

30^\circ

incline with

\mu_s = 0.3

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

(

\sin 30^\circ = 0.5

\cos 30^\circ = 0.866

). It does not stay by friction alone. Find the minimum force along the incline (up-slope) to hold it static.

Example 19

challenge

Two blocks are stacked: top

2\,\text{kg}

, bottom

3\,\text{kg}

, on a frictionless floor. Between them

\mu_s = 0.5

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

. A horizontal force pushes the bottom block. Find the maximum force so the top block does not slide off.

Example 20

challenge

A ladder problem simplified: a uniform

20\,\text{N}

rod leans so that the floor must supply horizontal friction of

8\,\text{N}

to keep it static. The normal force from the floor is

20\,\text{N}

. What minimum

\mu_s

prevents slipping?

Example 21

easy

3

kg block sits at rest on level ground with

\mu_s = 0.5

g = 10

m/s

^2

. Find the maximum static friction.

Example 22

easy

A horizontal push of

8

N is applied to a

4

kg block on level ground. If

\mu_s = 0.3

and

g = 10

m/s

^2

, find the static friction.

Example 23

easy

A box of weight

80

N on level ground has

\mu_s = 0.25

. Find the minimum horizontal force to set it in motion.

Example 24

easy

10

kg block on a level floor has

\mu_s = 0.4

g = 10

m/s

^2

. A force of

35

N is applied horizontally. Find the static friction.

Example 25

easy

5

kg block on a level surface barely slips when pushed with

30

N. Find

\mu_s

. (

g = 10

m/s

^2

Example 26

medium

5

kg block sits on a

25^\circ

incline with

\mu_s = 0.6

. Does it stay? (

g = 10

m/s

^2

\sin 25^\circ = 0.423

\cos 25^\circ = 0.906

Example 27

medium

2

kg block on a level surface with

\mu_s = 0.5

g = 10

m/s

^2

. A horizontal pull and a vertical lift of

5

N (upward) are applied. Find the new

f_{s,\max}

Example 28

medium

4

kg block on a level floor with

\mu_s = 0.5

is pushed at

30^\circ

below the horizontal with force

F

. Find

f_{s,\max}

F = 20

N. (

g = 10

m/s

^2

Example 29

medium

A book is pressed against a vertical wall by a horizontal force

F = 40

N. Mass

m = 2

kg,

\mu_s = 0.5

g = 10

m/s

^2

. Does it slide down?

Example 30

medium

3

kg block on level ground has

\mu_s = 0.4

g = 10

m/s

^2

. It is pushed horizontally with a steadily increasing force. Find the force at which it just begins to slip.

Example 31

medium

2

kg block sits on a board. The board is tilted slowly. Slipping begins at

\theta = 18^\circ

. Find

\mu_s

Example 32

medium

A crate sits in the bed of a truck,

\mu_s = 0.5

. The truck accelerates forward at

4

m/s

^2

(

g = 10

m/s

^2

). Does the crate slide?

Example 33

medium

On a level surface, max static friction on a block is

14

N, kinetic friction is

10

N. A constant

12

N push is applied. Does the block accelerate?

Example 34

medium

A car on a flat road accelerates from rest by static friction with the road. If

\mu_s = 0.7

and

g = 10

m/s

^2

, find the maximum acceleration.

Example 35

medium

4

kg block on a level surface,

\mu_s = 0.5

g = 10

m/s

^2

. A vertical downward force of

20

N also presses the block. Find the new

f_{s,\max}

Example 36

hard

A car rounds a flat curve of radius

50

\mu_s = 0.6

g = 10

m/s

^2

. Find the maximum speed without slipping.

Example 37

hard

10

kg block on a

30^\circ

incline with

\mu_s = 0.5

g = 10

m/s

^2

(

\sin = 0.5

\cos = 0.866

). Find the minimum horizontal force (toward the incline) keeping the block from sliding down.

Example 38

hard

5

kg crate is on a conveyor belt that accelerates horizontally at

a

. The friction coefficient is

\mu_s = 0.3

g = 10

m/s

^2

. Find the largest

a

for which the crate moves with the belt.

Example 39

hard

2

kg block sits on top of a

3

kg block; both on a frictionless floor. The contact coefficient is

\mu_s = 0.2

g = 10

m/s

^2

. A horizontal force is applied to the top block. Find the largest force without slipping.

Example 40

challenge

A uniform ladder of weight

W

leans on a frictionless wall and a floor with coefficient

\mu_s

. The ladder makes angle

\theta

with the floor. Find the minimum angle for which the ladder does not slip. (Ignore wall friction.)

← Back to Static Friction Formula Explained Practice Mode

Related Concepts

Friction Normal Force Kinetic Friction Equilibrium

Background Knowledge

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

frictionnormal force