Addition of Vectors

Imagine that you have a map that leads you to a buried treasure. Imagine that you have a map that leads you to a buried treasure. This map has instructions such as 15 This map has instructions such as 15 paces west northwest paces west northwest of the skull. The 15 paces is The 15 paces is a distance and west northwest is a direction. N

Quantities that are described by a magnitude (such as the distance on the previous slide) and a direction are called vectors. Quantities that are described by a magnitude (such as the distance on the previous slide) and a direction are called vectors. Those quantities that have no direction are called scalars. Those quantities that have no direction are called scalars.

Examples of scalars in physics are Examples of scalars in physics are masstime distancespeed workenergy Examples of vectors in physics are Examples of vectors in physics are displacementvelocity accelerationforce momentumangular momentum

The math associated with scalars is familiar to everyone. The math associated with scalars is familiar to everyone. The math associated with vectors is more involved. The math associated with vectors is more involved. Today you will explore the graphical addition of vectors. Today you will explore the graphical addition of vectors.

Let’s use a treasure map again as an example of the addition of vectors. Let’s use a treasure map again as an example of the addition of vectors. Let’s imagine the instructions tell you to go 4 miles east then 3 miles north. Let’s imagine the instructions tell you to go 4 miles east then 3 miles north.

4 miles 3 miles 5 miles

In this case you could have gone 3 miles north first and then 4 miles east next and still end up at the same location. In this case you could have gone 3 miles north first and then 4 miles east next and still end up at the same location. Your final position is 5 miles at north of east. Your final position is 5 miles at north of east. It would have saved time if that had been the one distance and one direction traveled in the first place. It would have saved time if that had been the one distance and one direction traveled in the first place.

We say that the 5 miles at north of east is the vector sum of the 4 miles east vector and the 3 miles north vector. We say that the 5 miles at north of east is the vector sum of the 4 miles east vector and the 3 miles north vector. The order of the addition does not matter. The order of the addition does not matter. Examples of addition of vectors follows. The method used is the Examples of addition of vectors follows. The method used is the head-to-tail method. head-to-tail method. You must know how to do these for your lab exams. You must know how to do these for your lab exams.

Head-to-Tail Method of Addition of Two Vectors

Head-to-Tail Method of Addition of Three Vectors

You will need to use a scale when you graph your vectors. For example, you might set 10 cm to represent 100 grams.

How to Construct Two Perpendicular Lines (With a Protractor) to form a Set of Coordinate Axes

W E S N

How to Construct a Second Set of Coordinate Axes Parallel to an Initial Set of Coordinate Axes

Mark the angle for the vector.

Remember the angle marked.

W E S N Resultant

W E S N Resultant Equilibrant