Lab 2 - physics 207 Lab report #2 PDF

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physics 207 Lab report #2...

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TITLE: Vectors INTRODUCTION: In this second lab, I was able to learn vectors and quantifying their measurements to understand magnitude and direction. Through the use of force table, my teammates and I set an equilibrium to vector quantities and I was able to do that by adding vectors. We found vector quantities mathematically and also analytically to observe changes when tension is added. While talking in reference to real life vectors, the cricket sport is an example of vector and trajectory. While bowling, players mentally calculate the speed of cricket ball to maximize their throw. This is a great example of usage of vectors in which just by the speed of the ball and angle at which it is bowled players can understand how far the ball will reach. PROCEDURE: Experiment 1: I repositioned two pulleys at the end of the force tables by unclamping them. Then I had to reposition two pulleys, one at zero and then one hundred and eighty degrees. After designating pan 1 at 0 degrees and pan 2 180 degrees, I put a pan on each. Pan 1 needed 50 grams and pan 2 needed 51 grams to test for equilibrium. My teammates and I continued to add and subtract masses to see how much weight we can add to pan 1 while it maintains equilibrium. Experiment 2: The random number generator gave me two initial masses and directions to set equilibrium. Then, by following similar procedures from experiment one, we had to reposition two pulley clamps according to the number generator. Followed by the setup of the experiment,

we experimentally found a third pan to balance out the system. In doing this, we saw that finding the resultant of the two vectors helped us. Experiment 3: Using the sample image from the lab manual, I set up pan 1 at 5 degrees, pan 2 at 355 degrees and pan 3 at 180 degrees. We had to designate point b as the angle between pan 1 and pan 2. Slowly, we added 50 grams to pan 1 and 2 respectively, and experimentally found the mass of pan until equilibrium. We did this until 80 degrees, incrementing b by 5 degrees, and recording the mass of pan 3 needed to achieve equilibrium. We recorded the data in a table found an equation for pan 3. Experiment 4: I used the number generator to obtain three sets of random masses and directions. Then my teammates and I used algebra to find the fourth vector, D, that helps achieve equilibrium when doing addition of the vectors. After that, we used trigonometry to convert the answer back to correct magnitude and degree format. DATA/RESULTS: Experiment #1 Sensitivity (g) = 53 g  This number indicates that the system will need around 53 grams to reach its equilibrium when placing the mass. Anything over that will disrupt the equilibrium.

Experiment #2 Given Randomly Generated Values

Mass (g) 25 25

Direction (°) 30 330

 We used these numbers to set up the mass system on the force table and achieve equilibrium, while comparing our measured mass and theoretical mass from experiment 1. 

Measured Mass need to balance the System (g) = 77 g



Theoretical Mass needed to balance the System (g) = 129.92 g



Grams difference = 52.92 g

Experiment #3 Table of Cos (b) (Angles°) vs. Mass of Pan 3 (g) Theoretical Mass of Pan 3 System (grams)

Measured Mass of Pan 3 System (grams) Angle (°) 5

190

199.2

10

190

197

15

190

193.2

20

190

188

25

190

181.3

30

180

173.2

35

180

163.8

40

160

153.2

45

154

141.4

50

132

128.6

55

120

114.7

60

112

100

65

90

84.5

70

72

68.4

75 80

60 40

51.8 34.7

 This table depicts the results of when we changed angle b between pan 1 and pan 2 and how the mass needed to balance the force table differ for different angles. As the angles increased between two pans, the mass needed to balance the system decreased.

Graph of Cos (b) (Angles°) vs. Mass of Pan 3 (g)

Cos(b) (Angle°) vs. Mass of Pan 3 (g) 250

2.25x x++229.8 231.29 f(x) = − 2.1 R² = 0.91 0.96

Mass of Pan 3 (g)

200

150

100

50

0

0

10

20

30

40

50

Cos(b) (Angle°)

60

70

80

90

 This graph represents the relationship between the mass needed for equilibrium and the angle of two pans. As the angle increased, the mass decreased, so we can infer a decreasing slope. An increase in angle means more force directed in the horizontal direction while less on the vertical side, so overall mass is less for establishing equilibrium. REPORT QUESTIONS: Question#1: In the first exercise, we only balanced two pans 180 degrees apart. However, as we progressed in exercises, we were able to add more mass on one side without disrupting equilibrium. Sensitivity was affected because the ring was not completely horizontal. The shape of the ring was curved on one side so one side needed more mass to balance. Another factor is the two pulleys were not the same. One pulley was straight while the other pulley was slightly slanted. Question#2: For the experimental results, we got 77 grams for balancing the system. However, the simulated value of mass was 129.92 grams, thus yielding a difference of 52.92 grams. This value is proved to be lower than our sensitivity, which was 53 grams. Question#3: Using our data, we created a scatter plot and found slopes. In the same graph, we also modeled a scatter plot for the analytical equation. The slope of the analytical line was -2.246. The difference in the slopes of the lines is 0.2, which is smaller than the uncertainty. This makes our theoretical answer very close to the actual one. Question#4: Using the given 3 sets of randomly generated masses and direction for vectors we calculated the fourth vector (vector D). We had to calculate the x and y components of each vector according. The net values of the x components and y components all add up to 0. We obtained Dx to be 24.633 and D y to be -18.724. Following that, we calculated the magnitude and

angle using the x and y component of vector D. The angle is -26.5 degrees and the magnitude is 30 grams. Comparably, our experimental results were 30.25 degrees and 35 grams. This is the result we obtained from using the force tables. Our answers most likely differed due to the sensitivity of the system.

CONCLUSION: In this second lab, we utilized force tables, mass and weights, pans and pulleys. We started with measuring sensitivity of the system. This was important because we understood the role of sensitivity ad what factors can influence our results, such as the asymmetrical shape of the ring we used for maintaining equilibrium. Experiment 2 required us to find a resultant vector for equilibrium which we used to compare our theoretical and actual values. Our results differed from the actual values by almost 50 grams. This is partly attributed to the sensitivity. The machine was not very precise because the pans came off the string multiple times and we had to maintain that the system received the least amount of human force that can contribute to the equilibrium. In experiment 3, we set up an experiment by incrementing the angle by 5 degrees between two vectors. This part of the experiment was rushed because of the time constraint we had, so we could not get accurate measurements of the masses. Also, during the experiment, the weight fell down multiple times and we had to add human force to the factor. In the final experiment, we attempted to find the last vector but there could be computational errors. Ultimately, this lab required a lot of precise measurements and tedious observations. When dealing with vectors, I learned that we have to understand the addition and subtraction of vectors and see what additional factors could disrupt proper equilibrium....