07-Sept,2016 . Lab #2: Free Fall Lab

Lab #2: Free Fall Lab

Dahlia - Ariel - Carlos

08-Sept-2016

The purpose of this lab is to examine the validity of the statement: in the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2. The second purpose of this lab is to help students know a bit about Excel such as how to enter data, how to fill down, or how to graph from  a certain set of data.

Part 1: Free fall

Set up:
Use the apparatus to record the series of dots which was represented to the position of the falling mass every 1/60th of a second
These dots was in a piece of paper tape.
Measure and record the position of each dot.

Data:
These pictures shown the progress we recorded the position of each dots and received data.

Then, we measured the position of each dots.

After that, we recorded them into Excel.

In this table:
- Column "time" shown 1/60s, 2/60s, 3/60s, and so on.
- Column "distance" shown the position of each dot.
- Column "delta" shown the position of each dot related to period dot.
                       Delta = position of dot number #(n+1) - position of dot number #n
- Column "Mid-interval time" shown the time for the middle of each 1/60th second interval.
- Column "Mid-interval speed" shown the average speed in each interval.

After that, we graphed our data.

Analysis:
1.
For constant acceleration, we can see that the velocity in the middle of a time interval is the same as the average velocity for that time interval.

2.
The value of g was the slope of the line of speed vs. time.

With v =925x + 45
        a= v' = 925
My result was lower that expected result.

3.
The value of g was the second derivative of the curve of position vs. time.
With y= 465 x^2 + 43x + 0.28
         v= y' = 930x+43
         a = v' = 930
My result was lower that expected result.

Conclusion:
From the analyzed data, I could see that the difference between each dot and the speed of them in the interval 1/60th second were increased patently.

From the fact, the gravity is 9.8m/s^2, but my group answer was 9.25m/s^2. This happened because of some reasons such as the frictions, the mistakes when we measured the positions of dots.
The absolute difference was 9.25-9.8=-0.55m/s^2.
The relative difference was (9.25-9.8)x100%/9.8 = -5.61%

Part 2:Errors and uncertainty

When doing this experience, Our group result was 9.25m/s^2; however, each group in the class received different results. The below table was what the class had.

After that, we entered these values into a sheet of Excel.

In which 948.25 was the average of g; 672.6875 was the average deviation value; and 25.9362 was standard deviation value.
To get the dev. from the mean, we used formula

From what we had, we received result:

However, the lowest value in our result was 893, and the acceptable value was 896-1000 m/s^2. Thus, 983m/s^2 became an "outlier", and we crossed out this value to make the result became more creditable.
This was what we had

And the value was 956 ± 32 m/s^2

1. From the class' values, I could realize that our value was lower than the real value.
2. Compare to the accepted value, I also saw that our value was lower than the real value.
3. Actually, there was no pattern in the class' value of g. There was different not because of the progress was wrong; there was different because of some errors called systematic errors and random error.
4. Random error was variation. We can not attribute the anything in particular.
    Systematic error came from our assumption about experiment, which are not true.

Conclusion:
In the real world, we can not do any experience in one time, and assign the result as its value. we have to do so many time, and of course, we cannot receive the same result in every single trial. Therefore, the uncertainty value will make the result we come up with become more acceptable. The lower of percent error and uncertainty value, the higher of creditable result.