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: **
3.7cm, 15.9cm, 22.4cm
12.6cm, 10cm, 24.50cm
123.48N*cm, 98N*cm, 240.1N*cm
Reference point was the middle of the rod or 15.9cm
I took the lengths of the rubberbands and multiplied them by 9.8N to get their individual forces.
You should use your rubber band calibration graphs of force vs. length to get the forces.
For the first row of numbers I obtained them by drawing a straight line and marking where the hooks hung and obtained those values, then I marked how long the rubberbands were, measured them and recorded them, and then for the forces I took the lenghts and multiplied them by 9.8 to get the force of the rubber band.
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
-265.58
46.5%, 36.9%, 90.4%
I took and added up the forces if they were downward then the value was negative, if the value was upward the value was positive therefore giving me and negative net force. Then for the percentages, I took the force and divided it by the net force and then multiplied by 100 to get the percent of the sum of the magnitudes of all the forces of all three rubberband systems.
** Moment arms for rubber band systems B and C **
12.2cm, 6.5cm
I took the fulcrum point and subtraced point b from it to get the moment arm of that force and then for point C I took C's point and subtracted it from the fulcrum and got the moment-arm for that particular force.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
30.87cm, 24.5cm, 60cm
12.2cm, 6.5cm
I got the first numbers by using the 4cm to 1N and then I counted the newtons and how many cm would correspond to the N that I calculated and then for the second part I measured how far from the fulcrum to points b and c .
** Torque produced by B, torque produced by C: **
6.5cm
-12.2cm
to get the torques I took the the distance in which it was away from the fulcrum point .
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
-5.7
46.7%, 53.3%
I added the two torques together and then to find the percent of the sum of the magnitudes I took the calculated net torque and divided it by the two individual torques to get the percentage for each of them.
** Forces, distances from equilibrium and torques exerted by A, B, C, D: **
0cm, 2.8N
3.7cm, -3.0N
15.9cm, -2.0N
22.4cm, 2.5N
I measured each rubber bands distance and then to find the torques I used the 4cm to 1 N and marked where the torques would be.
** 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: **
.3N
My picture shows that lines A and D are fairly close with their lines running upward, and then line B and C are very different, therefore showing that it fails to accurately depict the forces acting on the rod.
** Net torque for given picture; your discussion of whether this figure could be accurate for a stationary rod: **
13.1Ncm
yes, because although my answers may not be correct this is what I obtained from the torques actually acting on 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: **
0
-11.1, -31.8, 56 = 13.1
13.2%
,13.1, 13.2%
I took and added all of the torques together to get the magnitude of the force, and then I took the magnitude and divided it by 98.9 since that is what all of the torques added together were and divided by 13.1 which gave me a 13.2%.
** 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: **
33.8
24.5, 65.8
37.3%
24.5, 65.8, 37.3%
I took and added all of the torque together and then divided them by the total to obtain the percentages.
** In the second setup, were the forces all parallel to one another? **
They were not all parallel to one another, and I would estimate that they were off 70degrees, I estimated this by looking at my markings from the previous setup and this setup and there was about at 70degree difference in the two setups.
** Estimated angles of the four forces; short discussion of accuracy of estimates. **
I estimate that there was a deviation of about 10 degrees from 90, so therefore the angle would be 80degrees. And I think that my estimates are fairly accurate based on the fact that I drew the lines from set up to set up and estimated the differences between the two setups.
** x and y coordinates of both ends of each rubber band, in cm **
3cm, -14.7cm ; 3cm, 9.5cm
17cm, 31cm ; 17cm, 40cm
31cm , -6cm ; 27cm, 9cm
I simply marked my dots of where the system was located, and then I drew an x and y axis and then where the points were located I came up with the coordinates based on the dots that were previously there.
** Lengths and forces exerted systems B, A and C:. **
5.2cm, 50.96N
9cm, 88.2N
5cm, 13.06N
I used the pythagorean therorem to find the length of the rubber band system, and I took the difference in the x and y coordinates, squared them, took the square root and then got the length, and then I took the length * 9.8N to get the force.
** Sines and cosines of systems B, A and C: **
0, 99.9degrees
0,98.7degrees
6.9degrees, 99.8degrees
Using the x and y coordinates I took used the sine and cosine buttons on my calculator to find the angles.
** Magnitude, angle with horizontal and angle in the plane for each force: **
0 (because my x value is zero)
0 (because my x value is zero)
36.86
I could not get the acrtan of the first two since my x values were zero and you cannot divide by zero, but for the last one I took arctan and divided the yvalue by the x value and got the arc tan 36.86
** 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): **
2cm, 21cm, 2cm, 11cm, -6cm, -11cm
16.5cm, 21cm, -18cm, -35cm, 13cm, -35cm
21cm, 26cm, 7cm, 26cm, -7cm, -33cm
Based on the vectors, and the force based on the 4cm to 1N the lines that I drew, I drew based on my previous results, and then according to where they were plotted on the graph, then I found the coordinate that corresponded to that particular point.
** Sum of x components, ideal sum, how close are you to the ideal; then the same for y components. **
-2, 0 , -2
11.5, 0, -11.5
I added up all of the x and y values and then compared them to the ideal previously recorded earlier and then subtracted the calculated from the ideal and that is how I got my difference.
** Distance of the point of action from that of the leftmost force, component perpendicular to the rod, and torque for each force: **
-67.76
41.6
54.06
I took the force of each ABCand D and then I multiplied the force times the length of the line to find the torque.
** Sum of torques, ideal sum, how close are you to the ideal. **
27.9,0,-27.9
I added up all the torques and I know that the sum should be zero, but in this case it wasn't close enought to the ideal sum and it had a difference of 27.9.
** How long did it take you to complete this experiment? **
3hours and 30minutes
** Optional additional comments and/or questions: **
You are doing a lot of good things here and your analysis is overall good.
However your force information is flawed. You get forces from your rubber band calibration graphs.
Can you revise the first part of the experiment only, using this method to get your forces? I want to see what you get for the net force and the net torque.
Please submit a revision of that part only, indicating your revisions by &&&&. If you have questions I'll be glad to answer them.