20.2 CHAPTER 20. VECTORS AND SCALARS
Addition and subtraction of vectors ESAGO
Adding vectors
When vectors are added, we need to take into accountboththeir magnitudesanddirec-
tions. See video: VPgel at http://www.everythingscience.co.za
For example, imagine the following. You and a friend are trying to move a heavy box. You
stand behind it and push forwards with a force
→
F 1 and your friend stands in front and pulls
it towards them with a force
→
F 2. The two forces are in thesamedirection (i.e. forwards)
and so the total force acting on the box is:
F→ 1 F→ 2 →
FT ot=→
F 1 +→
F 2It is very easy to understand the concept of vector addition through an activity using the
displacementvector.
Displacement is the vector which describes the change in an object’s position. It is a vector
that points from the initial position to the final position.
Activity: Adding vectors
Materials:masking tape
Method:
Tape a line of masking tape horizontally across the floor. This will be your
starting point.
Task 1:
Take 2 steps in the forward direction. Use a piece of masking tape to mark your
end point and label itA. Then take another 3 steps in the forward direction. Use
masking tape to mark your final position asB. Make sure you try to keep your steps
all the same length!
Task 2:
Go back to your starting line. Now take 3 steps forward. Use a piece of masking
tape to mark your end point and label itB. Then take another 2 steps forward and
use a new piece of masking tape to mark your final position asA.
Discussion:
What do you notice?
1. InTask 1, the first 2 steps forward represent a displacement vector and the
second 3 steps forward also form a displacement vector. If we did not stop
after the first 2 steps, we would have taken 5 steps in the forward direction in372 Physics: Mechanics