How To Determine The Coefficient Of Friction

The coefficient of friction ($\mu$) is a measure of how much frictional force exists between two surfaces. It can be determined using the formula:

$$\mu ={\displaystyle \frac{F_f}{N}}$$

Where:

• $\mu$ is the coefficient of friction (dimensionless)
• $F_f$ is the force of friction (in newtons, N)
• $N$ is the normal force (in newtons, N)

Example 1: Calculating the Coefficient of Friction for a Box on a Surface

Problem: A box experiences a frictional force of 60 N on a surface, and the normal force acting on it is 150 N. What is the coefficient of friction between the box and the surface?

Calculation:

Given:

• $F_f=60\text{N}$
• $N=150\text{N}$

Using the formula:

$$\mu ={\displaystyle \frac{F_f}{N}}$$

$$\mu ={\displaystyle \frac{60}{150}}$$

$$\mu =0.4$$

Answer: The coefficient of friction between the box and the surface is 0.4.

Example 2: Calculating the Coefficient of Friction for a Car on a Road

Problem: A car experiences a frictional force of 8000 N on a road, and the normal force acting on it is 12000 N. What is the coefficient of friction between the car's tires and the road?

Calculation:

Given:

• $F_f=8000\text{N}$
• $N=12000\text{N}$

Using the formula:

$$\mu ={\displaystyle \frac{F_f}{N}}$$

$$\mu ={\displaystyle \frac{8000}{12000}}$$

$$\mu =0.67$$

Answer: The coefficient of friction between the car's tires and the road is 0.67.

Example 3: Calculating the Coefficient of Friction for a Sled on Ice

Problem: A sled experiences a frictional force of 15 N on ice, and the normal force acting on it is 300 N. What is the coefficient of friction between the sled and the ice?

Calculation:

Given:

• $F_f=15\text{N}$
• $N=300\text{N}$

Using the formula:

$$\mu ={\displaystyle \frac{F_f}{N}}$$

$$\mu ={\displaystyle \frac{15}{300}}$$

$$\mu =0.05$$

Answer: The coefficient of friction between the sled and the ice is 0.05.