Lab Report #3 Destiny Banks 1 PDF

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Lab Report summarizing an experiment conducted to add vectors...

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Lab Experiment #3: Addition of Vectors & Force Table Destiny Banks Southern University and A&M College SPHY213-LB-01 Dr. Gao June 29, 2020

I. Introduction Vectors can be described as physical quantities that need direction and magnitude to be expressed. They can be represented algebraically and graphically and can be added, subtracted, multiplied and divided. The objectives of this experiment are to utilize a force table to experimentally determine the vector sum of two perpendicular, compare experimental values with calculated values for magnitude and direction of a resultant force, and use the force table to demonstrate the vector addition of three forces. II. Materials Force table, pulleys, a ring, pulley clamps, strings, and mass sets and hanger. III. Procedures The force table will be set up according to its instructions and once the mass sets are hung on the apparatus, the strings will be pulled downward until they are close to the surface of the force table but are not touching it. The equilibrant will be measured by trial and error by finding the angle for the third pulley and the mass that must be suspended from it that will balance the other two forces. The forces are balanced when the knot is centered over the hole. The center knot will be in equilibrium if once the center knot is pulled slightly and it returns to the center. The direction and magnitude of the equilibrant will be recorded as the force of the third string. IV. Results

Data Table

Force FA FB FE

Direction 𝜃1 = 45° 𝜃2 = 150° 𝜃3 = 290°

125 g 175 g 185 g

Magnitude 6.25 cm 8.75 cm 9.25 cm Vector Sum

X Components 88.4 g -151.6 g 63.3 g

Y Components 88.4 g 87.5 g -173.8 g

0.1 g

2.1 g

Calculations FAx = 125cos45 = 88.4 FAy = 125sin45 = 88.4 FBx = 175cos150 = -151.6 FBy = 175sin150 = 87.5 FEx = 185cos290 = 63.3 FEy = 185sin290 = -173.8 Resultant = √0.12+2.12 = 2.1 g Direction = tan-1(-173.8/63.3) = -70° or 290° V. Conclusion Vectors are known to be a physical quantity that possess both magnitude and direction; however, they lack a set position. The equilibrium principle applies to all vectors because in order for an object to be at equilibrium, the sum of all

vectors/forces must be equal to zero or there are no forces acting on the object. If another vector/force is added, the system will no longer be at equilibrium. The X Component percent error was calculated to be 0.1% and the Y Component percent error was calculated to be 0.6% using the following formula: % error =

|vector sum| 1/3(|F1x |+|F2x|+|F3x|)

x 100%

This percent error could be attributed to minor errors determining angle measurements and the percent errors being so small shows that the measurements obtained, although not completely accurate, were close estimates....