PHY214L Vectors in 2D Lab Report PDF

Preview

Summary

This is the lab report for vectors in 2D with James Buchholz...

Description

Running Header: VECTORS IN 2-DIMENSIONS

Lab 2: Vectors in 2-Dimensions Paige Hutton Lab Partner: Xavier Castaneda PHY214L-D September 9th, 2020 California Baptist University

Hutton 2 VECTORS IN 2-DIMENSIONS Purpose: The purpose of this experiment is to calculate force vectors using three different methods: experimental, algebraic, and graphical. In order to do so, scalars and vectors needed to be distinguished first. A scalar quantity is a physical quantity that is completely specified by a number with units, while a vector quantity is a physical quantity that is specified by a magnitude with direction. For part one of the experiment, a force table and hanging masses will be used in order to measure forces at certain degrees. The second part of the experiment, vectors from the previous part of the lab will be added together by graphing them in the tip-to-tail method. Lastly, the final portion of this experiment is to calculate the resultant vectors by decomposing the vectors into their x- and y-components in order to solve for their angles and magnitudes. By accomplishing this, our goal is to calculate resultant vectors for three cases and compare the methods of achieving those resultant vector values.

Results:

Case 1: m A=50 g , θ A =0 ° m B =100 g , θ B=120 °

Case 2: m A=50 g , θ A =0 ° m B =80 g ,θ B=240 °

Case 3: m A=75 g , θ A =0 ° m B =120 g , θ B=30 ° m C =50 g ,θ C =110 °

Experimental

Algebraic

m r=87 g

m r=86.6

θr =¿

269 °

m r=¿ 75g

θr =180 °

m r=¿ -59.3

Graphical m r=¿ 8.7cm θr =¿ 269 °

m r=¿ 7.5cm

θr =¿ 98 °

θr =180 °

θr =¿ 98 °

m r=¿

m r=268.8

m r=¿ 2.09cm

θr =180

θr =¿ 213 °

θr =¿

209g 213 °

Part 1: Experimental Vector Addition 

Case 1: Case 2: Case 3:

The results of this part of the procedure were obtained by using a force table, using four pulleys, a set of masses, and 4 mass hangers attached to a ring on the force table. We are given three cases and based on the values given in each case, we are to determine the resultant vector. Once the resultant vector is obtained, the ring attached to all of the mass hangers should be at equilibrium around the peg in the center of the force table. m A=50 g , θ A =0 ° m A=50 g , θ A =0 ° m A=75 g , θ A =0 °

m B =100 g , θ B=120 ° m B =80 g ,θ B=240 ° m B =120 g , θ B=30 °

m C =87 g , θC=269 ° m c =80 g ,θ c =98 ° m C =50 g ,θ C=110 °

N/A N/A m D =204 g , θ A =215 °

Hutton 3 VECTORS IN 2-DIMENSIONS

Part 2: Vector Addition by Graphing 

For this portion of the lab, we used the results found from part one to convert the forces into vectors as precisely to case as possible. Every 10g became 1 cm, and using a protractor, vectors were drawn tip-to-tail at the angles either given or found in part one of the experiment. (Results on graphing paper)

Part 3: Vector Addition by Components 

For the final section of this lab, the vectors are broken down into its x- and y-components and solved for using trigonometry and the Pythagorean Theorem. Then they will be added together in order to get the x- and y-components of the resulting vector. Note: It is important to consider the angle’s placement on the unit circle and what quadrant it would be in to determine whether the x- or y-components are positive or negative. m a =50 m a =0 m a =50

Case 1:

x

y

Case 2:

x

m a =0 m a =75 m a =0 y

Case 3:

x

y

m b =−50 m b =86.6 m b =−69.3 m b =−40 m b =103.9 m b =60 x

N/A

y

x

y

x

y

N/A

y

x

m R =0 m R =86.6 m R =−19.3 m R =−40 m R =161.8 m R =107 x

y

m c =−17.1 m c =47 x

y

x

y

Questions: 1. A scalar quantity is a physical quantity that is completely specified by a number with units. In other words, a scalar is a magnitude, but with no direction. An example of a scalar would be a car odometer, as it displays a distance, but it lacks direction in which the distance was traveled. A vector quantity is a physical quantity specified by a number, but also has a directional characteristic. Therefore, a vector has magnitude and direction, such as velocity, acceleration, and force. For example, a car’s speedometer combined with the compass would be a vector, as the speed is the magnitude and the compass provides direction. 2. I believe that there could have been more than one combination of mass and angle that would have brough the system into equilibrium. There was slight error in using our force table because it seemed a bit wobbly in that the equilibrium would shift back and forth randomly without any changes. Besides that, I hypothesize that greater mass could just require for the angle to be changed according to the case in order for equilibrium to be changed. For example, if there is one small force and a larger opposing force, you could add a force with larger mass at an angle to equal the total of the one larger opposing force, and vice versa for a smaller force.

Hutton 4 VECTORS IN 2-DIMENSIONS 3. Percent error =

100

|observed− actual | actual

In this situation, the algebraic is said to be the standard. Using this, either the experimental or graphical values for each case will be used as the observed values, and the algebraic values will be considered the actual. Experimental

Algebraic

Graphical

Case 1

0.46%

STANDARD

90.0%

Case 2

226%

STANDARD

112%

Case 3

22.2%

STANDARD

99.2%

4. Some instrumental error that may have arisen during this lab experiment were mostly centered around the force table. As previously mentioned, the table itself was wobbly and the “peg” in the center was a large screw with corners directly at ring-level, which impeded us determining if the ring was entirely in the center. Additionally, I believe the wobbliness of the force table to be the cause of the shifting forces throughout the experiment. The strings were all taut but it seemed that after a short period of time, they would shift back and forth without anyone adding weight or fiddling with the pulley angles. This also made it difficult to balance the ring and determine if true equilibrium had been reached. As far as the graphical portion of the lab, most of these errors were human error. However, the protractors needed to be reversed in order to achieve the correct angles, which may have caused the human error. 5. My preferrable method whilst performing this lab was the experimental portion where we used the force table and the mass hangers. I am a visual learner, so it was very impactful to see the opposing forces and see the ring perfectly around the central peg when at equilibrium. It was a good demonstration to put forces into perspective for me. On the other hand, my least preferrable method whilst performing this lab was the graphical portion. Converting the grams into lengths was adequate but going from the force table to graphing shapes such as triangles and a trapezoid caused some confusion for me.

Conclusion: For the first portion of the procedure, this was the physical manifestation of the forces in work, shown by the equilibrium being reached based upon the masses and angles applied to the resultant vector. The second section of the lab was translating these magnitudes to paper and transforming them into closed shapes. This helped convey equilibrium in that the two uneven vectors also had a resultant vector which equaled out the forces. The final segment of this lab experiment was to calculate these vectors algebraically, mainly by using the angles found

Hutton 5 VECTORS IN 2-DIMENSIONS from the force table in part one and displayed in the graphed vectors in part two. The main idea was the decompose each given vector into is x- and y-components, add them together, and get the x- and y-components of the resultant vector. After analysis of our resultant vectors, these three methods appeared to be relatively similar in value. There were most certainly a few errors in calculating the percent error, since the experimental data was in grams and the graphical data was in cm. This could cause for quite large measures of uncertainty, but it seems there were extremely high, extremely low, and median percent error values. It seems that our smallest percent error came from the graphical experiment of case one, which would indicate that graphical was the second-best method of obtaining an accurate resultant vector. For the first portion of the procedure, this was the physical manifestation of the forces in work, shown by the equilibrium being reached based upon the masses and angles applied to the resultant vector....