Your 'torques' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your optional message or comment: **
** Positions of the three points of application, lengths of systems B, A and C (left to right), the forces in Newtons exerted by those systems, description of the reference point: **
From left to right, point B is 1 cm from the left end of the rod, point A is 7.5 cm from the left end of the rod, and point C is 12.3 cm from the left end of the rod.
Length of rubber bands: B = 7.6 cm, A = 7.9 cm, and C = 8.2 cm.
Forces exerted by rubber band systems: To find these forces, we use the force of tension constant for a rubber band (that was given in the previous experiment) of .19. Therefore, the forces are the rubber bands' lengths times .19: B = 7.6 cm * .19 = 1.44 N, A = .19 * 7.9 cm = 1.501 N, C = 8.2 cm * .19 = 1.56 N.
To find the force you use your calibration graphs. A rubber band is typically unstretched, or very slightly stretched, at a length of 7.6 cm, and does not exert a force of 1.44 N at that length.
The force constant was never specified. .19 was given as the weight in Newtons of a domino.
The reference point was the left end of the horizontal rod (each force applied point was measured as a distance away from the left end of the rod).
The forces in Newtons were obtained by mulitplying the respective rubber band lengths by the tension constant .19, as given in the other experiment we did before this one.
The first line shows the positions of the three points where the vertical lines intersect the horizontal line, and are measured from left to right. Thus, they are all points relative to the left end of the rod. The second set of numbers are the lengths of the rubber band systems, measured in cm. The third set of numbers are the forces of each system (calculated using the .19 tension constant, as stated above).
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
Net force = 4.501 N
Net force as a percent of magnitude sum = 19%
Net force = 1.44 N + 1.501 N + 1.56 N = 4.501 N
Net force as a percent of the sum of the magnitudes of the forces of all three rubber band systems = 4.501 N / (7.6 cm + 7.9 cm + 8.2 cm) = 4.501 N / 23.7 cm = .1899, or 18.99 percent (approximately 19 %)
Some forces are directed upward and some downward. The sum must take account of directions.
You wouldn't divide the net force in Newtons by the sum of magnitudes of rubber band lengths. The instruction was to divide the net force by the sum of the magnitudes of the forces.
** Moment arms for rubber band systems B and C **
B = 1.235 N
C = .912 N
moment arms are measured in cm, not in N.
Moment-arm force exerted by rubber band system B: 6.5 cm * .19 = 1.235 N
Moment-arm force exerted by rubber band system C: 4.8 cm * .19 = .912 N
There are no .19 N forces acting here.
To calculate the forces for the B and C systems, I took the displacement between the fulcrum, point A, and the respective systems, points B and C's horizontal distances from point A, and multiplied them by the tension constant of .19 for a rubber band (as given in the previous experiment).
The horizontal distances between rubber bands are unrelated to the tensions. Lengths are related to tension, but positin on the strap has no direct relationship with tension.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
With a scale of 4 cm to 1 Newton, :
Lengths (in cm): B = 10.3 cm, A = 10.4 cm, C = 11 cm
Distances from the fulcrum to the points of application (of downward forces B and C): B = 6.5 cm * (1N / 4 cm) = 1.625 N; C = 4.8 cm * (1N / 4 cm) = 1.2 N
To find the lengths of the vectors in cm of the forces exerted, I uesd the ruler to measure the distance between the point where each respective force was applied and where the farthest point of each rubber band lied on the board. To find the distances from the fulcrum to the points of application of the two downward forces, I used the distance of each downward force, B and C, from the fulcrum, or point A. I then multiplied each distance by 1 N / 4 cm to convert them to newtons on a scale of 1 N to 4 cm, as indicated by the instructions given above.
** Torque produced by B, torque produced by C: **
Rubber band B torque = 1.78 (+)
Rubber band C torque = 1.42 (-)
Torque of the force exerted by rubber band C = momentum arm * force = .912 N * 1.56 N = 1.42 N (toque measurement)
N * N would by N^2. However moment arm is not measured in N.
Torque produced by rubber band B about point of suspension = momentum arm * force = 1.235 N * 1.44 N = 1.78 N (torque measurement)
The results given here show the torques for the rubber bands B and C around a fulcrum point A. These were calculated by taking the forceo f each system times the momentum-arm calculationo of each system. I knew that C was negative, because it is traveleing in a clockwise position. Therefore, I knew that B must be positive, because it is moving opposite in a counterclockwise fashion.
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
.36 torques
1.13%
Net torque = 1.78 - 1.42 = .36 torques
Net torque as a percent of the sum of the magnitudes = .36 torques / (10.3 cm + 10.4 cm + 11 cm) = .36 torques / 31.7 cm = .0113; to get percent, .0113 * 100 = 1.13 %
As the calculations show above, the net torque was calculated by subtracting the negative C torque from the positive B torque. This was then divided by the sum of the magnitudes to find the percent of the sum of the magnitudes. In order to get a true percent, I muliplied this number by 100 to get 1.13 %. THus, there was some experimental error in this case, as the torque amount should be zero. It is still close, however, since I got .36 net torque. The percent error is then the 1.13 % that was calculated.
** Forces, distances from equilibrium and torques exerted by A, B, C, D: **
** The sum of the vertical forces on the rod, and your discussion of the extent to which your picture fails to accurately describe the forces: **
** Net torque for given picture; your discussion of whether this figure could be accurate for a stationary rod: **
** For first setup: Sum of torques for your setup; magnitude of resultant and sum of magnitudes of forces; magnitude of resultant as percent of sum of magnitudes of forces; magnitude of resultant torque, sum of magnitudes of torques, magnitude of resultant torque as percent of the sum of the magnitudes: **
** For second setup: Sum of torques for your setup; magnitude of resultant and sum of magnitudes of forces; magnitude of resultant as percent of sum of magnitudes of forces; magnitude of resultant torque, sum of magnitudes of torques, magnitude of resultant torque as percent of the sum of the magnitudes: **
** In the second setup, were the forces all parallel to one another? **
** Estimated angles of the four forces; short discussion of accuracy of estimates. **
** x and y coordinates of both ends of each rubber band, in cm **
** Lengths and forces exerted systems B, A and C:. **
** Sines and cosines of systems B, A and C: **
** Magnitude, angle with horizontal and angle in the plane for each force: **
** x and y components of sketch, x and y components of force from sketch components, x and y components from magnitude, sine and cosine (lines in order B, A, C): **
** Sum of x components, ideal sum, how close are you to the ideal; then the same for y components. **
** Distance of the point of action from that of the leftmost force, component perpendicular to the rod, and torque for each force: **
** Sum of torques, ideal sum, how close are you to the ideal. **
** How long did it take you to complete this experiment? **
** Optional additional comments and/or questions: **
Your data appear to be OK, but there are a number of errors and misconceptions in your work.
Don't try to correct everything, but insert a question or a brief sample revision in response to each of my comments above, marking your insertions with &&&&.
The main goal here will be to ensure that you understand the concepts of torque, moment arm, etc..