- Record the mass of the hanging mass and the stopper
- Create ones table
- Mark the 30cm,40cm,50cm,60cm, and 70 cm lengths on the string
- Place tube through the string
- Tie the string to the hanging mass and tie the stopper to the string
- Practice swinging the stopper with one hand holding the tube
- When you have got the hang of it, take your first cm and make sure it is a the rim of the tube
- Begin timing and count to 20 revolutions and stop
- Take down the time in which it took to do 20 revolutions
- Repeat steps 7-10 with the other measurements
Lab setup:
DATA COLLECTION AND PROCESSING
Aspect 1 – Recording raw data
Uncertainties
- Centimeters: 1cm ± .05cm
- Time: 1s ± .005s
- Mass: 1kg ± 0.000005kg
Masses
M1= Hanging Mass: 0.05080 ± 0.000005kg
M2= Stopper Mass: 0.01266 ± 0.000005kg
Time Trials of 20 revolutions ± 0.25
Aspect 2 – Processing raw data
How to derive rev/s:
0.25/20 +0.005/ 9.41= .01
20/9.41= 2.13
2.13*.01= .02
∴ = 2.13±.02
Rev/s Table
How to Convert into m/s -1
Rev/s* 2𝛑r
2.13±.02 * 2𝛑r
2.13 (2) (𝛑) (.3)
= 4.01
±.02* 2𝛑r
= ±.04
Table of m/s -1
Average Velocity of m/s-1
Below is the mathematical derivation of our formula for velocity (V).
Table for V =
How I found using the formula:
(0.05080 ± 0.000005kg)/(0.01266 ± 0.000005kg)*9.8*0.3 = v2
(0.05080)/(0.01266) = 4.07
(0.000005/0.01266) + (0.000005/0.05080) = = 0.0049
0.0049*(0.05080/0.01266) = 0.0049*4.07 = 0.002
4.07 ± 0.002 *9.8 = 39.2 ± 0.02 * 0.3 = 11.96 ± 0.002
Table for Vwith the given formula
Finding V with collected data
3.83= 14.669
± .04= ± .0016
V with data we collected
Aspect 3 – Presenting processed data
Percent error
Error
In the above graph we can see that the data is relatively constant except for a few points which may have been due to error. These points are from the data our group collected which seems to be quite accurate. The error bars are extremely hard to see, they same alike, but each of them have their own value.
The above graph is the graph of the accepted values from the formula we created. WE can see that this graph looks constant as opposed to the other graph and seems not to have much error involved. Once again the error bars are hard to see, but they too have their own individual error.
CONCLUSION AND EVALUATION
Aspect 1 – Concluding
The Circular Motion Lab data can explain in full detail that as the radius increases the velocity of the object increases. Several tables and graphs in our lab have proven the aforementioned. In our lab if we look at the first table of average velocity we can see that at the first radius the value of the velocity is 3.83±0.04. After increasing the radius to our highest radius we see a radical change in the velocity with it now being 5.97±0.04. The accepted theory in this matter is that as the radius increases the velocity will also. According to Giancoli; pg. 109, he supports this fact with explaining that a net force is required to keep the object revolving. Force directly relates to what is in the lab as f=ma, where a=. Giancoli states that a minimum force is needed to keep the motion circular, and if you think about it; it would take more velocity to keep an object with a larger radius in motion compared to an object with a smaller radius. Comparing our collected data values with our derived formula values we can say that for our lab our values are extremely valid as our percent error was only 10%. In this lab there were few errors, and that all of them were random errors. The random error that occurred was that we definitely did not collect data and that if we did collect more data the results would be much more precise then they are, however our data proves that with the data gathered we have good results. The other slight random error that may have contributed to the 10% of error would be how the radius line did not always stay at the rim of the test tube. In terms of uncertainties my group was somewhat lucky as all the uncertainties rounded which were supposed to be rounded to one sig. fig., rounded to the same number which made all my uncertainties the same for my average velocity. The graphs that were processed were quite similar. The error for each point was so little that is why the error bars on the graph are hard to see. The graph has a constant pattern and any of the points that are out of place are due to error which adds up to the 10 percent.
Aspect 2 – Evaluating procedure(s)
The design and method of the data was extremely valid because of our error. The fact being that our error were quite we can say the data is accurate and definitely is usable in the future. The accuracy of the measurements is quite precise as each and every measurement is taken into account along with the error. The equipment we used was a lowlight of the lab; the stop watches were not functioning properly and were slow. Our management of time was used to its full advantage, having received this lab weeks in advance we took our time with recording the data and refining our data in necessary. The graphs that were processed were quite similar. The error for each point was so little that is why the error bars on the graph are hard to see. The graph has a constant pattern and any of the points that are out of place are due to error which adds up to the 10 percent.
Aspect 3 – Improving the investigation
With reference to Aspect to where it states that an abundance of time was given; we could have taken more trails and got our data even more precise, it would have been really fun to see what would happen if the radius got much smaller and if the radius got a whole lot bigger. In the future we could definitely get better stop watches which would help a lot more. With stop watches being a major deal, another person good have joined the group and more times could have been taken per trial which would make the data reduced of errors greatly.
Dhruv Medepalli – Circular Motion Lab pg