Experiment 3
Vector Addition: Force Table
Objective:
The objective is 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 which 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 different graphical methods as well as the analytical method of finding a resultant, if necessary.
Procedure:
Set up a force table as shown in the following figure with its three 50.0-gram hanging weights.
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. 2) The string (not the edge of the clamp) represents the line of action of the force. 3) Each collar that slides around the circular platform for adjusting the angle for each force, is grooved. The groove of each slider (collar) must be flush with the edge of the circular platform for correct angle adjustment as well as measurement. |
The schematic diagram of a force table |
Take the following steps for each vector addition. Complete each row of Table 1 before going to the next row. This means that the %errors in each row must be calculated before the start of the experiment for the next row.
a) In each of the trials 1 and 2, place the weights for F_{1} and F_{2} in accordance with Table 1 (below) at the specified angles. The ring is the object under study. This means that all forces are acting on the ring. Place enough weights on the third cord (Force F_{3}) and adjust its angle until the system is in equilibrium. At equilibrium, the ring is exactly at the center of the circular platform as can be judged by the stud at the center. Force F_{3 } that is needed to bring the ring to equilibrium is called the "equilibrant." Record the angle and magnitude of F_{3}.
b) Note that if you add 180° to, or subtract 180° from, the angle of F_{3}, it gives you the angle of R, the resultant of F_{1} and F_{2} that you are looking for. Do this as well and record the values for R in Table 1. The magnitude of R is exactly equal to the magnitude of F_{3}, the equilibrant, and angle of R is 180° different from the angle of F_{3}. These last two values are your measured values for vector R, by the force table method (experimental).
c) Now, find the magnitude and direction (angle) of R by calculation (or the analytical method). First find R_{x} and R_{y}, then R and θ as usual. These calculated values are your accepted values for vector R.
d) Not only you need to add F_{1} and F_{2} graphically (by parallelogram method) in lab as part of the experiment, but also make sure that you include the graphical method (Parallelogram) in your report. Calculate a %error on each of R and θ, and record them in the last columns of Table 1.
Data:
Given: the given values are in Table 1.
Measured: Record your measured values in Table 1.
Table 1
Trials | Given | Measured F_{3} → |
Measured → R |
Calculated R |
%error | |||||||
F_{1} | F_{2} | |||||||||||
Magn.(gf) | Angle | Magn.(gf) | Angle | Magn.(gf) | Angle | Magn.(gf) | Angle | Magn.(gf) | Angle | on R | on θ | |
1 | 200 | 35.0 | 300 | 115 | ||||||||
2 | 150 | 130.0 | 350 | 210 | ||||||||
3 | 100 | 0.0 | 100 | 120 | ||||||||
4 | 150 | 40.0 | 150 | -40.0 |
Comparison of the results:
Provide the percent error formula used as well as the calculated values of percent errors.
Conclusion:
State your conclusions of the experiment.
Discussion:
Provide a discussion if necessary.
Questions:
Include the following questions and their answers in your report:
1) Two forces, one 500gf and the other 800gf, act on a body. What are the maximum and minimum possible magnitudes of the resultant force? Hint: Sketch many parallelograms that have their adjacent sides equal to 5cm and 8cm, for example, to represent 500gf and 800gf, respectively, but with different angles between those adjacent sides. If the different angles you choose are say, 0, 30, 60, 90, 120, 150, and 180 degrees, you will see how the magnitude of the resultant changes case to case and then you will be able to decide the maximum and minimum values for the resultant.
2) 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.
3) What is the relationship between the equilibrant vector and the resultant?