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: **
3cm, 9cm, 12cm
b = 7.5 cm, a = 7.8 cm, c = 8.1 cm
b = 2.03 N, a = 2.12 N, c = 2.20 N
I used the left end of the threaded rod which was 3 cm from the first contact point meaning that was the zero point.
My forces were put into a ratio where the base length was calibrated at 7 cm which equated to .19 N. or to as .19 N was to 7 cm as x N was to the actual measured length
My results means that for twice the length from the balance point I would only need 2.03 N to balance a force that was exerting 2.20 N
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
Net force = 2.20 + 2.03 = 4.23 - 2.12 = 2.11 N down
Percentage of net force = 2.11/6.35 = 33.2%
I believe the rubber band system above the rod was doubled, which would imply roughly twice the upward force you report, and would result in a much lower percent error.
My result of the net force was the total of the two rubber band force pulling down on the threaded rod minus the 2 rubber band force pulling up on the threaded rod. My percentage was the net force divided by the total forces added together.
** Moment arms for rubber band systems B and C **
b = 6 cm, c = 3 cm
The numbers mean the distance from the fulcrum or center point from which the center rubber bands were connected. The center point was treated as zero then measuring from that point I obtained 6 cm for band b and 3 cm for band c.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
b = 8.12 cm, a = 8.48 cm, c = 8.8 cm
Point b = 6 cm, Point a = 3 cm
The numbers for the first line are just a way to make a diagram easily readable. The second line represents the dimensions from the fulcrum point to the respective downward force attachment points.
** Torque produced by B, torque produced by C: **
Torque b = 12 Ncm positive, torque c = 6.6 Ncm negative
The torque figures were compiled by multiplying the Force by the distance and realizing which direction the rubber band would rotate the threaded rod without and equalizer force.
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
Net torque 5.6 Ncm
b = 46.6%, c = 84.8%
I calculated the net torque by subtracting the lesser negative torque for the higher positive torque. The percentages I calculated by dividing the net torque by the torque in its specific direction. I don't feel that this is correct but I really don't know were to proceed on this question.
** Forces, distances from equilibrium and torques exerted by A, B, C, D: **
a = 1.57 N negative, 0 cm, 0 Ncm
b = 1.57 N positive, 2 cm, 3.14 Ncm
c = 1.57 N negative, 9 cm, 14.13 Ncm
d = 1.57 N positive, 13 cm, 20.41 Ncm
My measurements of the rubber band stretches yielded 7.7 cm which equaled to 8 dominoes of Force. 8 dominoes of force was 1.57 N. The torques comes from the moment arm distances multiplied by the force
** 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: **
Vertical forces = 3.4 N
My picture has upward forces at the ends of the line and downward forces in the interior of the drawing. The rod is being pulled up and down at the same time where a bridge has fixed ends upon the ground and this isn't being depicted completely with the rubber bands.
** Net torque for given picture; your discussion of whether this figure could be accurate for a stationary rod: **
Net torque = +2 N cm
I think you meant to say the 26 N cm torque was counterclockwise so being positive. My picture seems to be stable with all the forces being the same. That's not to say I'm right because it would make good sense that the forces should have varied somewhat. I believe if the rod was stationary, it would be more secure where the floating rod will be less stable
** 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: **
9.42 Ncm
0 N magnitude, 37.68 Ncm
25%
9.42 Ncm, 37.68 Ncm
The numbers represent my force multiplied by the moment arm to get my torque magnitude. I'm real confident in my figures because I am not too sure what I'm doing.
** 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: **
-1.9 Ncm
1.9 Ncm, 44.46 Ncm
4.2%
-1.9 Ncm, 44.46 Ncm, 4.2%
I multiplied the distance from the pivot point by the force to get the torque. I then added the torques not which was positive and which was negative to get my net torque. My percentage came from the total torque divided into the net torque. I still ti=hink I am way off base on this info.
** In the second setup, were the forces all parallel to one another? **
From my measurements, my top bands were the same length thus the same force but one bottom band was much longer for the manipulating band and the other bottom band actually shortened up. My guess would have to be 2 degrees because it was barely noticeable with the lab conditions leading to inaccuracy.
** Estimated angles of the four forces; short discussion of accuracy of estimates. **
88 degrees for all the angles
I just guessed because the change was barely noticeable to my eye. Anything less than 5% is barely noticeable.
** 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? **
I spent better than 4 hours on this lab and I only had to do the first two parts. That may be why my answers started getting rough.
** Optional additional comments and/or questions: **
I got quite confused on the torque, magnitude, and resultant. I don't think or I missed the info from somewhere. Let me know where to get a little clearer understanding on this.
Most of your calculations look OK. However a force 6 cm from the axis of rotation will balance twice as much force exerted at the 3 cm distance. The fact that all your forces were so close leads me to wonder about the calibrations.
However you do appear to understand the concept and have a good idea of what should have happened here. I think you'll be fine when you get to torques in the text. So in the interest of your time let's not worry too much about those details.