Multiple forces from different directions (in this case, three forces) to a common point will result in a single force in a single direction (similar to an average). This is a known as the resultant force.

 

The resultant will be determined by two methods, the component method, which is the mathematical way and the experimental method, which is physically determining the resultant using the force table.

Next, the two results are compared for a percent difference.

After choosing a force system to use in the experiment (#2 was chosen), calculations will now begin using the component formulas:

 

Next, The magnitude and direction can be calculated with these equations: 

 

Now the force system and resultant can be setup and tested on the force table to verify the calculations made with the formulas. The differences will be evident and the percentage of differences can be determined.

 

Mathmatical Determination of R:

System #

2

Force Magnitudes

F1:

1.96N

F2:

.98N

F3:

1.96N

Force Components

F1x:

1.96N

F1y:

0

F2x:

.559N

F2y:

.804N

F3x:

1.38N

F3y:

1.38N

Resultant Components

Rx:

1.14N

Ry:

2.18N

Resultant Magnitude

R:

2.46N

Resultant Direction

:

242 deg

Experimental Determination of R:

Total Mass Added

m:

2.60kg

Resultant Force Magnitude

R:

2.55N

Resultant Force Angle

:

248 deg

Method Comparison:

Percent Difference in

R:

3.5%

Percent Difference in

:

2.5%

Concurrent Forces Diagram

There was a difference between the calculations and the experimental results of 3.5% for the magnitude and 2.5% for the direction. After recalculating several times and checking our numbers, we came to the conclusion that these differences are attributable to the following considerations concerning the physical make up of the force table:

1. The unit was not sitting on a proven level surface.
2. The stand has leveler legs, but were not employed, rather, we estimated level by sighting it and trusting our eyes.
3. The table was not exactly perpendicular to the center leg that went between the base and the table. We tried, but it was a bit wobbly even after we tried to tighten it.
4. The weights were dangling from different length strings and there was some disagreement as to whether or not it was a factor at all.
5. The "friction free pulleys" were nothing of the sort. Being plastic, they did vary in the way the weights would hang.
6. Finally, the way we each sighted the angles for the forces may have been slightly different depending on where we were standing and leaning over the table to see our work.

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