Kevin Nguyen
Lab Partners: Jose Rodriguez and Kevin Tran
Date of Lab performed: 05-24-2017
Statement: The purpose of this lab is to find the moment of inertia and frictional torque of the apparatus so that we can solve for the time it takes for the cart (that was attached to the small cylinder) to travel down a sloped surface.
Theory: To find the moment of inertia of the entire apparatus, we needed to find the individual moments of inertias of the the disk and the two side cylinders attached to it. To find those moments of inertias, we found the mass of the entire apparatus (given on the side of the disk), the diameters, and the thickness of the disk and the two cylinders. After getting those measurements, we found the individual masses of the two side cylinders and the disk by using the formula
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| Mass 1 and Mass 3 represents the mass of the side cylinders. Volumes 1 and 3 represents the volume of the side cylinders and volume 2 represents the volume of the disk |
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| Mass two represents the mass of the disk |
After finding the individual masses of the two cylinders and the disk, we used the formula
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| M represents mass, R represents the distance from the center of the axis of rotation. |
To find the moment of inertia of each part.
After finding the individual moments of inertia of the disk and two cylinders, we added them together to find the total moment of inertia of the entire apparatus.
Then we had to find the frictional torque of the apparatus.
To find the frictional torque, we used the concepts
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| Torque equals to the inertia of the system times the angular acceleration. |
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| The change in angular velocity over change in time equals to angular acceleration. |
We were tasked to find the time experimentally and theoretically.
First, we timed how long it took for the cart to travel down the slope (1 meter).
Second, we found the time theoretically using these equations.
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Summary:
We grabbed one of the apparatus that was available on the table.
We then measured the diameter of the disks and two cylinders. After taking necessary measurements, we measured the frictional torque on the apparatus.
We put a tape on the disk in order to easily indicate the rotational speed of the disk. We then recorded a high speed video of the disk spinning until it stops. To find the angular deceleration of the disk, we put the video on the logger pro program, set up a angular velocity vs time graph, and plotted the position of the tape each 2 frames until the disk stopped rotating. We then used the slope of the angular velocity vs time graph to find our angular deceleration, which allowed us to find the value for frictional torque.
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| The angular deceleration we got was -0.1049 rad/sec^2 |
Then, we set up our apparatus like below
The apparatus is connected to a 500 gram cart and the cart is on a track that is inclined 49 degrees. We measured how long it took for the 500 gram cart to travel one meter down the sloped track (from rest). We ran the experiment two more times (for a total of three times) in order to get an accurate average time.
Measured Data:
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| Experimental Time |
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| Dimensions of the apparatus |
Calculated Results:
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| The time that we calculated was 6.67 seconds |
Conclusion
The time that we calculated through theoretical means was very accurate since the calculated time was only off by 0.05 seconds compared to the average experimental time.
Although the results agreed with one another, there are sources of uncertainty that may have produced error in the results.
First, we assumed that there was no friction on the track. By making that assumption, the value of acceleration of the cart would have been slightly lower than what it should have been.
Second, air resistance on the cart was not considered, so the cart could have also been slower than what we've calculated.
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