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What is Net Force? - Definition, Magnitude & Equations

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  • 0:01 Definition of a Net Force
  • 1:12 Magnitude & Equation
  • 1:56 Examples
  • 3:34 Lesson Summary
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Lesson Transcript
Instructor
Richard Cardenas

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

Expert Contributor
Kathryn Boddie

Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. She has over 10 years of teaching experience at high school and university level.

In this lesson, we will define net force, and explore the magnitude of a net force, the relevant equations and examples that will help make the concept of net force clearer.

Definition of a Net Force

When you kick a soccer ball, the ball takes off and moves through the air. At that moment, there is a net force acting on the ball. When the ball starts to come back to the ground and eventually stops, there is a net force acting on the ball as well. Newton's Second Law says that when a net force is acting on an object, then that object must be accelerating, that is, its speed changes from second to second. When you first kick the soccer ball, it accelerates, and when the soccer ball begins to slow down to a stop, it is also accelerating.

A net force is defined as the sum of all the forces acting on an object. The equation below is the sum of N forces acting on an object.

NetForce1

There may be several forces acting on an object, and when you add up all of those forces, the result is what we call the net force acting on the object. If the net force adds up to zero, then the object is not accelerating, therefore it moves with a constant speed. If the net force adds up to a non-zero value, then the object is accelerating.

Magnitude and Equation

According to Newton's Second Law, when an object accelerates, then there must be a net force acting on it. Conversely, if a net force acts on an object, that object will accelerate. The magnitude of the net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object as shown in the formula below.

Net Force

If the net force acting on an object is zero, then the object is not accelerating and is in a state that we call equilibrium. When an object is in equilibrium, then two things can be true: either the object is not moving at all, or the object is moving with a constant speed. The formula for equilibrium is shown below.

Equilibrium

Examples

Consider a hypothetical situation in space. You are doing a spacewalk and are fixing something on your shuttle. While working on the issue with a wrench, you get angry. You throw the wrench away from you. What happens? Well, once the wrench leaves your hand, it will continue moving with the same speed that you gave it when you threw it. This is an example of a zero net force situation. The wrench will move with the same speed and will not accelerate in space. If you throw the same wrench on Earth, the wrench will fall to the ground and eventually stop. Why did it stop? There is a net force acting on the wrench causing it to slow down and stop.

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Additional Activities

Practice Problems - Net Force

In the following practice problems, students will use Newton's Second Law to examine the net force and/or acceleration of objects.

Problems

1. If the net force on a car is 3000 Newtons, and the mass of a car is 1000 kg, what is the car's acceleration?

2. Find the net force on a car with mass 1200 kg and acceleration 4 m/s^2.

3. If an object is in equilibrium and the object is moving, what can be said about the net force on the object? What can be said about the object's acceleration? What can be said about the rate at which the object is moving?

Solutions

1. Using the formula

we have:

3000 = 1000a

3 = a

So the acceleration of the car is 3 m/s^2.

2. Using the formula

with m = 1200 and a = 4, we have

So the net force on the car is 4800 Newtons.

3. If an object is in equilibrium, then its net force is zero by definition. Since the object is in equilibrium, it is not accelerating and so a = 0. Since this object is moving, but has acceleration 0, the object must be moving at a constant rate.

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