Resultant Force: Definition & Formula

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  • 0:03 Resultant Force Definition
  • 0:28 ID-ing Forces &…
  • 1:19 Resultant Force and Motion
  • 2:19 Some Example Problems
  • 4:34 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In lots of situations, more than one force may act on an object. In this lesson, learn how to find the resultant force of two forces on a single object and how to use this to determine how the object will move.

Resultant Force Definition

Two groups of people are in a tug of war, and each group is pulling on the rope as hard as they can. Who will win? Will one group be able to make the other group move?

Who will win this tug of war? You need to know the resultant force to find out!
tug of war

In order to answer these questions, you need to know how to find the resultant force. The resultant force is the single force that would produce the same effect on an object (the rope) as two or more forces that are applied to the object.

ID-ing Forces & Drawing Diagrams

To find the resultant force, you must first carefully identify the object you want to study. In the tug of war, each team is pulling on the rope, so the rope is the object whose motion we want to study.

Next, identify all the forces that are acting on the object. Each team is pulling on the rope, so there are forces acting on the rope in opposite directions.

A great way to clearly show the forces acting on an object is to use a free body diagram like the one you're looking at on screen. A free body diagram is a picture that represents the object with a dot in the center and uses arrows to represent the forces acting on the object.

free body diagram

Notice that each force is labeled with a different symbol so that you can easily keep track of the different forces. In this case, the force from the people on the right was labeled 'FR,' and the force from the people on the left was labeled 'FL.'

Resultant Force and Motion

Once you know the resultant force, you can use it to predict how the object will move (or not move). Way back in the 1600s, Sir Isaac Newton wrote a book called Mathematical Principles of Natural Philosophy, and in this famous book, he explained the laws of motion, which demonstrate the effect of forces on motion. There are three in total, but the first two laws are especially important for understanding how the resultant force will affect the motion of our object.

  1. The First Law of Motion: If the resultant force acting on an object is zero, it will not change its motion in any way (either the speed or the direction).
  2. The Second Law of Motion: If the resultant force is NOT zero, the object will accelerate in the direction of the net force, and the acceleration will be directly proportional to the resultant force and inversely proportional to its mass.

Taken together, these two laws explain what will happen in any situation in which there is a resultant force.

Some Example Problems

Let's look at the tug of war problem one more time and see if we can put all this together and figure out which way the rope will move:

In the beginning of the tug of war, the team on the left applies a force of 1600 N to the rope, and the team on the right also applies a force of 1600 N to the rope. What happens to the rope?

Let's start with a free body diagram and include the amount of each force.

free body diagram with balanced forces

Since the force to the right is 1600 N and the force to the left is also 1600 N, the resultant force is 0 N.

Knowing that the resultant force is zero, what does this mean for the motion of the rope? Remember, Newton's first law says that if the resultant force is zero, the object will not change its motion in any way. Since the rope isn't initially moving, that means that it will continue to not move. No one will win this tug of war!

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