Net Force Formula & Examples | What is Net Force? | How to Find Net Force

How to Find Net Force

The net force formula sums the forces acting on an object. Thus, the net force formula is as follows:

Fnet = F1 + F2 + F3....

The direction of the net force is determined by the sign. The general conventions for physics are that motion going backwards or down is negative and motion going forwards or up is positive.

Net Force Equations

The net force formula, or net force equation, described above can be applied in a variety of scenarios. For example, let's say an elevator has an upward force of 200N acing on it and a downward force of gravity acting on it with 150N. What would the net force be?

To solve this we simply add the forces involved using the net force equation where Fg is the force due to gravity and FApp is the applied force by the motor of the elevator.

Fnet = -Fg + FApp

Here the force due to gravity is negative since it is acting in the downwards direction.

For the next example, there is a toy car being pushed forward with an applied force of 8N. Friction against the surface holds the car back with 2N. How would you set up the net force equation here? Again, we simply add up the forces with forces going backwards or down as negative and forces going forwards or up as positive.

Fnet = FApp - Ff

Where Ff is the force due to friction. Friction is negative because it opposes the motion of the toy car forward.

Net Force Examples

Now that we know how to set up the equations for net force, let's look at solving using net force units and magnitude.

Imagine a lamp hanging from the ceiling. The weight of the lamp, or force due to gravity, acting on it is 50N. The tension in the cable holding it to the ceiling is also 50N. What is the net force?

Start by creating your equation:

Fnet = FT - Fg

Where Fnet is the net force, FT is the tension in the rope and Fg is force due to gravity, or weight.

Next, we can add in the values given in the problem.

Fnet = 50N - 50N = 0N

In this case there is zero net force. This means that there is no acceleration acting on the object and thus the lamp stays stationary. If the net force is non-zero, it means the object must be accelerating. If the net force is zero, the object may be stationary, as in this example, or moving at a constant speed without acceleration. For example, if a car is moving on the highway at 50mph continuously, the car has a net force of zero even though it is moving because it is moving at a constant speed and there is no acceleration.

Let's look at another example. Say a cyclist is biking forward with a force of 200N. There is a force of air resistance opposing their motion of 80N. What is the net force acting on the cyclist?

Fnet = FApp - Fair

Fnet = 200N - 80N = 120N.

Net Force with Vectors

The examples we have looked at thus far contain forces that act in a single plane of motion. However, in reality, forces act in varying directions and may cross different planes. To solve these type of problems, we can use vectors and geometry to calculate the components of the force acting in each plane to use in our net force equation.

For example, if one person pushes on a box forward with 40N and one person pushes the box up with 30N, the net force will be the sum of these vectors. Using geometry, we can align the two forces head to tail to create a triangle and use Pythagoras's theorem to calculate the hypotenuse, or the net force, which is equal to 50N.

Solving for the magnitude of net force with vectors

Sometimes there are multiple forces acting on an object at different angles. Forces that interact with the object at an angle can be broken down into their component horizontal and vertical parts, summed into the horizontal and vertical forces and then used in Pythagoras's theorem as explained above. Let's look at an example.

Say there is a box being pushed in five directions. One person pushes down with 40N, another person pushes up with 30N, one person pushes left with 50N, one person pushes right with 30N and a fifth person pushes at an upward angle of 30 degrees with 20N.

First, we need to break down the force of 20N into its component parts. To do this, we can use sine and cosine to determine the other components of the triangle. The sine of an angle is equal to the opposite side (in this case the vertical component) over the hypotenuse (in this case the known force).

sine (30) = Fy / 20N

Fy = 10N

For the horizontal component of the force we can use the cosine of the angle.

cosine(30) = Fx / 20N

Fx = 17N

Next, these can be added into the other components to solve for the horizontal and vertical forces acting on the box.

Fy = 30N - 40N + 10N = 0N

Fx = 17N + 30N - 50N = -3N

Next, we can use Pythagoras's theorem to calculate the hypotenuse from these two components and finally the total net force acting on the object as described above.

Calculating Acceleration

If the net force and the mass of an object is known, the acceleration can be calculated using Newton's second law, which is F = ma, where F is the net force, m is mass and a is acceleration. Let's look at an example.

The net force acting on a basketball is 2N. The mass of the basketball is 0.6kg. How much acceleration is acting on the ball?

F = ma

2N = 0.6kg * a

a = 3.33 m/s2

Additional Problems

The following problems can be used for additional practice. Refer to the examples above and be sure to show all of your work. Answers are included at the end.

1. A ball is being pushed by an applied force from a bat at 15N. The ball experiences an air resistance in the opposite direction of 4N. What is the net force?
2. A box is being pushed with 10N forward and 5N up. What is the net force?
3. A skateboard experiences a net force of 50N. If the mass of the skateboard is 5kg, what is the acceleration?

• Answers: 1. 11N, 2. 11.18N, 3. 10m/s2

Net Force Diagram

A net force diagram is also known as a free body diagram. It shows the forces acting on an object as arrows. This can be helpful in constructing the net force equation, as it is easy to visualize which way the forces are moving. As objects can be complex, typically free body diagrams are drawn using a dot to represent an object. For example, a person jumping out of a plane would have two main forces acting on them, the force due to gravity (Fg) acting downwards and air resistance (Fair) pushing them back up. Thus, the free body diagram would have one arrow going up for air resistance and one arrow going down for gravity.

A net force diagram uses a dot to represent the object and arrows to represent the forces

Thus, in this situation the net force equation would be:

Fnet = Fair - Fg

Let's say there is 80N of air resistance and 600N of weight, or force due to gravity. We can solve the equation above by plugging in these values.

Fnet = 80N - 600N

Fnet = -520N

Thus, the skydiver will fall downwards with a force of 520N.

Let's look at some more examples of net force diagrams. Say a driver is moving forward around a race track with an applied force of 800N from the engine. Friction between the tires holds the driver back with 200N. The car also experiences force due to gravity pushing the car down, and the normal force which extends perpendicularly out of any surface. The net force diagram would look as follows:

The net force diagram for a race car

The applied force pushes the car forward and the force due to friction holds it back. Gravity acts downward on the car and the normal force acts upwards.

Another example is a box being pushed up an incline. The box is pushed up with the applied force and friction holds it back. The box also experiences gravity pushing it down and the normal force pushing out from the surface of the incline. The free body diagram would look as follows:

An example of a free body diagram for a box being pushed up an incline.

Lesson Summary

Net force is the sum of all forces acting on an object. The net force can be calculated using Newton's second law, which states that F = ma, where:

• F is the net force
• m is the mass of the object
• a is acceleration

If net force is non-zero, there must be acceleration acting on the object. If net force is equal to zero the object is either moving at a constant speed or stationary. Net force can be calculated using the net force equation where

Fnet = F1 + F2 + F3....

Net force can also be used to solve problems where forces are in different planes using vector geometry, and if the net force and mass are known, acceleration can also be solved for.