Forces hold things in place and make them move. Some of the forces we can see. Others we know are there but can’t see. We need a way to show all of these forces. That is what vectors do.
Question: How do vectors show forces?
Open your Journal and write Project 4
Remember Project 1 where the block sits on the table
Draw a table with legs sitting on the floor
Draw the block sitting on the table
Gravity pulls down on the block so draw an arrow pointing down from the block
Note: Gravity always points toward the center of the Earth which is usually down
If only gravity was pulling on the block, it would fall to the ground so some force is pushing back on the block. The table is pushing back so draw another arrow next to the other arrow but pointing up.
How long should this arrow be? Vectors show speed and direction. We are not measuring speed but only showing direction in this Project.
Gravity pulls down. If the arrow pointing up is longer showing greater force, there would be more force pointing up than down. The block would float up off the table. It didn’t so the arrow isn’t longer than the gravity arrow.
If the arrow is shorter than the gravity arrow, the force of gravity would be greater than that of the table. The block would pull through the table and fall to the floor. It didn’t so the arrow isn’t shorter.
The arrows must be the same length as the forces are equal and opposite to each other.
Since the table isn’t floating away, gravity must be pulling down on it too. Draw vector arrows for gravity to hold each table leg on the floor.
Since the table isn’t sinking into the floor, the floor is pushing back against the table legs. Draw those vector arrows.
Next remember what happened when you pushed on the block. Your finger was a force acting on the block. Draw a vector arrow for that force.
Did the block move? Which way did it move? Since the block moved, there was no force pushing back against your finger so there will be no arrow.
Now wait a minute! When I pushed against my block of wood, the end of my finger flattened so the block did push back. But the block moved so the force the block pushed against my finger was much less than the push my finger gave the block. I will draw a little arrow from the block toward my finger.
Now let’s draw vectors for a paper airplane:
Draw the airplane flying
What force made the airplane fly?
You threw it so you exerted a force on it. Draw that arrow pushing the back of the airplane.
Is gravity acting on the airplane? Gravity acts on everything on Earth so draw an arrow pointing down for gravity.
What is pushing up on the wings to keep the airplane up? Air pushes up.
Does the air keep the airplane up all the time? It didn’t keep mine up. So there is an arrow for the air pushing the wings up but it is less than the gravity.
Where would the arrow for the fan pushing the airplane go? Draw it in.
Notice that this arrow is with the one from you throwing the airplane so the two add up.
Where would the arrow go for when the fan pushed against the airplane? For my airplane it would be the same length as the one for throwing the airplane because I did see it stop my airplane once.
This last set of drawings shows one way vectors help a physicist understand the forces acting on an object. When forces act together, they add up. When forces act against each other, they cancel each other out.
Another way vectors show how forces work is shown with the car going down the ramp.
Draw the ramp with a car on it.
The car is racing down the ramp so the vector arrow goes down the ramp. Or does it?
Gravity is pulling the car down but gravity pulls straight down. So there should be an arrow pointing down from the car.
But the car moved down the ramp. So there is another arrow from the tip of the gravity arrow to the ramp spot where the car will be after a certain amount of time.
In this case vectors show the movement of the car is made up of two different vectors, one pulling down and one pulling across.
Vectors usually show both direction and acceleration. They are a way to see how forces add and subtract from each other so you can tell where an object will go when several forces push or pull on it at the same time.
For now the accelerating force we will work with will be gravity. The next Project will look at some ways gravity pulls objects down.