Physics 3 Using Vectors To Show Forces

You are asked to join a game of tug of war by one friend. Each of you grabs an end of the rope and starts pulling. Neither of you can pull the other one.

Another friend comes over and grabs the rope with your friend. What happens?

At first the forces you and your friend exert on the rope are the same and opposite. The result is no force.

Let’s show this using vectors.

using vectors to show tug of war forces

A vector is an arrow pointing in the direction the force is going. In tug of war the forces go away from each other as both sides are pulling on the rope.

When the third person starts pulling, one force stays the same. The other force doubles. Can vectors show this?

using vectors to add forces

There is one vector arrow for each tug of war participant. Each arrow points the way that person is pulling. Two of the arrows are equal and opposite cancelling each other out. That leaves one arrow to show what happens in the game.

When you put the vectors together, they show what happened in your game of tug of war.


What Is a Vector?

As you can see, a vector is an arrow. The arrow shaft shows the amount of the force. You can do this with labels or drawing to scale.

The head of the arrow shows the direction the force is acting in.


Let’s Draw some Vectors


Paper or Graph paper



Drawing the Vectors:

Draw your block from Project 1

From the bottom center of the block draw a line 2 cm long straight down

using vectors to show gravity

Every object on Earth has this vector arrow pointing down. If that force didn’t exist, everything would float into space.

Put the head of the arrow on the end going down

What does this arrow show? What force is holding the block on the table?

You made the block move by pushing on it. Draw a line to the side of the block. How long should the line be?

using vectors gives information about forces

Using vector arrows for forces makes it easy to see how strong a force is, which direction it is going and how it is acting on an object.

The block moved. Think back to the game of tug of war. As long as the two forces were the same, the forces cancelled each other out.

If the force line showing you pushing the block is shorter than the gravity arrow, will the block move?

Your push vector must be longer than your gravity vector. Let’s make it 3 cm long. Now put the head of the arrow on.

Where does this go? Which way did the force push? It pushed against the block so the head of the arrow points at the block.

Can you draw the pulling force on the block using vectors? Try it. My drawing will be down below.


Using Vectors for Changing Forces

Put your block out on the table. This time push on the block from two adjacent sides at the same time.

two forces pushing block

Gravity always pulls on objects on Earth. This time we are interested in two forces pushing on two adjacent sides of the block at the same time. Which way will the block move? Can vectors be used to tell us?

Which way did the block go?

Draw your block on the graph paper again. This time have two pushing forces on adjacent sides on the block.

Now, copy one of the vectors from the tip of the opposite corner. Make sure it points in the same direction and is the same length.

using vectors to show movement

The vector arrows are the same ones as before only moved. they point the same way and are the same length. Moving the vectors lets you draw a resultant vector showing the actual path the block took when acted on by two forces.

Next copy the other vector with the end starting at the point of the other vector. Make sure it points in the same direction and is the same length.

If you draw a final vector from the point of the block to the point of the last vector, you have the direction the block moved when you pushed on it with two forces.

using vectors to show pulling

The vector arrow for gravity still points down. The other vector arrow now points away from the block as you were pulling on it.

Why Use Vectors?

You can see the forces acting on your block, right? You can see some of them but not others.

Using vectors makes what is happening easier to see. As we go on to look at work and simple machines, we will often use vectors to better understand what the forces are doing.