# Net force formula

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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 Fnet, is determined by adding the values of the normal force, denoted as FN, and the force of gravity, symbolized as Fg. This relationship can be expressed using the equation Fnet = FN + Fg.

In situations where the object is in motion, the net force formula becomes more comprehensive. It includes additional forces such as applied force (Fa) and frictional force (Ff), in addition to the normal force (FN) and the force of gravity (Fg). The formula for calculating the net force in such cases is expressed as Fnet = Fa + Ff + FN + Fg.

When an object is subjected to multiple forces (F1, F2, F3, …, Fn), the net force formula can be expanded accordingly. In this case, the net force (Fnet) is determined by adding up all the individual forces acting on the object, leading to the formula Fnet = F1 + F2 + F3 + … + Fn.

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## 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, FN = 6 N
• Force of gravity acting on a block, Fg = -6 N (downward)
• Net force acting on a block, Fnet = ?

Applying the formula, when an object is at rest:

• Fnet = FN + Fg
• Fnet = 6 – 6
• Fnet = 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, Fa = 15 N
• Friction force acting on a book, Ff = -5 N (left)
• Normal force acting on a book, FN = 20 N
• Force of gravity acting on a book, Fg = -20 N (downward)
• Net force acting on a book, Fnet = ?

Applying the formula, when an object is in motion:

• Fnet = Fa + Ff + FN + Fg
• Fnet = 15 – 5 + 20 – 20
• Fnet = 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, F1 = 40 N
• Force acting on the rope, F2 = -15 N (left)
• Net force acting on the rope, Fnet = ?

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

• Fnet = F1 + F2
• Fnet = 40 – 15
• Fnet = 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, F1 = 3 N
• Force acting on the car, F2 = 4 N
• Force acting on the car, F3 = 5 N
• Force acting on the car, F4 = 3 N
• Force acting on the car, F5 = 7 N
• Force acting on the car, F6 = 2 N
• Net force acting on the rope, Fnet = ?

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

• Fnet = F1 + F2 + F3 + F4 + F5 + F6
• Fnet = 3 + 4 + 5 + 3 + 7 + 2
• Fnet = 24 N

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