For an object resting on the flat surface, the value of **normal force **(F_{N}) is equal to its **weight** (mg). Using the equation of normal force: **F _{N} = mg**, the value of normal force acting on an object can be calculated.

Here’s the equation of normal force:

- When an object is resting on the flat surface,
**F**_{N}**= mg**

- When an object is placed on an inclined surface,
**F**_{N}**= mg × cos (****α****)**

- When an external downward force is acting on an object,
**F**_{N}**= mg + F sin (θ)**

- When an external upward force is acting on an object,
**F**_{N}**= mg – F sin (θ)**

Where,

α = angle of an inclined surface, deg

F = external force acting on an object, N

θ = angle between horizontal surface and external force, deg

Let’s solve some problems based on these equations, so you’ll get a clear idea.

## Normal Force Practice Problems

**Problem 1:** A flower pot of mass 2 kg is placed on the desk. Calculate the normal force acting on a flower pot. Take the value of gravitational acceleration, g = 9.81 m/s^{2}.

Solution:

Given data:

Mass of a flower pot, m = 2 kg

Gravitational acceleration, g = 9.81 m/s^{2}

Normal force acting on a flower pot, F_{N} = ?

Using the equation of normal force, (when an object is resting on the flat surface)

F_{N} = mg

F_{N} = 2 × 9.81

F_{N} = 19.62 N

Therefore, the normal force acting on a flower pot is **19.62 N**.

**Problem 2:** Calculate the normal force acting on a 3 kg book which is placed on an inclined surface. Assume that the surface is inclined at 45° angle.

Solution:

Given data:

Mass of a book, m = 3 kg

Angle of an inclined surface, α = 45°

Normal force acting on a book, F_{N} = ?

Using the equation of normal force, (when an object is placed on an inclined surface)

F_{N} = mg × cos (α)

F_{N} = 3 × 9.81 × cos (45°)

F_{N} = 29.43 × 0.7071

F_{N} = 20.8099 N

Therefore, the normal force acting on a book is **20.8099 N**.

**Problem 3:** One wooden crate of mass 20 kg is resting on the ground. In order to move this crate, 8 N of external downward force is applied on it at 30° angle. Calculate the normal force acting on a wooden crate.

Solution:

Given data:

Mass of a wooden crate, m = 20 kg

External downward force applied on a wooden crate, F = 8 N

Angle between horizontal surface and external downward force, θ = 30°

Normal force acting on a wooden crate, F_{N} = ?

Using the equation of force, (when an external downward force is acting on an object)

F_{N} = mg + F sin (θ)

F_{N} = [20 × 9.81] + [8 × sin (30°)]

F_{N} = 196.2 + [8 × 0.5]

F_{N} = 196.2 + 4

F_{N} = 200.2 N

Therefore, the normal force acting on a wooden crate is **200.2 N**.

**Problem 4:** Calculate the normal force acting on a 4 kg block, when it is pulled with an external upward force of 10 N at 45° angle.

Solution:

Given data:

Mass of a block, m = 4 kg

External upward force applied on a block, F = 10 N

Angle between horizontal surface and external upward force, θ = 45°

Normal force acting on a block, F_{N} = ?

Using the equation of force, (when an external upward force is acting on an object)

F_{N} = mg – F sin (θ)

F_{N} = [4 × 9.81] – [10 × sin (45°)]

F_{N} = 39.24 – [10 × 0.8509]

F_{N} = 39.24 – 8.509

F_{N} = 30.731 N

Therefore, the normal force acting on a block is **30.731 N**.

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**Related:**

- Force Equation
- Net Force Formula
- Applied Force Formula
- Magnetic Force Equation
- Centripetal Force Equation
- Centrifugal Force Equation
- Spring Force Equation
- Tension Force Formula
- Electric Force Equation

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