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.

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

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**

Materials:

Paper or Graph paper

Pencil

Ruler

**Drawing the Vectors:**

Draw your block from Project 1

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

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?

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.

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.

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.

**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.