phy 121
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: **
.55,8, 12.9
7.89, 8.2, 8.55
1.14, 3.58, 1.9
The left end of the rod.
Each rubber band is numbered so I looked on the table first for each rubber band. B's length was actually right on the chart, as was C's (since we used that one to set up the lab). A was two rubber bands, so I chose one and looked it's lenght up on the chart. It wasn't there, so I looked at the corresponding graph, slid over on the x axis to the correct length, went up to where the line crossed that point and over to the y axis for the force. Since A was two rubber bands I then multiplied by 2.
The results give the length of the rubber bands and the force they exerted.
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
.54
8%
The first number is the net force of the three rubber bands, and the 2nd number is the percentage of the net force of the sum of the magnitudes of the 3 rubber bands.
Add up the net force of all three rubber bands (3.58-1.14-1.9 = .54)
Add up the magnitude for all three forces (1.14+3.58+1.9=6.62)
Divided the net force by the sum of the magnitudes (.54/6.62) = .08 = 8%
** Moment arms for rubber band systems B and C **
7.45, 4.9
These # are the distances away from the fulcrum that the force exerted by rubber bands B and C, respectively, are applied. I measured them, but I also could have subtracted point B form point A and point A from point C.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
4.56, 14.32, 7.6
7.45, 4.9
I multiplied the Newtons I reported earlier for each vector by 4, since 4cm = 1 N. The numbers represent the magnitude of each vector.
** Torque produced by B, torque produced by C: **
33.972, -37.24
These # are the torque, or turning force, of rubber bands B and C respectively. I multiplied the moment arm (distance of force application from fulcrum) for each rubber band by its force in N to get these #. Torque B = 7.45 * 4.56N. Since I multiplied N by distance would my results be in Joules? It's still force so I don't think so. What is the unit for torque? Still Newtons?
What are the units of the quantities you multiplied? This will tell you what the units are of the product.
In this case I believe you multiplied cm of moment-arm by Newtons of force. The unit of your torque would therefore be cm * N. This is not a standard unit, but it is perfectly okay for the present. Standard units would be m * N or cm * dynes.
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
-3.268
4%
The net torque is negative, meaning that theoretically the force of rubber band C is stronger than rubber band B by about 4%. I calculated the net torque (33.972 - 37.24 = -3.268) and the sum of the magnitude of the torques (33.972 + 37.24 = 71.212). I divided the net torque by the sum magnitude (-3.268 / 71.212 = .0459 = 4%
** 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? **
70 mins + 25 mins to type up.
** Optional additional comments and/or questions: **
Excellent work. See my notes and let me know if you have additional questions.