Chapter 3.2 – Adding Vectors

Adding Vectors The process of adding vectors has also been previously discussed in our section of Newton’s Laws. The net force (or resultant) was determined by adding up all the force vectors. In that chapter, the rules for adding vectors were kept simple.

Practice: Finding the Resultant of 1-D Vectors Similar to Solving for (Net Force)

In this chapter, the task of adding vectors will be extended to more complicated cases in which the vectors are representing 2-D motion.

There are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors. The 2 Methods that we will learn how to use: 1. Pythagorean Theorem (using Trig) 2. Head – to – Tail Method ( using graphs)

Calculating Resultants Using the “Head – To – Tail” Method 1. Add the vectors by first attaching them head to tail. 2. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish 3. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. 4. The direction of the resultant can be determined by using a protractor and measuring its counterclockwise angle from the horizon.

EXAMPLE #1 Add the following vectors together and find the resultant 20 m, 45 deg. + 25 m, 300 deg. + 15 m, 210 deg. Scale: 1 cm = 5m

Step #2 Draw your vectors “Head – to- Tail” Draw the resultant in red. Draw the resultant from the start to finish.

The order in which you draw or attach) your vectors doesn’t matter, as long as you don’t change the magnitude or the direction.