The coefficient of friction (\(\mu\)) is a measure of how much frictional force exists between two surfaces. It can be determined using the formula:
\[ \mu = \dfrac{F_f}{N} \]
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:
\[ \mu = \dfrac{F_f}{N} \]
\[ \mu = \dfrac{60}{150} \]
\[ \mu = 0.4 \]
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:
\[ \mu = \dfrac{F_f}{N} \]
\[ \mu = \dfrac{8000}{12000} \]
\[ \mu = 0.67 \]
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:
\[ \mu = \dfrac{F_f}{N} \]
\[ \mu = \dfrac{15}{300} \]
\[ \mu = 0.05 \]
Answer: The coefficient of friction between the sled and the ice is 0.05.
