Determining the force of friction (\(F_f\)) is essential for understanding how objects move across surfaces. The force of friction can be calculated using the formula:
\[ F_f = \mu \cdot N \]
Where:
- \(F_f\) is the force of friction (in newtons, N)
- \(\mu\) is the coefficient of friction (dimensionless)
- \(N\) is the normal force (in newtons, N)
Example 1: Calculating the Force of Friction for a Sliding Box
Problem: A box with a mass of 20 kg is sliding on a horizontal surface with a coefficient of friction of 0.4. The normal force acting on the box is equal to the weight of the box. What is the force of friction acting on the box?
Calculation:
Given:
- \(m = 20 \, \text{kg}\)
- \(\mu = 0.4\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(N = m \cdot g = 20 \cdot 9.8 = 196 \, \text{N}\)
Using the formula:
\[ F_f = \mu \cdot N \]
\[ F_f = 0.4 \cdot 196 \]
\[ F_f = 78.4 \, \text{N} \]
Answer: The force of friction acting on the box is 78.4 N.
Example 2: Calculating the Force of Friction for a Car on a Road
Problem: A car with a mass of 1500 kg is moving on a road with a coefficient of friction of 0.7. What is the force of friction acting on the car?
Calculation:
Given:
- \(m = 1500 \, \text{kg}\)
- \(\mu = 0.7\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(N = m \cdot g = 1500 \cdot 9.8 = 14700 \, \text{N}\)
Using the formula:
\[ F_f = \mu \cdot N \]
\[ F_f = 0.7 \cdot 14700 \]
\[ F_f = 10290 \, \text{N} \]
Answer: The force of friction acting on the car is 10290 N.
Example 3: Calculating the Force of Friction for a Skier on Snow
Problem: A skier with a mass of 70 kg is gliding on snow with a coefficient of friction of 0.05. What is the force of friction acting on the skier?
Calculation:
Given:
- \(m = 70 \, \text{kg}\)
- \(\mu = 0.05\)
- \(g = 9.8 \, \text{m/s}^2\)
- \(N = m \cdot g = 70 \cdot 9.8 = 686 \, \text{N}\)
Using the formula:
\[ F_f = \mu \cdot N \]
\[ F_f = 0.05 \cdot 686 \]
\[ F_f = 34.3 \, \text{N} \]
Answer: The force of friction acting on the skier is 34.3 N.
