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?
Materials:
Paper
Pencil
Ruler
Procedure:
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
Your drawing doesn’t need to be fancy. A simple set of boxes will work like this will work fine.
Draw the block sitting on the table
Gravity pulls down on the block so draw an arrow pointing down from the block
Gravity pulls down on the block so it sits on the table. The vector arrow points down.
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.
The table pushes back against the block just as hard as gravity pulls it down so a vector arrow the same size pointing up is added to the block.
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 is not floating away, gravity is pulling down on the legs so a vector arrow pointing down is put in each leg.
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.
The floor pushes up against the table legs just as hard as gravity pulls down on the legs so the arrows are the same length as those vectors but pointing up.
Since the table isn’t sinking into the floor, the floor is pushing back against the table legs. Draw those vector arrows.
A vector arrow showing the push on the block is added aimed at the block which was the direction of the force.
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.
Every pair of force vectors have the arrows equal and opposite except for the last pair. The pushing force arrow must be longer than the block resistance force arrow for the block to move.
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.
Paper airplanes are fun to fly. They fly and fall because of forces pushing and pulling on them. Those forces can be drawn as vectors.
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.
Throwing a paper airplane pushes it forward so the vector arrow pushes against the tail end.
Is gravity acting on the airplane? Gravity acts on everything on Earth so draw an arrow pointing down for gravity.
Like the sheet of paper, air pushes up on the wings of the paper airplane so the vector arrow points up toward the wing.
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.
The paper airplane doesn’t fly forever so gravity pulls down on it which the vector arrow shows.
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.
When the air from the fan pushes the paper airplane, the vector arrow pushes against the airplane’s tail adding to the thrust vector from you throwing it.
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.
When the air from the fan blows against the paper airplane, the vector arrow must point toward the airplane.
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?
The car is moving down the ramp so the vector arrow points down the ramp but is this correct?
Gravity is pulling the car down but gravity pulls straight down. So there should be an arrow pointing down from the car.
Gravity pulls down on the car so a vector arrow points 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.
The gravity arrow and the forward arrow meet at the vector arrow on the ramp’s point as the two add up to that vector.
In this case vectors show the movement of the car is made up of two different vectors, one pulling down and one pulling across.
About Vectors
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.