Lab 4 Vector Addition of Forces

Vector Addition of Forces

Purpose: The purpose of this lab was to study vector addition by:

1.    Graphical means

2.    Using components

3.    Using a circular force table to check results

Equipment:   -Circular force table                 -Masses

                       -Mass holders                    -String

                      -Protractor                          -Four pulleys

Procedure used:

1.    We were given three masses in grams as well as three angles as shown in figure 1. And obtained a scale of 1cm=20grams and made a vector diagram showing these forces, and graphically fond the resultant. We determined the magnitude (length) and direction (angle) of the resultant force using a ruler and protractor as shown in figure 1.  figure 1  
   

     Mass given                    degrees given

          150g                                      0˚

        110g                                       70˚

        250g                                       135˚

We then divided by the ratio given 1cm=20g to get

Grams changed to

 New grams         same degrees

7.5cm                                    0˚

5.5cm                                    70˚

12.5cm                                  135˚

Vector addition and degrees with length from lab are total was 14.0cm. we used tan^(-1)(14.0cm/0.54cm)=87.79 degree are new degree.

2.    Made a second vector diagram that showed the same three forces again. Found the resulting vector again, by components as shown in figure 2. We also showed the components of each vector as we as the resultant vector on are diagram as shown below.figure 2 we used tan^(-1)(14.0cm/0.54cm)=87.79 degree are new degree

3.    We then mounted three pulleys on the edge of our force table at the angles given above. We then attached strings to the center rings so they each run over the pulley so each run over the pulley and attached the mass holder as shown in figure 3A. We then hang the appropriate masses= force in grams on each string. We then set up a fourth pulley and mass holder at 180 degrees opposite from the angle we calculated for resultant of the first three as shown in figure 3a and 3b.  
figure 3a

Diagram showing how we verified the results. figure 3b Shows our mounted pulleys at equilibrium.  And our % error was =0.14% .

4.     

Unit analysis

      

150gx1cm/20g=7.5cm

110gx1cm/20g=5.5cm

250gx1cm/20g=12.5cm

 X Comp=7.5cos (0˚) +5.5cos (70˚) +12.5cos (135˚) =0.54cm

Y comp=7.5sin (0˚) +5.5sin (70˚) +12.5sin (135˚) =14.01cm

V xy=abs((.54)^(2)+(14.01)^(2))^(1/2)=14.02cm

Resulting angle vector. Tan^(-1)(14.02cm/.54cm)= 87.79˚

Dimensional analysis

gx cm/g=cm

g x cm/g=cm

g x cm/g=cm

 X Comp= cos (degrees) + cos (degrees) +  (degrees) = cm

Y comp= sin (degrees) + sin (degrees) + sin (degrees) = cm

V xy=abs((x)^(n)+(x)^(n))^(n)= cm

Resulting angle vector. Tan^(-1)(cm/cm)= degrees

Conclusion

Our conclusion was that the percent error was 0.14% meaning we did things right in our lab. Based also on the scale the middle strings were right on the middle with the ring exactly in the center.  Also it was low because of the fact that we were given 3 vectors and trying to find the 4 vector.  Overall we learned how to add vectors based on their components using the head to tail method.