The **normal force equation** provides a means to calculate the force exerted on an object in different situations. In the case of an object resting on a flat surface, the normal force (F_{N}) is equal to the weight of the object (mg). This relationship is expressed by the equation F_{N} = mg. When dealing with an object on an inclined surface, the equation for the normal force becomes F_{N} = mg × cos (α), where α represents the angle of the inclined surface.

In scenarios involving external forces, the normal force equation can be modified accordingly. When a downward external force is applied to an object, the equation becomes F_{N} = mg + F sin(θ), where F denotes the magnitude of the external force and θ is the angle between the horizontal surface and the direction of the external force. Conversely, if an upward external force is acting on the object, the equation becomes F_{N} = mg – F sin(θ). It is important to note that α and θ are measured in degrees, while the unit for the external force, F, is newton (N). Additionally, m and g represent the mass and acceleration due to gravity, respectively. By utilizing these normal force equations, one can accurately calculate the normal force exerted on an object in various scenarios.

## Practice problems

### Problem #1

Determine the normal force acting on a 2 kg flower pot placed on a desk. The gravitational acceleration is given as g = 9.81 m/s^{2}.

**Solution**

Given data:

- Normal force acting on a flower pot, F
_{N}= ? - Mass of a flower pot, m = 2 kg
- Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula, 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 placed on an inclined surface inclined at a 45° angle.

**Solution**

Given data:

- Normal force acting on a book, F
_{N}= ? - Mass of a book, m = 3 kg
- Angle of an inclined surface, α = 45°

Applying the formula, 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

A wooden crate with a mass of 20 kg is resting on the ground. An external downward force of 8 N is applied to the crate at a 30° angle. Calculate the normal force acting on the 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}= ?

Applying the formula, 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

Find the normal force acting on a 4 kg block when an external upward force of 10 N is applied at a 45° angle.

**Solution**

Given data:

- Normal force acting on a block, F
_{N}= ? - 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°

Applying the formula, 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**.

## Related

## More topics

- Force equation
**Normal 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

## External links

- https://study.com/academy/lesson/the-normal-force-definition-and-examples.html
- https://www.omnicalculator.com/physics/normal-force
- https://www.wikihow.com/Find-Normal-Force

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.