Normal Force Calculator

Calculate Normal Force

Mass (m):

kg g lb

Gravitational Acceleration (g):

m/s² ft/s²

Surface Angle (α):

degrees radians

Calculate Example

How to Calculate Normal Force

Normal force is a crucial concept in physics, representing the force exerted by a surface on an object resting on or moving along that surface. Understanding how to calculate normal force is essential for solving problems involving friction, inclined planes, and various other scenarios in mechanics.

What is the Formula?

The formula for calculating normal force depends on the situation. For an object on a flat, horizontal surface, the formula is simple:

\[ N = mg \]

For an object on an inclined plane, the formula becomes:

\[ N = mg \cos(\alpha) \]

Where:

• \(N\) is the normal force
• \(m\) is the mass of the object
• \(g\) is the acceleration due to gravity
• \(\alpha\) is the angle of inclination of the surface

What are the calculation steps?

1. Identify the situation: Is the surface flat or inclined?
2. Determine the mass of the object and the acceleration due to gravity.
3. If the surface is inclined, measure or calculate the angle of inclination.
4. Apply the appropriate formula:
   • For a flat surface: \(N = mg\)
   • For an inclined surface: \(N = mg \cos(\alpha)\)
5. Perform the calculation to find the normal force.

Example Calculation

Let's calculate the normal force for an object on an inclined plane:

Given:

• Mass of the object (m) = 10 kg
• Acceleration due to gravity (g) = 9.8 m/s²
• Angle of inclination (α) = 30°

Step 1: Identify the situation

The object is on an inclined plane, so we'll use the formula \(N = mg \cos(\alpha)\).

Step 2: Plug in the values

\(N = 10 \text{ kg} \times 9.8 \text{ m/s²} \times \cos(30°)\)

Step 3: Calculate

\(N = 98 \times 0.866 = 84.87 \text{ N}\)

Therefore, the normal force acting on the object is approximately 84.87 N.

Diagram of Normal Force

The following diagram illustrates the concept of normal force on an inclined plane:

This diagram shows an object (blue circle) on an inclined plane. The red arrow represents the gravitational force (mg), and the green arrow represents the normal force (N). The angle α is the inclination of the plane. The normal force is always perpendicular to the surface, while the gravitational force always points straight down.