Static Friction Examples in Physics

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.

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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: 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 θ\theta has μs=0.4\mu_s = 0.4. Find the largest angle at which it remains at rest.

Answer

θmax⁡≈21.8∘\theta_{\max} \approx 21.8^\circ

First step

1
At impending slip: mgsin⁡θ=μsmgcos⁡θmg\sin\theta = \mu_s mg\cos\theta.

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Example 2

medium
A 66 kg block on level ground with μs=0.3\mu_s = 0.3, g=10g = 10 m/s2^2. A rope pulls at θ=37∘\theta = 37^\circ above horizontal with F=25F = 25 N. Does the block move? (sin⁡37∘=0.6\sin 37^\circ = 0.6, cos⁡37∘=0.8\cos 37^\circ = 0.8.)

Example 3

medium
A 55 kg block on a 30∘30^\circ incline, μs=0.4\mu_s = 0.4, g=10g = 10 m/s2^2. Find the friction force needed to keep it static, and whether it actually does. (sin⁡30∘=0.5\sin 30^\circ = 0.5, cos⁡30∘=0.866\cos 30^\circ = 0.866.)

Example 4

hard
Two blocks AA (22 kg, top) and BB (33 kg, bottom) sit stacked on a frictionless floor. Between them μs=0.4\mu_s = 0.4. A horizontal force FF is applied to BB. Find the largest FF for which AA does not slide. (g=10g = 10 m/s2^2.)

Example 5

hard
A 2020 kg block sits on level ground, μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2. A rope pulls at θ\theta above horizontal. Find the angle that minimizes the pulling force needed to set it in motion.

Example 6

hard
A 0.50.5 kg coin sits at radius 0.20.2 m from the center of a turntable, μs=0.4\mu_s = 0.4, g=10g = 10 m/s2^2. Find the maximum angular speed before the coin slips.

Example 7

challenge
A car on a banked curve of radius 8080 m, banking angle 20∘20^\circ, μs=0.3\mu_s = 0.3, g=10g = 10 m/s2^2 (sin⁡=0.342\sin = 0.342, cos⁡=0.940\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 μsN\mu_s N with μs=0.5\mu_s = 0.5 and N=40 NN = 40\,\text{N}. Find the maximum static friction force.

Example 2

easy
A 5 kg block sits on level ground, μs=0.4\mu_s = 0.4, g=10 m/s2g = 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 N15\,\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 N24\,\text{N} with normal force N=60 NN = 60\,\text{N}. Find μs\mu_s.

Example 6

easy
A book on a level desk has μs=0.6\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 μs=0.3\mu_s = 0.3, g=10 m/s2g = 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 N50\,\text{N}. A worker pushes with 30 N30\,\text{N}. What friction force acts on the crate?

Example 9

medium
A 4 kg block on level ground, μs=0.5\mu_s = 0.5, g=10 m/s2g = 10\,\text{m/s}^2, is pushed with 15 N15\,\text{N}. Does it move? Give the friction force.

Example 10

medium
A 6 kg block on a level surface, μs=0.4\mu_s = 0.4, g=10 m/s2g = 10\,\text{m/s}^2, is pushed with 30 N30\,\text{N}. Does it slip?

Example 11

medium
A block sits on an incline at angle θ\theta. As θ\theta increases, it begins to slide at θ=30∘\theta = 30^\circ. Find μs\mu_s.

Example 12

medium
A 10 kg block on a 20∘20^\circ incline, μs=0.5\mu_s = 0.5, g=10 m/s2g = 10\,\text{m/s}^2 (sin⁡20∘=0.342\sin 20^\circ = 0.342, cos⁡20∘=0.940\cos 20^\circ = 0.940). Does it stay at rest?

Example 13

medium
A 3 kg block on level ground has μs=0.6\mu_s = 0.6, μk=0.4\mu_k = 0.4, g=10 m/s2g = 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 NN = 50\,\text{N}. If μs=0.5\mu_s = 0.5, g=10 m/s2g = 10\,\text{m/s}^2, will it stay (not slide down)?

Example 15

medium
A block needs at least 12 N12\,\text{N} to start moving and only 8 N8\,\text{N} to keep moving at constant speed, with N=40 NN = 40\,\text{N}. Find μs\mu_s and μk\mu_k.

