Laboratory Experiment: The Sole Effect on a Simple Pendulum

Experiment Performed By: Nolan M and Jackie O
Experiment Performed On: February 3, 2010

NOTE FROM AUTHORS: Welcome aboard Nolan and Jackie's Pendulum Express! This webpage is dedicated to the pendulum experiment performed by Nolan M and Jackie O at Polytechnic School in the Conceptual Physics ninth grade class. All procedures, data, and analysis were performed and hand-recorded by these students. This experiment was a modern translation of Galileo's archaic study of the pendulum. Rather than a pulse-rate, however, a stopwatch was used to record data in this experiment. Enjoy the research and findings. We hope that by the end of your visit to this website, you will have witnessed, understood, and appreciated just what we had during our pendulum laboratory experience.

Purpose of Experiment:
Through data collection and multiple trials, the purpose of this experiment was to identify what variable(s) would contribute to the time (in seconds) for a simple pendulum to complete one full swing, or its period.

Variables Tested:
1) Mass of Bob
2) Angle of Drop
3) Length of String

Set-Up:

Materials:
- 1 ring-stand
- 1 metal clamp
- 1 200g bob
- 1 100g bob
- 1 50g bob
- 1 string (measured to lengths of 0.4m, 0.25m, and 0.1m)
- 1 meter stick
- 1 protractor
- 1 stop-watch

How to Set Up the Device:
1) Attach the metal clamp to the top of the ring-stand.
2) Attach the string to the metal clamp and measure out the desired length.
3) Proceed to complete the experiment by attaching a bob of different mass to the loop in the string, varying the angle of drop with the protractor, or differentiating the length of string with the meter stick.

Procedure:
1) Set up the pendulum apparatus.
2) We chose to begin with examining the effect of the mass of the bob on the pendulum's period. Different-massed bobs of 200g, 100g, and 50g were chosen and each separately attached to the loop in the bottom of the string. Then, from a set angle and string length (30degrees and 0.5m), the time (in seconds) for three swings of the pendulum was recorded. Three trials with each weight were performed. To determine the period from these, the average was found from all three trials and then an additional division by three to obtain the time of one swing, or the pendulum's period.
3) Next, we varied the angle from which the pendulum was dropped. Three distinct angles were chosen (20degrees, 10degrees, and 5degrees) and the time for three pendulum swings was recorded for each of these angles. (Mass of the bob was set at 200g and string length at 0.5m.) Three trials were performed for each angle and at the end of this step, the average was found from the three trials and then an additional division by three.
4) The last test was to vary the length of the string that held the pendulum. Three different lengths were chosen (0.4m, 0.25m, and 0.1m) and at a set mass and angle (200g and 0.5m), the time for three pendulum swings was recorded. Three trials were again performed and at the end, the average of these trials was found and then divided by three to determine the pendulum period's time.
5) The pendulum device was disassembled.

NOTE: Three trials were performed in this data collection but to maintain better accuracy, many more trials can be done.

Hypothesis:
We hypothesized that the time of the pendulum period will only be affected by the length of the string to which the weight is attached, rather than the mass of the weight or the angle of drop.

Data
Change in Mass of Bob



Change in Angle of Drop


Change in Length of String

Analysis
When altering the mass of the bob, we found that the time it took to complete one period remained relatively constant, only affected by inevitable experimental errors which will be discussed in the next section. The times remained constant because acceleration, or the force of gravity, will always be the constant 9.8m/s^2 for objects of different masses. Only a greater force will be required for objects of greater masses. This is according to Newton's Second Law of Motion, F=ma. The "a" value, or the force of gravity, will be the same for all of the bobs, neglecting air resistance, so the varying "m" values will affect the resulting "F" value.

F = m*a
F = 200g*(9.8m/s^2)
F = 1960N

F = m*a
F = 100g*(9.8m/s^2)
F = 980N

F = m*a
F = 50g*(9.8m/s^2)
F = 490N

After testing the change in the angle in which we dropped the bob, we found little change in the times as well. As we increased the angle of release, we also increased the height at which the pendulum was dropped. This increase in height also increased the pendulum's potential energy, according to the equation PE=mgh. (With the "m" value and "g" value remaining constant in all equations and the "h" value being the only variable, we can conclude that the PE differentiated from the changes in the "h" value.) But because the pendulum had to swing to the same height halfway through its period, it was necessary for it to use the potential and converted kinetic energy to swing to that same height from which it was released. Therefore, we can state that the angle of release, or the height at which the bob was dropped, did not affect the time of the pendulum's period.

NOTE: The height of release was not recorded during the experiment and the equations that follow are just to prove the point that with an increase in height, the potential energy is also increased.

