PRINCIPLE INVESTIGATOR:
ASSISTANT INVESTIGATOR:
EXPERIMENT NUMBER: #5
EXPERIMENT NAME: Composition of Force
EQUIPMENT: Force Table, Pulleys, Thread, Slotted masses, and Hangers.
OBJECTIVE:
To resolve a vector in to its rectangular components and to find the sum of the three vectors using both graphical and trigonometric techniques. Also, to check the validity of the computations by experiment.
THEORY:
Using Graphical and trig metrical techniques we should be able to find the resultants for vectors. If the given θ we should be able to use Ax=cosθ or Ay=Asinθ to find the length of a vector. If given Ax and Ay the use A2=Ax2+Ay2 the Pythagorean thermo to find A. When adding vectors simply use Rx=Ax+Bx+Cx or Ry=Ay+By+Cy. In part A, given a force of 0.981 Newton’s at 30 degrees. Then set up this force on the force table. In part B, Given the three forces F1 = 0:490 N at 0 degrees, F2 = 0:736 N at 30 degrees, and F3 = 0:589 N at 135 degrees. Then set up these forces on the force table. In part C, Using the forces given in Part B, compute graphically the components of each of the forces. Compute the vector sum graphically by laying them out head to tail. In part D, Using the forces given in Part B, compute trigonometrically the x and y components of each force, and their sums and find the resultant F.

PROCEDURE: We set up a force of .981 Newton’s at 30 degrees on the force table. We then balanced the force using a piece of string and a hanger on the end of it. We then removed the pin and the ring stayed directly over the pin hole. We then tested for equilibrium using trig components. We then did the same test using F1= .49 N at 0 degrees, F2=.736 N at 30 degrees, F3=.589 at 135 degrees. Then we completed the same numbers graphically by laying the vectors out. Lastly we found the sums and the resultants.

DISCUSSION: This experiment intended to show that forces add vectorially, by using the method of vector addition to find a resultant force that could be easily compared to a physical force. Unfortunately, the measured forces disagree with the predictions, well beyond the limits of uncertainty, in half the cases. It is impossible to say without having observed the data collection process whether this is due to the error sources discussed in the analysis section or to a violation of Newtonian mechanics, but the former seems far more likely. The way to be certain would be to repeat the experiment and try to reproduce the unexpected result, watching more carefully for mistakes. By using the force table it made it easy to find the equilibrium for then experiments. Although, it is also the least accurate; if the loop was not 100% directly over the center of the hole of the force table then it could mean that something is a little off, either by the direction or the force.
In Part A, I found the % error was:
Fx = 0% and Fy = .2037%.
In part B: The net force was found to be 1.23 N.
In Part C, the % of error was:
F1 = .102%, F2 = .136%, F3 = 0%, Fu = 8.29%.
Trigonometric Net force Fxnet = -.5697 N Fynet= -.1578 N
Graphical Net force Fxnet = -.5050 N Fynet= -.1577 N
Fxnet % error = 11.35% Fynet% error= .06%
In part D, the % of error was:
F1x = .102%, F2x = 16.67%, F3x = .37%
F1y = 0%, F2y = 1.94%, F3y = .5%
F=.35%
The best way to find the exact direction and force to make equilibrium is to use the trigonometric solution. Then you can use exact numbers and not just judge the force and direction using your naked eye. The graphical solution is adequate but it still is not as precise the trigonometric solution. For example, in part A, the graph paper showed Fx= .85 N and Fy= .5 N. The trigonometric solution showed that Fx was actually equal to .8495709211 N and Fy= .4905 N. Although very close, the trigonometric solution turned out to be more accurate.