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.  Resultant is a single force that can replace the effect of a number of  forces.  "Equilibrantis a force that is exactly opposite to a resultant.  Equilibrant and resultant have equal magnitudes but opposite directions.  Review the introduction section of Experiment 2 for additional information on the graphical method as well as the analytical method of finding a resultant, if necessary.

Procedure:

Obtain a force table and set it up as shown in the following figure with its three 50.0-gram weight hangers as shown by F1, F2, and F3 . 

Figure 1: The schematic diagram of a force table

Observe the following points while using a force table:

1) The direction of the forces must be set by adjusting the strings at the desired angles.  When reading or adjusting an angle, one must look straight down onto the string corresponding to that angle.   Doing this minimizes or eliminates parallax error.

2) Each string represents the line of action of a force.

3) Each  grooved collar may be slid around the circular platform (that looks like a 360o protractor) to adjust the desired angle for each force.  The groove of each slider is curved internally with a curvature that matches the curvature of the circular platform.  When mounted, its internal curve must be flush with the edge of the circular platform for the correct reading the angle it is set at.

Take the following steps for each vector addition.  Complete the rows of Table 1 one at a time.  Do not start the next case until the % errors in each case (row of Table 1) is determined and recorded.

a) In each case, place weights F1 and F2 on two of the weight hangers in accordance with Table 1 at the specified angles.  The ring at the center can be treated as the object under study.  

   The forces that you create by placing weights on the weight hangers act on the same object (the ring) and are indeed concurrent forces.  Place enough weights on the third cord (Force F3) 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 its center.  Force F3 that brings the ring to equilibrium is called the "equilibrant. Record the angle and magnitude of F3 .

b) The goal is to find R (the resultant of F1 and F2 ).   Having found F3 is like you have found R.   Note that if you add 180o to, or subtract 180o from the angle of F3, it gives you the angle of R.  Do this addition or subtraction of 180o and record the values so found for R in Table 1.  The magnitude of R is exactly equal to the magnitude of F3 (the equilibrant), but the angle of R is 180o different from the angle of F3 .  The last two values you obtain for R are your experimental values or the measured values for R.

c) Now, find the magnitude and direction of R by calculation (the analytical method) as well.   First find Rx and Ry, then R and θ.  These calculated values are your accepted values for R. 

d) Calculate a %error on each of R and θ, and record them in the last columns of Table 1.

Data:  

Given:  The magnitude and direction of each set of vectors to be added are given in Table 1.  

Measured:   Record your measured values in Table 1 in the space provided.

 Table 1

Trials Given Measured

F3

Measured

R     

Calculated

R

%error
  F1 F2
  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                

 

Calculations:

 

Provide a full calculation for one case here, but only show the results for other cases in Table 1.

Comparison of the results: 

         Provide the percent error formula used as well as the calculated values of percent errors in this section as well as Table 1.

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? 

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?