PHY241401
Activity 9
Tony Gagliano
November 2, 1999

 
 

Equilibrium

  
Purpose: This is an experiment to not only prove the equilibrium condition, but to also show the differences in the methods used for calculating the results. The percent difference will show how much disparity is involved between methods.
   
 
   
Theory: This lab is going to make evident the fact that a scale model in the lab will demonstrate the same forces as a full size working model. It will take all three methods of calculating to arrive at a reasonable average or error percentage. The accuracy of the experiment will depend on the quality of the "physical" part of the experiment and the
   
 

 

   
Procedure: Using the scale model in the lab, we were able to determine the forces on T,F, and W by measuring the distance between the three points. Then we established the angles making sure angle A is set at 60o and the sum of the 3 angles is 180o.

Next, we put the 1 kg weght in place at the end of the boom to get the reading from the spring balance. Then multiply that reading by g to determine T ot tension.

To determine the force on F we pull straight back (parallel) on the end of the boom with another spring balance until the boom starts to pull away from from it's pivot point. That mass reading will by multiplied by g for the force value.
   
Results:

Graphical Method
 

Crane Data:

Crane Dimensions AB:

. 74 m

Crane Angles A:

60o

AC:

. 99 m

B:

75o

BC:

. 89 m

C:

45o
   

Sum of angles A+B+C =

180o

 

Mass reading in string:
1.2 kg
Mass reading on boom:
1.5 kg
Directly determined forces F:
15 N
T:
12 N
Results of equilibrium equations:   Discepency in x components: .01 N
    Discepency in y components: .73 N
         
Results of graphical method: T: 11.9N Percent error: . 83%
  F: 13.2N Percent error 12%
         
Results of analytical method T: 11.9 N Percent error: .83%
  F: 13.0 N Percent error: 13%
   
Conclusion: Once again we found a situation where the percent error on one of the component had a relativly high percentage of disparity. In this case F experienced a 12-13% difference in both graphical and analytical methods compared to the experimental method. This has to be atributible to to physical make up of the equipment and how we set it up. The crane wasn't in bad shape, it was the way we clamped the pieces together and how we measured from point to point.

It is still obvious that the graphical and analytical methods were close iin their results, thus proving the dependablity of those two methods. I suppose the whole thing could have benn sumized on the drawing board and come to a reasonable conclusion as to the force values and how they are exerted.
 

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