Lab Report 3 Outline for PHYS 2108

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Louisiana State University *

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2108

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Mechanical Engineering

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Dec 6, 2023

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1 Name: Date:9/14/2023 Partners: PHYS 2108 Section: 13 Lab Title: Vectors Lab Report 3 Prelab (2 points) Purpose To focus on breaking down vectors into their respected x- and y- components. The components are recombed to calculate the resultant vector. Procedure (Please keep under ½ page) Using a force table, four force situations were found. The first situation had the pulley at 0˚ and 180˚ with an additional 50g on each hanger pans. The second situation had pulley 1 at 0˚ and pulley 2 at 120˚. A third pulley was added originally at 180˚ with 100g but more weight and location of the pulley was altered to balance the system. The third situation had pulley 1 at 0˚ with 100g mass and pulley 2 at 105˚ with 200g mass. Pulley 3 was 200g and adjusted to balance the system. The fourth situation used the same positions of pulley 1 and 2 but rotated by 45˚. Pulley 3 was placed to bring the table back to balance. During Lab (Findings) Analysis (13 points) Please attach and label ALL CALCULATIONS. Show equation, plugging in values, and box your answer. Attach labeled sketches. Data Table 1: Forces in 1-D Total mass Angle Force (weight) x-comp y-comp F1 150g 0˚ 1.47N 1.47 0 F2 150g 180 1.47N -1.47 0 Sum of Components: 0 0 X comp: 1.47N cos (0) = 1.47 Y comp: 1.47N sin (0) = 0

2 Magnitude Angle Resultant 0 0 From + x-axis Observations of washers: When removing the washer from the pin and releasing it from rest, there was no change in position. The hanger pans remain the same. Data Table 2: Equal forces in 2-D Total mass Angle Force (weight) x-comp y-comp F1 150g 0˚ 1.47N 1.47 0 F2 150g 120˚ 1.47N -0.735 1.27 F3(measured) 150g 238˚ 1.47N -0.779 -1.25 F3(predicted) 150g 240˚ 1.47N -0.735 -1.27 % Error in Angle 0.83% Data Table 3:

3 Unequal Forves in 2-D Total Mass Angle Force (weight) x-comp y-comp F1 150g 0˚ 1.47N 1.47 0 F2 150g 105˚ 2.45N -0.634 2.37 F3 (measured) 260g 250˚ 2.55N -0.871 -2.39 F3(predicted) 250g 255˚ 2.45N -0.836 -2.37 % Error in Angle: 1.96% Data Table 4: Change of Coordinates Total mass Angle Force (weight) x-comp y-comp F1 150g 45˚ 1.47N 1.04 1.03 F2 250g 150˚ 2.45N -2.12 1.23 F3(measured) 255g 295˚ 2.50N 1.06 -2.27 F3(predicted) 250g 295˚ 2.45N 1.08 -2.26 % Error in Angle: 0%

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4 Reflection (10 points) 1. The two forces that help balance the washer in the center is equal. If a correction mass was added there would be an imbalance of weight. Each force would have a different mass whether that be one’s heavier than the other etc. 2. The washer did not move. The two force vectors are still balanced because they did not move. 3. The system does not need a correction mass. F 3 has the total mass of 150g with an angle of 238˚ and a force weight of 1.47N. The x and y components were -0.735 and -1.46. For the prediction the total mass was 150g with an angle of 240˚ and a force weight of 1.47N. The x and y components of the prediction were -0.735 and -1.27. The percentage error was 0.833%. 4. The arrangement needed the correction mass. The location of the pulleys can cause an uneven distribution of mass on the force table. The resultant of the forces did not equal the force of the two other forces. 5. No, the resultant vectors do not depend on absolute coordinates. The shifting point of the pulleys will affect the mass of each point needing more mass to have balance. Application (10 points) 1. The component method requires a 90˚ angle to stop the x and y components from overlapping in value. If the angle was 60˚, the y-component will overlap the x- component therefore, the resultant vector will be skewed. 2. F= sqrt((20 2 +3 2 ) = 20.2lbs Tan -1 (2/30) Theta = 8.53˚ 3. F x + 60,000sin(45) = 70,000 60,000sin(45)= 42426.4068 70,000-42426.4068=27,573.6 (F x ) F y – 60,000cos(45)=0 F y =42,426.4 N F= sqrt((27,573) 2 +(42.426.4) 2 )

5 Conclusion (4 points) Include lab summary (2 points) and sources of error (2 points). Do not say human error! We calculated the x and y components of vector forces in four different situations. The situations had adjustments to find ways to balance the system. The measurements of F1 and F2 would equal the predicted F3. One of the weights was labeled 199.9 g instead of 200.0g. The force table was not properly taken care of therefore it would not balance correctly.