Justin Geeslin

Eng Physics I - M 1:00

Experiment Two – Vector Addition

1. Procedure

There are different ways to compute the values of vectors. The first way is the graphical method. This is done just be taking given lengths and drawing them in proportion to each other with varying direction. To demonstrate, draw one vector labeled A. At the tip of A, draw another vector labeled B. The angle between these two vectors should appear less than 180 degrees. Now, from the beginning of A to the end of B, you should be able to draw another vector to connect the two. This vector is labeled R. If the triangle was draw to proportion you should be able to simply measure your drawing of R and get the length. However, it is not necessary to draw everything to proportion. Use the component method, one must compute the length of R and any missing angles from given data. Let A = 3 and let B = 2 at 60 degrees. With this data, all the missing data can be derived. In order to find are we must employ the following formulas:

Ax = Acosө	Ay = Asinө
Bx = Bcosө	By = Bsinө
Rx = Ax + Bx	Ry = Ay+ By
R = √Rx + Ry

Using the formulas and the given data as follows:

Ax = 3cos0	Ay = 3sin0
Bx = 2cos60	By = 2sin60
4 = 3 + 1	1.732 = 0 + 1.732
√19= 16 + 3

This gives us the length for R. When all the sides are found one needs to then find the angles. We can find ө by using tanө = Ry/Rx. In this case, tanө = 1.732/4. This formula returns the value of ө as 23.4 degrees. The technique that is the component method can also be used for polygons as well as triangles.

In the next example, vectors are demonstrated by balancing forces with relation to angles. For example, if we had one vector of 600 grams at 135 degrees. And a 300 gram force at 225 degrees is would take a 670 gram force at 162 degrees the counter the other two forces. We can check this by using the same formulas as above.

Ax = 6cos135	Ay = 6sin135
Bx = 3cos225	By = 3sin225
-6.37 = -4.25 + -2.12. 40.6	2.12 = -2.12 + 4.24 4.49
√44= 40.6 + 4.49

Questions

1. The resultant vector would be zero because the vectors themselves return to where the originated.

2. The component method is more accurate because when you draw the figure it is easy to miscalculate and the angles are harder to obtain just by looking at them

3. Yes, it would still be balance although the same amount of force exhibited upon the table would not be the same as on earth. The forces would have decreased proportionally to each other.