Example 16

medium
On a flat bed of a truck, a 5 kg5\,\text{kg} crate has μs=0.4\mu_s = 0.4, g=10 m/s2g = 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 μs=0.6\mu_s = 0.6, g=10 m/s2g = 10\,\text{m/s}^2. A 20 N20\,\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∘30^\circ incline with μs=0.3\mu_s = 0.3, g=10 m/s2g = 10\,\text{m/s}^2 (sin⁡30∘=0.5\sin 30^\circ = 0.5, cos⁡30∘=0.866\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 kg2\,\text{kg}, bottom 3 kg3\,\text{kg}, on a frictionless floor. Between them μs=0.5\mu_s = 0.5, g=10 m/s2g = 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 N20\,\text{N} rod leans so that the floor must supply horizontal friction of 8 N8\,\text{N} to keep it static. The normal force from the floor is 20 N20\,\text{N}. What minimum μs\mu_s prevents slipping?

Example 21

easy
A 33 kg block sits at rest on level ground with μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2. Find the maximum static friction.

Example 22

easy
A horizontal push of 88 N is applied to a 44 kg block on level ground. If μs=0.3\mu_s = 0.3 and g=10g = 10 m/s2^2, find the static friction.

Example 23

easy
A box of weight 8080 N on level ground has μs=0.25\mu_s = 0.25. Find the minimum horizontal force to set it in motion.

Example 24

easy
A 1010 kg block on a level floor has μs=0.4\mu_s = 0.4, g=10g = 10 m/s2^2. A force of 3535 N is applied horizontally. Find the static friction.

Example 25

easy
A 55 kg block on a level surface barely slips when pushed with 3030 N. Find μs\mu_s. (g=10g = 10 m/s2^2.)

Example 26

medium
A 55 kg block sits on a 25∘25^\circ incline with μs=0.6\mu_s = 0.6. Does it stay? (g=10g = 10 m/s2^2, sin⁡25∘=0.423\sin 25^\circ = 0.423, cos⁡25∘=0.906\cos 25^\circ = 0.906.)

Example 27

medium
A 22 kg block on a level surface with μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2. A horizontal pull and a vertical lift of 55 N (upward) are applied. Find the new fs,max⁡f_{s,\max}.

Example 28

medium
A 44 kg block on a level floor with μs=0.5\mu_s = 0.5 is pushed at 30∘30^\circ below the horizontal with force FF. Find fs,max⁡f_{s,\max} if F=20F = 20 N. (g=10g = 10 m/s2^2.)

Example 29

medium
A book is pressed against a vertical wall by a horizontal force F=40F = 40 N. Mass m=2m = 2 kg, μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2. Does it slide down?

Example 30

medium
A 33 kg block on level ground has μs=0.4\mu_s = 0.4, g=10g = 10 m/s2^2. It is pushed horizontally with a steadily increasing force. Find the force at which it just begins to slip.

Example 31

medium
A 22 kg block sits on a board. The board is tilted slowly. Slipping begins at θ=18∘\theta = 18^\circ. Find μs\mu_s.

Example 32

medium
A crate sits in the bed of a truck, μs=0.5\mu_s = 0.5. The truck accelerates forward at 44 m/s2^2 (g=10g = 10 m/s2^2). Does the crate slide?

Example 33

medium
On a level surface, max static friction on a block is 1414 N, kinetic friction is 1010 N. A constant 1212 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 μs=0.7\mu_s = 0.7 and g=10g = 10 m/s2^2, find the maximum acceleration.

Example 35

medium
A 44 kg block on a level surface, μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2. A vertical downward force of 2020 N also presses the block. Find the new fs,max⁡f_{s,\max}.

Example 36

hard
A car rounds a flat curve of radius 5050 m. μs=0.6\mu_s = 0.6, g=10g = 10 m/s2^2. Find the maximum speed without slipping.

Example 37

hard
A 1010 kg block on a 30∘30^\circ incline with μs=0.5\mu_s = 0.5, g=10g = 10 m/s2^2 (sin⁡=0.5\sin = 0.5, cos⁡=0.866\cos = 0.866). Find the minimum horizontal force (toward the incline) keeping the block from sliding down.

Example 38

hard
A 55 kg crate is on a conveyor belt that accelerates horizontally at aa. The friction coefficient is μs=0.3\mu_s = 0.3, g=10g = 10 m/s2^2. Find the largest aa for which the crate moves with the belt.

Example 39

hard
A 22 kg block sits on top of a 33 kg block; both on a frictionless floor. The contact coefficient is μs=0.2\mu_s = 0.2, g=10g = 10 m/s2^2. A horizontal force is applied to the top block. Find the largest force without slipping.

Example 40

challenge
A uniform ladder of weight WW leans on a frictionless wall and a floor with coefficient μs\mu_s. The ladder makes angle θ\theta with the floor. Find the minimum angle for which the ladder does not slip. (Ignore wall friction.)
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Background Knowledge

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

frictionnormal force