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:
2.8, 14.8, 23.7
7.8, 7.5, 8.1
1.5, 1.1, 1.9
The lengths were measured from end to end next to a ruler on the grid paper.
The force in Newtons was obtained by finding the force that corresponded to the length the rubber band was stretched. For rubber bands B and C, the specific lengths for each rubber band and corresponding force had been recorded in the rubber band calibration. To find the force for the rubberbands in position A, I used the calibration graphs to find the force that corresponded to the length and added these together.
Net force and net force as a percent of the sum of the magnitudes of all forces:
-2.3
51%
Moment arms for rubber band systems B and C
12, 8.9
Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C.
6.0, 4.4, 7.6
12, 8.9
Torque produced by B, torque produced by C:
+72
-68
Net torque, net torque as percent of the sum of the magnitudes of the torques:
+4
2.9%
I found the sum of 72 + (-68) which equaled the net torque of +4. The I divided 4 by the total of 72 + 68 to find the percentage of 2.9%.
Forces, distances from equilibrium and torques exerted by A, B, C, D:
4.4, 0, 0
1.2, 4.6, +5.5
4.4, 17.2, +75.7
3.0, 21.3, -63.9
(Mine is the mirror image of yours, the fulcrum in on the right hand side because I was mixed up when setting up the experiment)
a mirror image is no problem, but thanks for pointing it out
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:
-1.5
The sum of the vertical forces does not accurately depict the picture because the forces have a different impact depending on their distance from the fulcrum.
Net torque for given picture; your discussion of whether this figure could be accurate for a stationary rod:
+6
The net torque gives an accurate depiction of the actual torques because it takes into account the distance each is from the fulcrum and the force applied at these positions.
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:
+17.3
1.84, 13.0
14%
17.3, 145, 12%
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:
+37.3
4.4, 26.8
16%
37.3, 327, 11%
In the second setup, were the forces all parallel to one another?
about 5 degrees variation
Estimated angles of the four forces; short discussion of accuracy of estimates.
85, 95, 85, 85
I'm horrible at estimating so its only acurrate to my ability to estimate correctly.
x and y coordinates of both ends of each rubber band, in cm
1.2, 1.0, 1.5, 8.9
13.0, 16.7, 10.9, 23.0
26.6, 0.2, 23.9, 8.0
Lengths and forces exerted systems B, A and C:.
7.9, 1.5
6.6, 0
8.3, 1.9
I found the length of the rubberbands and the forces exerted by using the pythagorean theorum. For the rubber band system A, I found the length of the rubberbands using the Pythagoran theorum, and then plugged the length into the equation for the graph for each rubberband. Then I added the forces together and they equaled a negative number. But since it can't exert a negative force, I wrote the force is 0.
The coordinates you observed might be in error. I don't think any of these rubber bands would be stretched at all at a length of 6.6 cm.
Sines and cosines of systems B, A and C:
-1, -.04
.95, -.32
-.94, .33
I have a question about this statement and ones like it: The sine is negative if the y component downward, positive if the y component is upward. Downward and upward relative to what? The point of origin of my x,y axis? How do you know whether the line is downward, upward, left or right?
Magnitude, angle with horizontal and angle in the plane for each force:
1.5, 87.8, 272
0, 71.6, 108.4
1.9, 70.9, 289
I found the angle using the following math Ex. B ARCTAN(7.9/.3)= 87.8 degrees. The angle of the force vector in the plane is 360 degrees - 87.8 degrees = 272 degrees.
I'm not sure I understand what you mean by the angle in the plane.
Angles in the plane are measured counterclockwise from the positive x axis. It looks like you did this part correctly.
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):
-0.4, -6.0, -.1, -1.5, -.36, -7.9
0, 0, 0, 0, -2.1, 6.27
2.5, -7.2, .625, -1.8, 2.7, -8.4,
Sum of x components, ideal sum, how close are you to the ideal; then the same for y components.
.055, 2.1, -2.05
-10.03, -13.1, -3.07
Distance of the point of action from that of the leftmost force, component perpendicular to the rod, and torque for each force:
0, -7.9, 0
13.3, 6.27, 83.4
21.4, -8.4, -180
Sum of torques, ideal sum, how close are you to the ideal.
-96.6, -154, -57.4
How long did it take you to complete this experiment?
all day
Optional additional comments and/or questions:
I need more explanation and visual examples of what you expect us to do in these labs.
Some of the coordinates on the last part might have been in error, which led to results inconsistent with what would have been anticipated.