Vectors and forces - A full completed physics lab report. All of the labs remain the same each year. PDF

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A full completed physics lab report. All of the labs remain the same each year. ...

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Vector Addition of Forces

1. Introduction: A vector quantity is defined as a quantity that has both a magnitude and direction. A good example of vector quantities are forces which are defined as any interaction that, when unopposed, will change the motion of an object. Forces are said to be concurrent when multiple act on one body and pass through a common point. All these forces can be added together to produce a resultant that is equal to the vector sum of other forces. Because vector quantities include magnitude and direction, both of these properties must be considered when adding them together. This is known as the vector sum, which is shown with this equation: R = F1 + F2 + F3. R represents the resultant and F1, F2, and F3 are the forces being added together. Each force added contains x and y components and magnitudes. To find the x and y component of

each force, you must take the sign (+/-), magnitude, and trigonometry into consideration. As a result, the x-component can be found with this equation: F1x= F1cos θ

;

1

and the y-component can be found with this equation: F1y=F1sin θ

1

,

while the magnitude of the force is represented by F1=|F|. Once the x and y components of each vector has been found, the respective x and y component of the resultant can be found using vector addition: Rx = F1x + F2x + F3x and Ry = F1y + F2y + F3y. The magnitude of the resultant is found using the Pythagorean theorem a2 + b2 = c2 (take the square root), and the final angle is found taking the inverse tan tan θ

R=

Ry Rx

.

2. Objective: The objective of this experiment was to find the equilibrant via the parallelogram and component method. In the parallelogram method, three forces were suspended from the center of a force table, and were adjusted in order to reach equilibrium. The same steps were reiterated for the component method except in the component method, four weights were suspended and adjusted to reach equilibrium. 3. Questions & Analysis 1. The true value of the resultant in Table 2 is zero. 2. The values for the resultant in Tables 1 and 2 differ from the true value because of random, human error. This could have been the result of individual bias when trying to achieve equilibrium. The measurer may have thought the apparatus was in equilibrium when it was not. As a result, wrong measurements were taken resulting in values that differ from the true value. 3. No, a non-rectangular coordinate system can not be used for the component method. The component method uses trigonometric functions, and in order to use trigonometric functions, a right angle (90°) is needed.

Sample Calculations:

4. Discussion/Conclusion: In conclusion, the vector addition of forces was studied. A vector quantity is defined as a quantity with both a magnitude and direction. Both of these characteristics were taken into consideration when adding them together, giving us our vector sum. The equilibrant was found via the parallelogram and component method. When performing the parallelogram method, three weights were suspended from the center of the force table and adjusted until it reached equilibrium. The magnitude of force 1 was found to be 146g; the magnitude of force 2 was found to be 100g; and the magnitude of force 3 was found to be 124g. A scale was set at 1cm = 20 g to produce numbers that were manageable. On this scale, force 1 was 7.3cm, force 2 was 5.0cm, and force 3 was 6.2cm. A parallelogram was drawn to scale and the resultant of forces 1 and 2 was estimated to be 6.5cm (with an angle of 122°) or 130gm. When subtracting the difference between the resultant and force 3, the result was 6gm which equaled 0.3cm. The same steps were reiterated for the component method except four weights were suspended from the center and adjusted until it reached equilibrium. In order to find the magnitude and angle of R, the four forces were broken up into their respective x and y components, using trigonometric functions such as sine and cosine. This resulted in an overall x-value of -20.2 and an overall y-value of 57.48. The Pythagorean theorem was performed on these results and the magnitude of R was found to be 60.92N. The inverse tangent was taken and the angle R was found to be -70.64°. My experimental values differed from the true values due to random error. This random error could have been due to human error, more specifically individual bias. The

measurer may have thought the apparatus was in equilibrium when it was not. As a result, wrong measurements were taken resulting in values that differ from the true value....