Using Force Arrows in Physics Diagrams

Instructor: Betsy Chesnutt

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

Force arrows are a very useful way to represent the forces that act on a system. This lesson explains how force arrows can be used not only to show the forces simply, but also to predict the motion of the object that they act on.

What are Forces?

Amil is trying to move a box of books across the floor. How can he make it move? He's got to push on it! When he pushes on it, what he is really doing is exerting a force on the box. A force is a push or pull that changes the motion of an object. Forces can make objects start or stop moving, speed up or slow down objects that are already moving or make objects change direction.

There are two essential components of a force, known as magnitude and direction. The magnitude of a force is the total amount of force exerted. If Amil pushes on his box of books a little harder, then the magnitude of the force he is exerting will go up. The direction that the force is exerted is equally important. If Amil wants to move his box across the room, it won't help much to push on the top of the box, no matter what the magnitude of his force is! He needs to push in the direction he wants it to start moving!

Drawing Force Arrows

Force arrows are used to represent both the magnitude and direction of forces. The length of the arrow corresponds to the magnitude of the force, with longer arrows indicating forces with larger magnitudes. The direction of the arrow corresponds to the actual direction that the force is being exerted. Force arrows are used by scientists and engineers to predict the motion of an object based on the forces that are applied to it.

Let's go back to Amil and his box for a moment. To represent the force that he is exerting on the box, we can draw the box and then show the force using a force arrow, like this:

You can represent the force of Amir
force arrows

How would our force arrow change if he pushed the box with twice as much force? Because the magnitude of the force is doubled, the length of the force arrow should also be doubled.

If the force doubles, then the force arrow should be twice as long. The length of the force arrow corresponds to the magnitude of the force
force arrows with a bigger force

Now, what if he didn't push directly to the right, but instead his arms made a 30-degree angle with the ground? In that case, the direction of the force arrow needs to change to show the direction in which the force is applied.

The direction of the force arrow should reflect the direction in which the force is applied
force arrow at an angle

Free-Body Diagrams

In many physics problems, it is important to identify all the forces that act on an object accurately. These forces are then represented using force arrows on a picture called a free-body diagram. To create a free-body diagram of an object, you need first to identify all of the forces that act on an object.

Let's try to identify all the forces that act on Amil's box of books. You already know that there is a force exerted by Amil on the books, but this is not the only force that acts on the box of books. The Earth's gravity is responsible for a force that pulls down on the box and keeps it from floating away.

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