# Net force

Net force refers to the sum of all the forces that are acting on an object. Imagine a scenario where two forces are applied to an object from opposite directions – one pushing to the right with a force of 10 N and the other pushing to the left with a force of 5 N. The net force in this case would be the difference between these two forces, which is 5 N to the right. It’s like finding the ‘overall force’ on the object, whether it’s a push or a pull. This net force, as defined by Newton’s second law, has a significant impact on the object’s motion. According to the law, if a net force is applied to an object, it can cause the object to accelerate, meaning it will speed up, slow down, or change its direction.

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## Formula

The net force formula is used to calculate the overall force acting on an object in different situations. When the object is at rest, the net force (Fnet) is simply the sum of the normal force (FN) and the force of gravity (Fg), represented by the equation Fnet = FN + Fg.

In situations where the object is in motion, the net force formula becomes more comprehensive, taking into account additional forces. It includes the applied force (FA) and the frictional force (Ff), along with the normal force (FN) and the force of gravity (Fg). The formula in this case is expressed as Fnet = FA + Ff + FN + Fg.

When an object experiences multiple forces (F1, F2, F3, …, Fn), the net force formula expands accordingly. In this scenario, the net force (Fnet) is determined by summing up all the individual forces acting on the object, leading to the formula Fnet = F1 + F2 + F3 + … + Fn.

### Practice problems

#### Problem #1

In a tug-of-war competition, two teams, team A (on the right side) and team B (on the left side), pull a rope in opposite directions. Team A applies a force of 50 N, while team B exerts a force of 20 N. Calculate the net force on the rope and determine the direction of the resulting motion.

Solution

Given data:

• Force applied to the rope by team A, FA = 50 N
• Force applied to the rope by team B, FB = -20 N (left)
• Net force acting on the rope, Fnet = ?

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

• Fnet = FA + FB
• Fnet = 50 – 20
• Fnet = 30 N

The net force on the rope is 30 N. Since the net force is positive, it means that team A’s force is greater than team B’s force. As a result, the rope will move in the direction of team A, which is to the right.

#### Problem #2

A box rests on the floor with a normal force of 8 N supporting it and a gravitational force of 12 N acting downward. What is the magnitude and direction of the net force acting on the box?

Solution

Given data:

• Normal force acting on the box, FN = 8 N
• Force of gravity acting on the box, Fg = -12 N (downward)
• Net force acting on the box, Fnet = ?

Using the formula, when an object is at rest:

• Fnet = FN + Fg
• Fnet = 8 – 12
• Fnet = -4 N (downward)

The magnitude of the net force is 4 N, and the direction is downward (negative sign indicates the downward direction). The net force of 4 N is responsible for keeping the block in equilibrium, as the forces are balanced.

#### Problem #3

Five people come together to help move a van stuck on the road. Each person applies a different force: 5 N, 6 N, 7 N, 4 N, and 8 N. Calculate the total net force exerted on the van to determine if it can be pushed forward and freed from its predicament.

Solution

Given data:

• Force applied by the person 1, F1 = 5 N
• Force applied by the person 2, F2 = 6 N
• Force applied by the person 3, F3 = 7 N
• Force applied by the person 4, F4 = 4 N
• Force applied by the person 5, F5 = 8 N
• Net force acting on the van, Fnet = ?

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

• Fnet = F1 + F2 + F3 + F4 + F5
• Fnet = 5 + 6 + 7 + 4 + 8
• Fnet = 30 N

Therefore, the net force acting on the van is 30 N.

#### Problem #4

A crate lies on a table, experiencing a force of 25 N applied in one direction and a frictional force of 7 N opposing it. The crate is balanced by a normal force of 30 N and the force of gravity. Determine the resulting net force on the crate.

Solution

Given data:

• Applied force acting on the crate, FA = 25 N
• Friction force acting on the crate, Ff = -7 N (left)
• Normal force acting on the crate, FN = 30 N
• Force of gravity acting on the crate, Fg = -30 N (downward)
• Net force acting on the crate, Fnet = ?

Using the formula, when an object is in motion:

• Fnet = FA + Ff + FN + Fg
• Fnet = 25 – 7 + 30 – 30
• Fnet = 18 N

Therefore, the net force acting on the crate is 18 N.