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: **
0.45,8.1,12.6
7.55,7.72,7.61
0.524,1.580,1.142
The reference point was the left end of the threaded rod
I inserted the trendline equations for each rubberband into my graphing program and evaluated each one at their stretch length
these number are the forces applied at given points along the rod.
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
-0.086
2.65%
I took the upward force and subtracted the downward forces and reported the difference. The difference was negative which means there is extra downward force.
** Moment arms for rubber band systems B and C **
7.65,3.9
these are the distance from the pivot point to each applied force.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
2.10,6.32,4.57
7.65,3.9
These numbers represent the force applied as a vector. Imultiplied the force of each rubberband by 4.
** Torque produced by B, torque produced by C: **
-4.45 N*cm
+4.01 N*cm
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
-0.44 N*cm
5.20%
These are the torques about the suspension point. I multiplied the force time the distance from the fulcrum.
** Forces, distances from equilibrium and torques exerted by A, B, C, D: **
1.80 N, 0 cm, 0 N*cm
1.87 N, 1.7 cm, -3.18 N*cm
0.81 N, 11.45 cm, -9.27 N*cm
1.11 N, 15.10 cm, +16.76 N*cm
The forces are for the trendline I imported into my graphing program. I multipled that number time the distance from the left most force point of application to get my torque.
** 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: **
+0.23 N
My picture show the forces acting up and down on the rod at each location. Since the sum of all my forces should equal 0, the picture is not exactly accurate. There would also be a uniform load which equals the weight of the bar that acts in a downward direction.
This force will not act in the plane of the system if the board is lying flat on the tabletop. If you have it propped up so that the y axis is upward, then it will be a consideration, and could well explain the net force you observe. Otherwise the explanation is simply that the rubber bands aren't all that reliable, even if they are accurately calibrated.
Considering the weight of the bar is substaintial to the size of the rubber bands forces, it should not be ignored. This would explain why I have a net force of +0.23.
** Net torque for given picture; your discussion of whether this figure could be accurate for a stationary rod: **
+4.31 N*cm
The net torques should equal zero. But as said above, there should be a torque associated with the weight of the 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: **
+4.31 N*cm
+0.23 N, 5.59 N
4.11%
+4.31 N*cm, 29.21 N*cm, 14.76%
** 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: **
+2.02 N*cm
-0.04 N, 7.64 N
0.52%
+2.02 N*cm, 51.74 N*cm, 3.90%
I got the forces from my graphing program. Multiplied the force time the distance for applied point A for the torques.
** In the second setup, were the forces all parallel to one another? **
No the forces were not parallel. They were only off by a degree or two at the most with this slight change. Force C stayed up and down, since that is the force I modified. Forces b and d rotated opposite of each other.
** Estimated angles of the four forces; short discussion of accuracy of estimates. **
force B would be about 89 degrees, force C would be about 88 degrees, force D would be about 89 degrees
I made my estimates be drawing the lines and measuring them with a protractor. I think these estimates are fairly close. There was only a mild change in location of the rod anyway.
** 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? **
2.5 hours
** Optional additional comments and/or questions: **
Good work. Everything is within the margins of error expected for the rubber bands, which do not behave in a completely predictable manner.
See my comments and let me know if you have questions.