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SMC|Academic Programs|Physical Sciences|Addition of Vectors

Addition of Vectors

Procedure:

1) Using the force table and spring scales provided set up a tug-of-war using three different forces. DO NOT situate the forces in a highly symmetrical configuration. When establishing an equilibrium configuration make sure the circular ring is centered on the pin, and that you are keeping the spring scales horizontal.

2) When you have arrived at a situation of equilibrium record the readings on the spring scales and the angles the cords make with one another (you can use the angle markings on the force table as a reference). Also provide an estimate of the uncertainty of each of your recorded forces (for example, magnitude of 12.5 ± 0.5 N, angle 120 ± 5 degrees ).

  Magnitude and uncertainty Angle and uncertainty
Force 1    
Force 2    
Force 3    

3) On a separate page, make a sketch of the forces acting on the ring taking care to label the magnitudes of each of the forces along with their respective angles. Draw a small ring in the middle of a blank piece of paper and make sure the forces are not drawn tiny!!!

4) Repeat steps 1-3 using four different forces acting on the ring.

   Magnitude and uncertainty Angle and uncertainty
Force 1    
Force 2    
Force 3    
Force 4    

Analysis/Questions

1) Is force a vector or scalar? Explain your reasoning. If several forces act on an object what procedure would allow one to determine the total force acting on that object?

   

2) Determine the net force acting on the ring for the situation involving three forces by adding the forces graphically on the page where you have already drawn the forces. Using a protractor and ruler  find the net force (direction and magnitude) acting on the ring.

   Magnitude and uncertainty Angle and uncertainty
Net force (3 forces)    

3) Repeat step (2) for the case of four forces acting on the ring.

   Magnitude and uncertainty Angle and uncertainty
Net force (4 forces)    

4) For the case of three forces acting on the ring add the forces algebraically. To accomplish this resolve each of the three forces into x and y components. Determine the total x and y for the sum of the three forces. From these components Fx and Fy determine the magnitude and direction of the sum of the three forces. Compare these results with those found in (2) above.

   x -component y-component
Force 1    
Force 2    
Force 3    
Net force    
Net force Magnitude:                              Angle:                                    

5) Ideally you should have found that no net force acts on the ring. Due to your errors, however, this will not be the case. Can you come up with a rough measure of how to quantify your error?  

 

6) To what extent is the quantitative estimate of your percentage error you proposed in part (5) in agreement with the uncertainties in your measurements of the forces acting on the ring?