For the Projects we’ve done so far we’ve accepted that the paper, the car, the balls and the jar moved. What is motion?
Look up motion in the dictionary. What does it say?
My dictionary says motion isthe act of changing place or moving.
We used vectors earlier to show the direction of a force. Vectors can also help us show where and how far something is moving.
Another concept in physics is displacement. This is how far something moves from its original position. This is not the same as the distance something moves.
Question: How can vectors show how something moves?
Materials:
Sheets of Grid paper [quarter inch is fine]
Pencil
Procedure:
Draw a line across a sheet of grid paper about ten squares from the top
The line is a street
Make a little mark across this line every second square
These marks show blocks
Draw a little house at the middle mark on the line
On a map east goes to the right, west to the left, north up and south down.
Trip 1:
You leave the little house and walk three blocks east to the market
Above the line you can make a fancy house and market. Below the line is room for the vectors. The first one goes from the house east to the market. It has an arrow on the tip pointing the direction you walked.
To show this draw a line from the mark in front of the house three blocks east or and put a little arrow at the end of the line.
Now you walk three blocks west back to the little house
You now walk back home so the vector arrow goes from the market to your house. The arrow is now on the end at your house as you walked that way.
Draw another line from the market to the little house and put a little arrow on the end
Conclusions:
How far did you walk?
This is distance. Your total distance is 3 blocks east plus 3 blocks west or 6 blocks.
What is your displacement?
Notice on your graph the arrows are equal and opposite. The vectors say you did not go anywhere.
Displacement is how far something moves away from where it started. In this case the displacement is 0 because you started and ended at the same place.
Trip 2:
Draw another line about ten squares below the first line and put a little mark in the middle
The long green line is the street running east and west with a mark showing your house in the middle. You can draw houses above the line if you wish.
This time each square is a block
You go to a friend’s house five blocks west of your house
The first vector is you going five blocks west so the line goes five squares to the left.
Draw this vector
The two of you decide to go to another friend’s house seven blocks east of where you are
Going seven blocks east means going past your house plus another two blocks and the vector shows this.
Draw this vector
Later you and your first friend go to your homes for dinner
You go only a short distance and your friend keeps going so two vectors are needed. I labeled them with a y for you and an f for friend so i would know which was which.
Draw these vectors
Conclusions:
Trip 2:
What distance did you walk?
What distance did your first friend walk?
What distance did your second friend walk?
What is your displacement at your first friend’s house?
What is your displacement at your second friend’s house?
What is your first friend’s displacement at your second friend’s house?
What is your total displacement?
What is your first friend’s total displacement?
Observations:
Your lines and vectors
On Your Own
Draw another line about ten squares below your last vector line
Mark your home in the center
Walk the five blocks west to your friend’s house
[Hint: This may be easier if you use more than one color for the vectors such as one to you alone, one for you and your first friend, one for the three of you and one for your two friends.]
The two of you walk seven blocks east to your other friend’s house
The three of you go five blocks east to a park for the afternoon
The three of you go to your house for supper
Your two friends go back to your first friend’s house for the night
Conclusions
What distance did you go?
What was your displacement?
What distance did your first friend go?
What was your first friend’s displacement?
What distance did your second friend go?
What was your second friend’s displacement?
What I found Out:
I used four different colors and labeled the vectors to keep track of them. Another way would be to do three graphs, one for each person. That method would make it easier to see how far and where each person went.
I walked 5 blocks W + 7 blocks E + 5 blocks E + 7 blocks W or 24 blocks. My displacement was 0 because I started and ended at home.
My first friend walked 7 blocks E + 5 blocks E + 7 blocks W + 5 blocks W or 24 blocks. My first friend’s displacement is 0 because of starting and ending at home.
My second friend walked 5 blocks E + 7 blocks W + 5 blocks W or 17 blocks. My second friend’s displacement is 7 blocks because of starting at home and ending at my first friend’s house.