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: **
1cm,16.4cm,26.4cm
13.2cm,13.3cm,16cm
1.32N,21.8N,42.24N
The reference point was the left end of the rod.
The forces in Newtons were obtained through my calibration graphs. I multiplied the two corresponding numbers together (arm measurements and rubber band measurements), then multiplied the answer by .1 since Newtons include measurements of meters instead of centimeters.
It appears that you multiplied the length of the rubber band by the distance from your reference point. Multiplying a distance in cm by a length in cm does not give you Newtons; torque is in any case not measured in force units (e.g., Newtons) but in units of force * length (e.g., N * cm or N * m or dyne * cm). To get a torque you need to multiply the force of the rubber band by the distance from your reference point.
What force corresponded to each of the rubber band lengths, and what torque the therefore get for each?
I obtained these results through measurement of the rubber bands after following the experiment. I then proceeded to find how much force was used in Newtons.
** Net force and net force as a percent of the sum of the magnitudes of all forces: **
-21.76N
94.8
I obtained the first result by adding together the three forces in Newtons of the box above. The B and C stretches were negative and the A stretch was positive. For the second number, I added the first and last (B and C) stretches and multiplied them by 2.176 and found the percentage.
The forces will be those you obtain from the calibration graphs. The quantities you reported earlier were in any case to have been torques, not forces; see my note above.
** Moment arms for rubber band systems B and C **
15.4,10
These numbers represent the distance from point B to point A (the first number) and point C to point A (the second number). These measurements are named the moment-arm of the force. This simply means the distance from the fulcrum to the force of the rubber band.
** Lengths in cm of force vectors in 4 cm to 1 N scale drawing, distances from the fulcrum to points B and C. **
2.7N,1.125N,2.925N
15.4cm,10cm
The first row of numbers are the lengths of the vectors representing the forces exerted by systems B, A, and c. I found these numbers by measuring the lengths of the pulls and dividing that number by four, meaning one Newton for every four centimeters. The next line is the distance from the fulcrum to the points of application of the two 'downward' forces, giving the distance from the fulcrum to the point of application of force B then to the distance from the fulcrum to the point of application of force C.
** Torque produced by B, torque produced by C: **
+41.58,-29.25
These results are the torque of the force exerted by rubber band B and C about the point of suspension. The positive and negative numbers represent the directions they have.
The forces and moment arms you just reported were
2.7N,1.125N,2.925N
and
15.4cm,10cm
The torques you report should be obtained from these quantities; the torques you report don’t quite seem to match. You need to show specifically what you multiplied by what to get your toques.
** Net torque, net torque as percent of the sum of the magnitudes of the torques: **
12.33
12.66
I obtained the first result by finding the net torque and I found the second number by making my net torque a percent of the sum of the magnitude.
This means that the net torque is the two torques added together (negative representing the clockwise direction, and counter clockwise as positive).
** 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? **
2 hours
** Optional additional comments and/or questions: **
Much of your work looks good. It shouldn't take much to make the necessary corrections.