The **net force formula** is used to determine the total force acting on an object in different scenarios. When an object is at rest, the net force, represented as F_{net}, is determined by adding the values of the normal force, denoted as F_{N}, and the force of gravity, symbolized as F_{g}. This relationship can be expressed using the equation F_{net} = F_{N} + F_{g}.

In situations where the object is in motion, the net force formula becomes more comprehensive. It includes additional forces such as applied force (F_{a}) and frictional force (F_{f}), in addition to the normal force (F_{N}) and the force of gravity (F_{g}). The formula for calculating the net force in such cases is expressed as F_{net} = F_{a} + F_{f} + F_{N} + F_{g}.

Furthermore, when an object is subjected to multiple forces (F_{1}, F_{2}, F_{3}, …, F_{n}), the net force formula can be expanded accordingly. In this case, the net force (F_{net}) is determined by adding up all the individual forces acting on the object, leading to the formula F_{net} = F_{1} + F_{2} + F_{3} + … + F_{n}.

## Practice problems

### Problem #1

A block is resting on the floor and is balanced by a normal force of 6 N and a gravitational force of 6 N. Determine the net force acting on the block.

**Solution**

Given data:

- Normal force acting on a block, F
_{N}= 6 N - Force of gravity acting on a block, F
_{g}= -6 N (downward) - Net force acting on a block, F
_{net}= ?

Applying the formula, when an object is at rest:

- F
_{net}= F_{N}+ F_{g} - F
_{net}= 6 – 6 - F
_{net}= 0 N

Therefore, the net force acting on a block is **0 N**.

### Problem #2

A book is lying on a desk. When a force of 15 N is applied to the book, a friction force of 5 N acts in the opposite direction. If the book is balanced by a normal force of 20 N and the force of gravity, calculate the net force acting on it.

**Solution**

Given data:

- Applied force acting on a book, F
_{a}= 15 N - Friction force acting on a book, F
_{f}= -5 N (left) - Normal force acting on a book, F
_{N}= 20 N - Force of gravity acting on a book, F
_{g}= -20 N (downward) - Net force acting on a book, F
_{net}= ?

Applying the formula, when an object is in motion:

- F
_{net}= F_{a}+ F_{f}+ F_{N}+ F_{g} - F
_{net}= 15 – 5 + 20 – 20 - F
_{net}= 10 N

Therefore, the net force acting on a book is **10 N**.

### Problem #3

Two persons, Person 1 (standing on the right side) and Person 2 (standing on the left side), are pulling a rope in opposite directions. Person 1 applies a force of 40 N, and Person 2 applies a force of 15 N. Calculate the net force acting on the rope.

**Solution**

Given data:

- Force acting on the rope, F
_{1}= 40 N - Force acting on the rope, F
_{2}= -15 N (left) - Net force acting on the rope, F
_{net}= ?

Applying the formula, when multiple forces are acting on an object:

- F
_{net}= F_{1}+ F_{2} - F
_{net}= 40 – 15 - F
_{net}= 25 N

Therefore, the net force acting on the rope is **25 N**.

### Problem #4

A car gets stuck on the road, and six people are pushing it in the right direction. The six individuals apply the following forces: 3 N, 4 N, 5 N, 3 N, 7 N, and 2 N. Calculate the net force acting on the car.

**Solution**

Given data:

- Force acting on the car, F
_{1}= 3 N - Force acting on the car, F
_{2}= 4 N - Force acting on the car, F
_{3}= 5 N - Force acting on the car, F
_{4}= 3 N - Force acting on the car, F
_{5}= 7 N - Force acting on the car, F
_{6}= 2 N - Net force acting on the rope, F
_{net}= ?

Applying the formula, when multiple forces are acting on an object:

- F
_{net}= F_{1}+ F_{2}+ F_{3}+ F_{4}+ F_{5}+ F_{6} - F
_{net}= 3 + 4 + 5 + 3 + 7 + 2 - F
_{net}= 24 N

Therefore, the net force acting on the car is **24 N**.

## Related

- 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/learn/lesson/net-force-formula-examples-how-find.html
- https://www.wikihow.com/Find-Net-Force
- https://sciencing.com/net-force-definition-equation-how-to-calculate-13720445.html
- https://lambdageeks.com/how-to-find-net-force-with-mass-and-velocity/

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.