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# Coefficient of Friction Problems and Solutions

This tutorial covers some problems on friction force and coefficients of friction, which are important concepts in physics. You will see how to apply the formulas and principles of friction to various situations, such as sliding, rolling, and inclined planes.

The solutions are explained step by step, with diagrams and equations.

This tutorial is suitable for high school and college students who want to practice and improve their skills on friction problems.

## Coefficient of kinetic friction: Problems

Problem (1): A constant force of $10\,{\rm N}$ is applied to a $2-{\rm kg}$ crate on a rough surface that is sitting on it. The crate undergoes a frictional force against the force that moves it over the surface.
(a) Assuming the coefficient of friction is $\mu_k=0.24$, find the magnitude of the friction force that opposes the motion.
(b) What is the net force on the crate?
(c) What acceleration does the crate obtain?

Solution: The kinetic friction force is the force that opposes the motion of a moving object. Its magnitude is given by the formula $f_k=\mu_k F_N$, where $\mu_k$ is the coefficient of kinetic friction, and $F_N$ is the normal force on the object due to contact with a surface.

In all problems involving the coefficient of friction, you must apply Newton's second law in the vertical direction to find the normal force if it is not given.

(a) The crate does not move vertically or lift off the surface, so the forces in this direction are balanced. The free-body diagram below shows that two forces act on the crate: an upward normal force $F_N$, and a downward weight force $W=mg$.

Thus, $F_N=mg=2\times 10=20\,{\rm N}$ Now that the normal force is known, we can use the kinetic friction force formula $f_k=\mu_k F_N$ to find its magnitude: $f_k=\mu_k F_N=0.24\times 20=4.8\,{\rm N}$
(b) '' Net force'' means the sum vector of forces. In the horizontal direction, two forces act on the crate: external force $F$, and friction force $f$. These two forces apply in the opposite direction.

The subtraction of these two forces gives us the net (resultant) force on the crate. So, $F_{net}=F-f_k=10-4.8=5.2\,{\rm N}$
(c) According to Newton's second law of motion, if a force of $F$ is applied to a body of mass $m$, then it undergoes an acceleration whose magnitude is given by $a=\frac{F}{m}$. So, the acceleration that this crate experiences is found as $a=\frac{F_{net}}{m}=\frac{4.8}{2}=2.4\,{\rm m/s^2}$

## Summary:

In this tutorial, you learned how to use the coefficient of friction to solve friction problems in physics.

Overall, to find the friction force in a problem, you must first determine the normal force on the object. Then, recognize which friction force, static or kinetic, is involved in the question.

In the end, substitute the given numerical values to find the desired quantity.

Author: Dr. Ali Nemati
Page Published: 9/30/2021