Acceleration due to gravity lab

[hotshot1kille]

Homework Statement

We did a lab using a pendulum attached to a string about 1.12m long. We let it go from 20 degrees and counted 10 cycles and recorded how much time it took for the pendulum to complete 10 cycles. This lab is done assuming, there is no air resistance or any other force other than just gravity. We did 3 test cases.

Test case 1- time it took for the pendulum to complete 10 full cycles is 23.41 s.

Test case 2- time it took for the pendulum to complete 10 full cycles is 23.41 s.

Test case 3- time it took for the pendulum to complete 10 full cycles is 23.44 s.

Find the average time for 10 cycles.

Using this average time, calculate the period of the pendulum.

Using the period of the pendulum and its length, calculate the value of "g".


I don't know how to do average time, and if i get the average time wrong then i get number 2 wrong and then my answer for number 3 will be wrong. So i did make an attempt, can someone check if i am doing it right and if my answer seem fine for all questions. Please and Thank you.

Homework Equations

T= 2∏ √ L/g

Period: Δt/Nc

Average time for 10 cycles : Δt/ Nc

The Attempt at a Solution

1. Find the average time: Test case 1: 23.41s/10 =2.341 seconds per cycle.

Test case 2- 23.41s/10 =2.341 seconds per cycle.

Test case 3- 23.44/10 = 2.344 seconds per cycle.

2. Period= Δt/ Nc

Test case 1 and 2: 2.341s / 10 = 0.2341

Test case 3: 2.344/10= 0.2344


3. Find g.

4∏^2 (L)
---------- = g
T^2

4∏^2 (1.12m)
--------------- = g
0.2341^2

g= 806.81 m/s^2

 

[Delphi51]

The average of 2.341, 2.341 and 2.344 is their sum divided by three. That is, about ten times the .2341 you used in the calc. That will give you a decent value for g, but not a great one. In my experience, it takes considerable practise to get good times and far better to count 100 swings rather than 10. Also, mistakes can be made in measuring the length - not just the length of the string, but the distance from the pivot point to the center of mass of the bob.

 

[hotshot1kille]

So average time is : (23.41+23.41+23.44) / 3 = 23.42

period= (23.42)/10 = 2.342

so then gravity would equal to

4∏^2 (1.12m)
--------------- = g
2.342^2

g= 8.06 m/s^2

does this seem fine?

 

[Delphi51]

Yes, the calc looks good! How about the measurement of L; did you include the distance from the end of the string to the center of the bob? If not, take an estimate and add it.

 

[hotshot1kille]

Yea what we did in class was that they were already made. We just got up and took one, the lab says it has to be roughly within 1.2- 1.5m. I told my teacher i have about 1.1m, and he said it is fine, because like the 0.1m won't make a big difference for such a small calculation. He also mentioned that imagining that there is only gravity acting upon it do not worry about resistance, shape of the ball and how round it is.

 

[Delphi51]

Well, if you added .1 to the length, you would have 8.9 instead of 8.0 for your answer.
But I doubt if your bob was 20 cm long.

Students often get 9.6 to 10 m/s² from this experiment because air resistance, etc. really doesn't make much difference. Note that the time measurement is squared, so its error strongly affects the result. That's why it is important to go to great lengths to measure the time accurately.

It would be interesting to try to estimate the accuracy of your time measurements and perhaps deduce from that the accuracy of the calculated value for g. The stopwatch is very accurate, so your main error is going to be due to hitting the button at the wrong time. If you time something known to be very accurate, like a clock second had, you will probably find an error of something like 0.1 second. Try increasing or decreasing your average time by that much and see how it affects the result. Of course your average over 30 swings should reduce your error by a factor of sqrt(30) . . . unless there was some kind of consistent error in the timing process such as being faster at pressing start than in pressing stop due to anticipating the end of the tenth swing.

 

[hotshot1kille]

Oh ok i see your point of view. Thank you so much i will fix it and get back to you.