Lab 4 Vector Addition of Forces

This lab was by far the most conceptual. The purpose of this lab was to study vector addition by graphical means and by adding components. A circular force table was used to check our results. To do this lab we needed a protractor, ruler, mass holders, masses, circular force table and four pulleys.

 The lab started off with the instructor giving each group three masses (which represented magnitude of a vector) and an angle to go with each one. We were instructed to use 100 grams at 0 degrees, 200 grams at 71 degrees, and 160 grams at 144 degrees.

We were told, as our first step to take a ruler, graphing paper, and protractor and to add all these vectors by hand. We were instructed to draw the vectors to scale, having 1 cm=20 grams and to find the resultant vector.

Here we found a resultant vector, we called R, to be 284 grams and 83 degrees. Then we were told to make a second vector diagram, this time using components of each vector to to draw the resultant vector.

Now came the fun part, putting our calculations to work. We mounted three pulleys on the edge of the force table at the angles given to us. Then we attached the strings from the center ring so that they each ran over the pulley and attached a mass holder to the opposite end of it.

We were told to hang the appropriate mass at the three appropriate angles and to set up a fourth mass at a fourth angle to cause equalibrium. This fourth angle happened to be 180 degrees opposite the resultant vector found earlier in our calculations.

We were then told to visit a website, as seen above, and insert all of our data in order to form a resultant vector. The scale on the website is in incriments of 10. We found out that we were correct. There were no error in our calculation and the computers.

The only real calculation  came from adding components of vectors to find the resultant vector.We had to find each x component of the given vectors and each y component of the given vectors. Once we did that we added all the x components and all the y components and got our resultant vector components. From these two values we could use the pythagreon theorom to find the magnitude of our resultant vector, and to find the angle it made we used the inverse tangent property of the y component divided by the x component

Angle	Magnitude	X Component	Y Component
0	100	100*cos(0) = 100	100*sin(0) = 0
71	200	200*cos(71) = 65.1	200*sin(71) = 189
144	160	160*cos(144) = -129	160*sin(144) = 94.0
		X Component Result	Y Component Result
		36.1	283
		Magnitude Result	Theta Result
		((36.1^2)+(283^2))^.5 = 285.3	Tan^-1(283/36.1) = 82.7

In this lab I learned that if all of our vectors are added up, 180 degrees off the resultant vector, with same magnitude would balance it out on a circular force table. I had some idea that this would work out because I am in calculus 3c, and that class is all about vectors. The error came from using protactors and rulers to estimate the resultant vector of adding the three given vectors. There was also error in adding weight to the pullies. I even saw one of the weight say 49.5 on it while having 50 grams engraved in it. It's also possible for the pullies to have grease spots or not such smooth rotation after being used over the years hence adding more marginal error. Another place we could find error was lining up the pullies and the right degree on the circular force table, both human error and significant error played a major role.