Objects with Two or More Forces: Finding the Total Force Result

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  • 0:01 What Is a Force?
  • 1:02 Figuring Out the Total Force
  • 1:51 Example Calculation
  • 3:47 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what a force is and how it relates to motion, and find the total force result in a variety of force situations. A short quiz will follow.

What is a Force?

A force is just a push or pull, measured in newtons. Or in general, it is any action that can change the motion of an object. If an object has no forces on it, and then you apply a force by, for example, pushing it, the object will accelerate. An acceleration is a change in the velocity of an object over time. So if the forces on an object are unbalanced, the object's velocity will change.

This might mean, for example, pushing on a moving shopping cart to make it stop moving, or it might mean throwing a ball to cause its speed to increase from zero to some value.

But what happens when objects have more than one force on them?

If you push an object to the right with a force of 6 newtons, and someone else pushes to the left with a force of 6 newtons, the object won't accelerate. The two forces cancel each other out.

Thus, you can see that what matters is the total force. So, how do you figure out the total force on an object?

Figuring Out the Total Force

In physics, we talk about something called the independence of motion. This means that vertical motion and horizontal motion are separate. In most normal situations, the x and y directions don't impact each other.

So when it comes to figuring out the total force, we have to look at the vertical and horizontal directions separately. We can figure out the total force by subtracting one force from the other. For example, if a block is being pushed with a force of 7 newtons left and 4 newtons right, the total force on the block is 3 newtons left. 7 - 4 = 3. Or another way to put it is that the 4 newtons right are canceled out, balanced by 4 of the newtons to the left. All that remains is the extra 3 newtons to the left. So the total force will be 3 newtons left.

Example Calculation

Let's go through an example of how to calculate the total force on an object.

Here is a diagram of the forces on an ice skater from above:

Diagram for ice skater example
diagram of forces on ice skater

They have a force of 5 newtons right, a force of 2 newtons left, a force of 8 newtons up and a force of 8 newtons down. What is the total force on the ice skater?

First let's look at the up-and-down direction force. 8 newtons up and 8 newtons down cancel out. 8 minus 8 is zero. So there is a total force of zero in the up-and-down direction; that part's easy. Next, let's look at the left-and-right direction. 5 newtons right and 2 newtons left. 5 - 2 = 3. So the total force is 3 newtons right. The total force must be to the right, because there is more force in that direction than there is to the left. Or in other words, two of the newtons to the right cancel out the two newtons to the left, and there are 3 newtons to the right left over. So that's the final answer: 3 newtons to the right.

One more example: here is a diagram of an office chair on wheels, being pushed around by you and a few of your friends:

Diagram for chair example
diagram of forces on chair

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