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Adding vectors
When adding vector quantities remember that the directions have to be taken into account.
The result of adding vectors together is called the resultant.
When adding two vectors together:
- the greatest (maximum) resultant is equal to their sum
- the smallest (minimum) resultant is equal to their difference
- the resultant can have any value between these limits depending on the angle between the two vectors
In problems, vectors may be added together by scale diagram or mathematically.
- Question
A woman walks 40m east then 30m south.
Find the total distance travelled
- Answer
Total distance travelled = 40 + 30 = 70 m
- Question
Now find the resultant displacement.
- Answer
To do this we need to use a scale drawing.
Use a large scale diagram for accuracy.
Scale 1 cm = 5 m
(Mark starting point A, turning point B and finish point C)
length of vectors consistent with scale
When measured on the scale diagram:
- the resultant displacement between points A and C = 50 m (10cm on the diagram)
Or mathematically:
Size of resultant displacement =
Direction of resultant displacement
- Question
Two forces of value 100 N act on the object shown below.
Find the resultant force on the object.
- Answer
Length of vectors consistent with scale
By scale drawing
Scale 1 cm = 10 N
Size of resultant force = 100 N
Direction of resultant displacement = 60° to either force
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