Phy 121
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: **
0.3, 7.3, 11.3
7.77, 9.9, 10.65
1.52, 3.68, 4.19
The left end of the rod was used as the reference point for the positions of the rubber bands in the first line above.
The measurements of the lengths of the rubber bands were plotted on the corresponding calibration graphs and the coordinating force from the graph was found. For A, I added the forces found from my first and fourth rubber bands since both were contributing in this experiment.
This indicates that a force of 1.52 N pulling down at .3 cm and a force of 4.19 N pulling down at 11.4 cm is the force required to counteract the 3.68 N force pulling up at 7.35 cm.
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
-2.03 N
22%
The net force of -2.03 N was obtained from the sum of all the forces, -1.52 N, 3.68 N, and -4.19 N. The magnitude of the net force (2.03) was then divided by the sum of the magnitudes of all the forces (1.52, 3.68, and 4.19 = 9.39) to get the percentage (22%) the net force is of the sum.
** Moment arms for rubber band systems B and C **
7.05, 4.05
The first number above (7.0) is the moment-arm in cm for the force exerted by the rubber band system B, the distance from the center supporting system. The second number above (4.0) is the moment-arm in cm for the force exerted by the rubber band system C, the distance from the center supporting system.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
6.08, 14.72, 16.76
7.0, 4.0
The numbers in the first line represent the length of the force vectors for B, A, and C found by multiply the force found above by 4 since we are using 4 cm = 1 N. The second line is again our distances from the center system A to B and from A to C.
** Torque produced by B, torque produced by C: **
+10.64, -16.76
The first number indicated above is the torque for B, found by multiplying the moment-arm (7 cm) by the force (1.52 N). The second number is the torque for C, found by multiplying the moment-arm (4 cm) by the force (4.19 N).
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
-6.12
22%
To get the net torque (-6.12) I added the torques found above (+10.64 and -16.76). To get the percentage of the sum of the magnitudes I then divided the net torque by the sum of the magnitudes of the torques (10.64 + 16.76 = 27.4). This seems to be the percentage of error since ideally the net torque would be zero.
** 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? **
1 hour
** Optional additional comments and/or questions: **
I am taking my time in doing these experiments and don't understand why it seems nothing ever turns out close to ideal. I am trying to be careful and accurate.
This experiment was done with rubber band. The calibration of the rubber bands carries an inherent 10% margin of error, and you get another 10% in making your measurements for this experiment. Plus at least one of the rubber bands was stretched much further than in the calibration, so you had to extrapolate into 'unknown territory' to get that force.
With this system, errors in the range of 20% are to be expected. Some of the other experiments have a much higher degree of precision.
You did a very good job here.