Friction Worked Examples Cheat Sheet

This cheat sheet covers worked examples for friction forces in common high school physics problems. Students need it because friction questions often combine force diagrams, Newton’s second law, and careful sign choices. It focuses on deciding whether friction is static or kinetic, finding the normal force, and solving for acceleration or required applied force.

The core idea is that friction acts parallel to a surface and opposes relative motion or possible slipping. Static friction can adjust up to $f_s \le \mu_s F_N$ , while kinetic friction is usually modeled as $f_k = \mu_k F_N$ . Most examples begin with a free-body diagram, then use $\sum F = ma$ separately along perpendicular axes.

On inclines, weight components such as $mg\sin\theta$ and $mg\cos\theta$ are essential.

Key Facts

Kinetic friction has magnitude $f_k = \mu_k F_N$ and acts opposite the direction of sliding motion.
Static friction satisfies $f_s \le \mu_s F_N$ , so its value changes as needed until it reaches $f_{s,\max} = \mu_s F_N$ .
On a horizontal surface with no vertical acceleration, the normal force is $F_N = mg$ if no other vertical forces act.
Newton’s second law is applied as $\sum F_x = ma_x$ and $\sum F_y = ma_y$ for chosen axes.
For an object on an incline, the weight components are $mg\sin\theta$ down the ramp and $mg\cos\theta$ into the ramp.
For an object on an incline with no acceleration perpendicular to the surface, the normal force is $F_N = mg\cos\theta$ .
An object begins to slip on an incline when $mg\sin\theta > \mu_s mg\cos\theta$ , which simplifies to $\tan\theta > \mu_s$ .
The coefficient of friction has no units because $\mu = \frac{f}{F_N}$ is a ratio of two forces.

Vocabulary

Friction: Friction is a contact force that acts parallel to a surface and opposes sliding motion or the tendency to slide.
Static friction: Static friction is friction between surfaces that are not sliding, with magnitude up to $f_{s,\max} = \mu_s F_N$ .
Kinetic friction: Kinetic friction is friction between surfaces that are sliding, with magnitude $f_k = \mu_k F_N$ .
Normal force: The normal force $F_N$ is the perpendicular contact force a surface exerts on an object.
Coefficient of friction: The coefficient of friction $\mu$ is a unitless number that describes how strongly two surfaces resist sliding.
Free-body diagram: A free-body diagram is a sketch that shows all external forces acting on one object.

Common Mistakes to Avoid

Using $f_s = \mu_s F_N$ automatically for static friction is wrong because static friction can be any value from $0$ to $\mu_s F_N$ .
Forgetting that friction opposes motion or possible motion is wrong because the friction direction depends on how the surfaces slide or would slide.
Using $F_N = mg$ on every problem is wrong because angled surfaces, pulls, pushes, or vertical acceleration can change the normal force.
Mixing the incline components is wrong because $mg\sin\theta$ is parallel to the ramp and $mg\cos\theta$ is perpendicular to the ramp when axes follow the incline.
Treating $\mu$ as a force is wrong because the coefficient of friction is unitless and must be multiplied by $F_N$ to find a friction force.

Practice Questions

1 A $12\,\text{kg}$ box slides across a horizontal floor with $\mu_k = 0.25$ . Find the kinetic friction force using $g = 9.8\,\text{m/s}^2$ .
2 A $20\,\text{kg}$ crate rests on a horizontal floor with $\mu_s = 0.40$ . What is the maximum static friction force before it starts moving?
3 A $5.0\,\text{kg}$ block slides down a $30^{\circ}$ incline with $\mu_k = 0.20$ . Find the acceleration down the incline using $a = g\sin\theta - \mu_k g\cos\theta$ .
4 A student says static friction always equals $\mu_s F_N$ . Explain why this is not correct and describe when static friction reaches that value.

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Friction Worked Examples Cheat Sheet

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