Experiment 3
Vector Addition: Force Table
Objective:
To experimentally verify the parallelogram law of vector addition by using a force table
Equipment:
A force table, a set of weights, a protractor, a metric ruler, a scientific calculator, and graphing paper.
Theory:
Concurrent forces are forces that pass through the same point. A resultant force is a single force whose effect is the same as the sum of a number of forces. The equilibrant of a system of forces is equal in magnitude and opposite in direction to the resultant of those forces. Review the introduction section of Experiment 2 for additional information on the polygon and analytical methods of solution, if necessary.
Procedure:
Set up a force table as shown in the following figure with three hanging weights.
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Be careful about the following points while using the force table: 1) The direction of the forces must be set by adjusting the strings at the desired angles. The angles must be read from directly above the strings to prevent parallax error. Also position the ring in center while setting the angles. 2) The string (not the edge of the clamp) represents the line of action of the force.
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A schematic diagram of a force table |
A. Trials 1 and 2
In each of the trials 1 and 2, place the weights for F1 and F2 in accordance with Table 1 at the specified angles. The ring is the object under study. Place enough weights on the third cord (Force F3) and adjust its angle until the system is in equilibrium with the ring centered on the small circle at the center of the apparatus. Force F3 that is required to bring the other two forces to equilibrium is called the "equilibrant." Record the angle or magnitude of F3. Also find the magnitude and direction of F3 by calculation (or the analytical method). First find Rx and Ry, then R and θ as usual.
B. Trials 3 and 4
In trial 3, F1 is unknown and in trial 4, F2 . The procedure is the same as above.
C. Calculate the percent errors (one on magnitude and one on direction) between the analytical (accepted) and experimental results for each Trials.
Data:
Given: the given values in the following chart.
Measured: specified by the question marks.
Table 1
| Trials
|
F1 | F2 | F3 | |||
| Magnitude
(gf) |
Angle ( ° ) | Magnitude
(gf) |
Angle ( ° ) | Magnitude
(gf) |
Angle ( ° ) | |
| 1 | 200. | 35.0 | 300. | 115.0 | ? | ? |
| 2 | 150. | 130.0 | 350. | 210.0 | ? | ? |
| 3 | ? | ? | 100. | 0.0 | 100. | 120.0 |
| 4 | 150. | 40.0 | ? | ? | 150. | - 40.0 |
Comparison of the results:
Provide the percent error formula used as well as the calculation of percent errors.
Conclusion:
State your conclusions of the experiment.
Discussion:
Provide a discussion if necessary.
Questions:
Two forces, one 500gf and the other 800gf, act upon a body. What are the maximum and minimum possible values of the resultant force? Hint: Sketch a parallelogram and investigate possible directions.
Could four forces be placed in the same quadrant or in two adjacent quadrants and still be in equilibrium? Draw a sketch and explain your answer.
