# Net force

Net force is the total force resulting from the combination of all individual forces acting on an object. Simply put, it’s what you get when you add up all the pushes and pulls to determine the overall force on the object. For instance, if a car is being pushed forward with a force of 300 Newtons while friction exerts a backward force of 100 Newtons, the net force is 200 Newtons forward. This net force causes the car to accelerate in the direction of the stronger force. The concept of net force is essential for predicting how and why objects move or remain stationary in different scenarios.

To understand how forces interact and influence the motion of objects, we can use various equations to calculate the net force acting on them.

When an object is at rest, the net force (Fnet) is acting on it is the sum of the normal force (FN) and the force of gravity (Fg).

$$F_{net} = F_{N} + F_{g}$$

For objects in motion, the calculation of net force becomes more complex. It includes the applied force (Fa), the force of friction (Ff), along with the normal force (FN) and the force of gravity (Fg).

$$F_{net} = F_{a} + F_{f} + F_{N} + F_{g}$$

When multiple forces are acting on an object, the net force is the sum of all individual forces (F1, F2, F3, …, Fn) acting on it.

$$F_{net} = F_{1} + F_{2} + F_{3} + … + F_{n}$$

where Fn is the nth individual force acting on the object.

Contents

## 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.

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