PE = m*g*h
PE = 200g*(9.8m/s^2)*5m
PE = 9800J

PE = m*g*h
PE = 200g*(9.8m/s^2)*10m
PE = 19600J

PE = m*g*h
PE = 200g*(9.8m/s^2)*20m
PE = 39200J

The variable with the only significant impact on the pendulum's period was the length of the string to which the bob was attached. As we lengthened the string, we noted that the distance that the pendulum traveled was more than that of a shorter string. The speed, or rate, of the pendulum also decreased with a longer string. But as a result of this decrease, the period, or time, increased. This is according to the equation d=rt. As the "d" value increased and the "r" value decreased, we concluded that the "t" value was increasing to support the distance that the pendulum was traveling. As a result, the length of the string was the sole effect on a simple pendulum in this experiment.

NOTE: Because the distance that the pendulum traveled and the rate of the pendulum were not recorded, the following equation is only used to prove that as distance increases and rate decreases, the time must increase.

d = r*t
1m = (5m/s)*(1/5)s
1m = 1m

d = r*t
5m = (1m/s)*5s
5m = 5m

Sources of Experimental Error
There were a numerous amount of experimental errors that affected the time of the pendulum's period. The first source of error was in dropping the pendulum: A slight push when releasing the bob could have given the pendulum an initial velocity instead of putting it in free fall. T
he way the pendulum was released might not have caused it to follow a straight line path. This would cause a "wobbling" effect which would decrease the distance that the pendulum traveled and therefore, the length of the period. 
The protractor was also a source of error in that the pendulum was not released at the exact same angle each time, as this would be impossible. 
Also, the stopwatch method of recording the time was very inaccurate because the time at which the pendulum was released and the time at which the stopwatch was started were probably not quite together. So a device such as a photo gate would have definitely provided better results in this area. 
Another could have been finding the time of three swings and then dividing by three, as this might not have given the exact period length. But this did prove more accurate than we had presumed it would.
Finally, there was the inevitable air resistance on the pendulum device.

Summary
At the beginning of the experiment, we hypothesized that the length of the string would be the only factor to affect the pendulum's period. After collecting the data, we noted that our hypothesis was held true and the mass of the bob and angle of drop held no significant impact on the period length. After further analysis of these results, we concluded that mass did not affect the time because every object will undergo the same acceleration. Angle of release will only increase potential and kinetic energy in order for the pendulum to reach the same point at which it was dropped. And finally, the length of the string increased the distance the pendulum traveled but decreased the rate that it traveled which therefore increased the period of time. The experiment was altogether affected by errors in the release of the pendulum, recorded time, and air resistance on the device. But despite these errors, the overall experiment was a success in that we were able to determine what factor altered the length of time for a simple pendulum's period: the length of the string.  

(Period C: Ms. Bush)

Comments

Catherine Lehman - Feb 16, 2010 6:11 PM

It is very apparent that you both spent a lot of time on this lab, mostly because of the extra information. I would have liked though if your graphs and tables were centered, it would pull the whole website together. Your website is set up in the appropriate order, which I know will be apreciated for whoever is grading it. For future reference I would suggest to follow the the sentence per paragraph guidelines, because even though I did not count each sentence it appears that there are extra sentences.

Sarah Grimmett - Feb 16, 2010 6:12 PM

The picture of the pendulum clearly shows your setup and all the materials you used, and that made the procedure very clear. Also good job on putting a list of materials and how to set it up in addition to your procedure, which made this even more detailed and precise. However impressive, the equations in your analysis were a little hard to follow and didn't seem to relate to the overall project. However, your summary clearly shows the results of the experiment and your data is quite clear. Great job!
Sarah G :)

Lily Armstrong - Feb 16, 2010 6:43 PM

You guys did a really good job presenting your information. It was very clear and readable, as well as being very good quality data! Your analysis was especially impressive. I think that your procedure paragraph got a little bit wordy, but other than that, I think you did some fantastic work.

jp olinski - Feb 16, 2010 6:46 PM

This lab has a lot of great information, especially the background including Galileo. All the information gives you a better understanding of how the experiment works. The graphs are a little bit hard to read, but not to bad. The calculations in the analysis give a different representation of the experiment and add a lot. Overall a very thorough, well thought out lab.

Ryan Schiller - Feb 16, 2010 8:54 PM

Your hard work definitely shows, your site is extremely well written. I love you thorough analysis! I think it would be nice if in your hypothesis you explained why you thought what you thought! Your site is a work of art!

Rita G - Feb 17, 2010 10:10 AM

You obviously put a ton of work into this site, and everything is extremely well written. The only issue I really had is breaking up online paragraphs because they're hard to read (Holmgren much?). Your data is easy to understand and your explanations are well-thought-out and thorough. Overall, you did an excellent job.
Rita G.

Alex Piñon - Feb 17, 2010 12:21 PM

This is a good looking site. The layout is in a good, well thought out order. It would have been nice if you put the graphs ans charts side by side. You did a good job on the writing portions too.

olivia treister - Feb 17, 2010 4:56 PM

This report is very thorough and i loved the note from the authors! The data is accurate and the analysis is remarkable. My one complaint is that the color in which you guys choose to write in is a little hard to read. But my complaint is canceled out by of the background that was included and i can see that you guys put a lot of effort into it. Nice Job!!!!!!!!!!