We already had the apparatus set up for us, it looked like this:
Materials needed: machine that turns, a ruler to hang the string with a mass at the end
Procedure:
We predicted equations as well as things that were constant. Some things that we knew would not change: length of the string, radius 1, and height of the machine. Some things did change such as radius 2, the angle of the string, the height of the object to the ground. All of these depend on how fast these objects are moving. We also set up the sum of the force equations on the bottom picture.
This is the equation that we came up with to solve for theta. Notice that little h will be measured when we do the experiment and everything else stays constant.
If you were a little confused by my variables above you can refer to this picture for how we labeled the apparatus. We did the sum of forces in the y direction as well as the x direction. In the x direction we set it equal to mrw^2 because the acceleration is in the x direction.
1. Measure the height (of the whole apparatus), radius(from the center to the string), and the length of the string. These measurements stayed constant throughout the whole experiment. Keep in mind that when the thing is spinning (the faster or slower it goes) theta changes.
2. We recorded six trials altogether each time spinning the whole thing a little faster. Every time we moved it faster we had a new time per revolution and a new height at which the object hit our "piece of paper) each time.
Professor Wolf controlled the apparatus as well as measured the height. The object would hit the paper slightly and every time we made it faster the height would increase. We slowly moved the paper up and up each time and when the mass hit the paper, we measured the height. We timed 10 rotations and just divided it in order to rule out some hiccups in the rotations.
3. Using logger pro, we want to find the relationship between angular speed and T
We combined the two forces by dividing it (sum of the forces in the x direction // sum of the forces in the y direction) so we get our new equation tan theta = r*w^2 / g. We want to solve for w (in the orange) and we plugged our own calculations of (theta) and (r) so that leads to the bigger equation you see on the right of the equation. We also did another equation with T and we found that by substituting w=2pi/T so that's where we got the Tequation in blue.
4. To find the relationship we put in all these equations into Logger Pro and then we graphed the w v angle and we got
We fit a Ax line to it and A should have been about .99. The correlation between the two is linear and almost perfect. Which means they are proportional.
Conclusion:
The purpose of this lab was to find the relationship between angular speed and theta. What we found was that when theta is bigger it goes faster. The angle is always changing with respect to speed or how fast this apparatus was moving. There was uncertainty in the lab because one, sometimes when the object was spinning it wasn't the same height on each side so on one side it was slanting. So the height there was definitely some uncertainty. Second, the last trial that we did the height measuring device that we had set up did not reach the actual height of the object so we added another ruler to the measuring device and the only way we did that was to use a clamp and add another ruler. This added some uncertainty because we weren't sure if the ruler started out at zero to the height. Another uncertainty in measurements was that it hit the paper at different distances. We tried to move it so that once it hits the paper we took that height but sometimes it would skim the paper sometimes it would hit the side of the paper and sometimes it hit in the middle of the paper which left us with some uncertainty.
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