The normal force (\(N\)) acting on an object is a perpendicular force exerted by a surface against the object's weight. It can be determined using the formula:
\[ N = \dfrac{F_f}{\mu} \]
Where:
- \(N\) is the normal force (in newtons, N)
- \(F_f\) is the force of friction (in newtons, N)
- \(\mu\) is the coefficient of friction (dimensionless)
Example 1: Calculating the Normal Force for a Box on a Surface
Problem: A box experiences a frictional force of 50 N on a surface with a coefficient of friction of 0.25. What is the normal force acting on the box?
Calculation:
Given:
- \(F_f = 50 \, \text{N}\)
- \(\mu = 0.25\)
Using the formula:
\[ N = \dfrac{F_f}{\mu} \]
\[ N = \dfrac{50}{0.25} \]
\[ N = 200 \, \text{N} \]
Answer: The normal force acting on the box is 200 N.
Example 2: Calculating the Normal Force for a Car on a Road
Problem: A car experiences a frictional force of 9000 N on a road with a coefficient of friction of 0.6. What is the normal force acting on the car?
Calculation:
Given:
- \(F_f = 9000 \, \text{N}\)
- \(\mu = 0.6\)
Using the formula:
\[ N = \dfrac{F_f}{\mu} \]
\[ N = \dfrac{9000}{0.6} \]
\[ N = 15000 \, \text{N} \]
Answer: The normal force acting on the car is 15000 N.
Example 3: Calculating the Normal Force for a Table on a Floor
Problem: A table experiences a frictional force of 40 N on a floor with a coefficient of friction of 0.2. What is the normal force acting on the table?
Calculation:
Given:
- \(F_f = 40 \, \text{N}\)
- \(\mu = 0.2\)
Using the formula:
\[ N = \dfrac{F_f}{\mu} \]
\[ N = \dfrac{40}{0.2} \]
\[ N = 200 \, \text{N} \]
Answer: The normal force acting on the table is 200 N.
