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: **
resubmition
** 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: **
LINE 1
1.25, 7.75, 11
LINE 2
Length of rubber bands
B 8.4 cm
A 7.9 cm
C 9.1 cm
LINE 3
Forces
B 1.0 N
A .19 N
C 2.0 N
LINE 4
What I did was I drew the rod exactly according to scale, which was 15.5 cm. I placed the B rubberband system at 1.25 cm from the edge on the left. The A system was located in the middle which was at 7.75 cm. System C was located 3.25 cm beyond the A system, @ 10.55 cm.
LINE 5
to obtain the Forces in Newtons I used the information gathered in my cm v. Force calibration curve that I constructed on July 12 for the rubberband calibration experiment.
LINE 6
To obtain my results I measured the distances and then converted them to Newtons for my experiment.
I then checked my work using the formula force * distance = force * distance.
For this formula to work there has to be a mid point, kind of like a seesaw and then weights distrubuted on each side of the rod.
So to check my work I used the equation
f1*d1=f2*d2
1 N * 6.5 cm = 2 N * 3.25 cm
6.5 N * cm = 6.5 N * cm
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
Fnet = Force in A + B + C
.19 N + 1 N + 2 N = 3.19 N
** Moment arms for rubber band systems B and C **
3.19 N / ( ( 8.4 cm * 1 N ) + ( 7.9 cm * .19 N ) ( 9.1 cm * 2 N ) )
3.19 N / 28.101 cm * N
0.114 cm
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
&&&&&Moment-arm for the system B
&&&&&distance from A to B on rod = 6.5 cm
&&&&&distance from top of point B to bottom = 8.4 cm
&&&&&6.5 ^ 2 + 8.4 ^ 2 = 10.61 cm
** Torque produced by B, torque produced by C: **
&&&&&Distance from A to B on rod =6.5 cm
&&&&&Distance from top of point B to bottom = 7.9 cm
&&&&&6.5^2 + 7.9^2 = 10.23 cm
&&&&&distance from A to C on rod = 3.25 cm
&&&&&distance from top of point C to bottom = 9.1 cm
&&&&&3.25 ^ 2 + 9.1 ^ 2 = 9.7 cm
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
&&&&&B = 8.4 cm = 2.1 N ( down )
&&&&&A = 7.9 cm = 2.0 N ( up )
&&&&&C = 9.1 cm = 4.55N ( down )
&&&&&From A to B = cm
&&&&&6.5^2 + 8.4 ^ 2 =
&&&&&From A to C = cm
&&&&&9.1 ^2 + 3.25 ^ 2 = 9.7
The moment arm is the displacement from axis to the point where the line of the force crosses the axis. Since the forces are perpendicular to the rod, the moment arms are equal to the displacement from axis to the point of application.
My previous note indicated this, but did not terminate at the correct point so the note appeared to include your incorrect calculation of the moment-arm. I'm sorry for the confusion.
The point is that the magnitudes of the moment-arms are just 3.25 cm and 6.5 cm.
The vectors represent forces. The lengths of the vectors or of the rubber bands are drawn in cm, but the vectors represent forces in Newtons and the lengths of the rubber bands have nothing to do with the moment arm. So the two sides you used in the Pythagorean theorem don't represent the same sort of quantity.
In this case the magnitudes of the moment arms are just 6.5 cm and 3.25 cm.
** 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? **
** Optional additional comments and/or questions: **
just making sure all of my stuff is straight before I try to figure this out. my tutor is really helping understand this alot better.
See my note. The HTML representation of my previous note was misleading.