Physics 105, Fall Term, 2009

Reading: Chapter 3.1-3.2

Did you complete the reading assignment? Yes No

1) A vector has two components, a magnitude and a direction.

2) The magnitude of a vector is its length and can be found from its x and y components.

3) To add or subtract vectors, combine the x components of each vector and the y components of each vector separately; use the Pythagorean theorem on the resulting total x and y components to find the total vector length.

If you are traveling to a destination, it does very little good to know how fast you are going unless you know which direction you are traveling. Without knowing the correct direction, you may never make it there. This is a basic example of why vectors are used in physics. You will need to use vectors all semester (and when you take Physics 106 also) so you need to become very familiar with how to work with vectors. The following link will help you to become visually familiar with vectors and vector addition/subtraction: http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html.

You will see in the simulation a bucket of red arrows in the top right of the screen. You can click and drag a vector from this bucket onto the axes at any time. Clicking on a vector will display its length (in the absolute value sign), x component length, y component length, and angle from the x-axis. You may move a vector by clicking on its stem and dragging it somewhere else. You can also change the length and direction of a vector by clicking on the head and dragging it somewhere else.

Place a vector anywhere on the grid with its tail on the origin. Now move it around to a few different positions on the axes by clicking and dragging on the tail. Which values change? (select all that apply)

Total Length (|R|) Direction (θ) X component length (R_{x}) Y component length (R_{y}) None

Now grab the vector by the head and drag it around. Which values changed? (select all that apply)

Place 2 vectors of different lengths on the origin, both going in only the x direction. Now click the 'Show Sum' box in the top of the green box to the right. A green arrow will appear on the screen showing the sum of the vectors on the screen. How does the value and direction of the green arrow compare to the value of the red arrows?

The green arrow values are the values of teh red arrows added together.

Now drag one of the arrows so that its tail is connected to the head of the arrow still connected to the arrow on the origin. Drag the green arrow so its tail is touching the y-axis. How do the lengths of the arrows compare?

The length of the green arrow is the length of both red arrows combined.

Now click on the head of the second arrow and rotate it 180° so that it is in the opposite direction. How do the the lengths of the arrows and the values of the vectors compare now?

The value of the green vector is equal to the value of the second green vector subtracted from the first green vector.

Rotate the head of the second arrow so that it has both an x and y component and place the tail of the green arrow at the origin. How are vectors added graphically?

Head to head Tail to tail Head to tail Tail to head

Drag the red vectors anywhere on the screen (aside from the trash can). Which values for the sum change? (select all that apply)

Now put as many vectors as you would like on the screen putting them all together head to tail and click on 'style 1' for the component display in the green box.

How do the x and y components of the red vectors and the green vector compare?

The addition of all the Rx and Ry values of the green arrows is equal to the Rx and Ry of the green vector.

Where is the head of the green vector located?

At the same place as the head of the last red vector.

The comments entered in these last two boxes go into a big anonymous data file that I will use to guide the lectures of the day. That means two things:

1) If you have a specific question or concern and would like an individual answer you will need to come by the office or send an email. 2) If you really want to get an anonymous comment to me before the lecture, it must be submitted before 11am that day.

Was there anything that you didn't understand in the reading assignment? What was confusing to you?

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