March 2, 2015 Free Fall Lab

Objective: Determine the acceleration of a free fall body is 9.8m/s^2 under no external force except gravity.

The Set-Up:

The Spark Generator

The apparatus for this experiment is the spark generator. The spark generator has a cylinder on the top, when the spark generator is turned on, the cylinder falls, as it falls, it leaves mark every 1/60th second. A long strip of paper is attach to the spark generator to record the spark that the spark generator generates.

Data Collection: 

The strip of paper with spark marks

For convenient reason, we are given the strip that already had spark marks on it. We measure the marks on the strip using meter stick, we measure with the unit of centimeter. This is our data.

Mark No.	Distance (cm)
1	1.4
2	3.1
3	4.9
4	7
5	9.3
6	11.9
7	14.7
8	17.8
9	21.3
10	24.9
11	28.8
12	33
13	37.5
14	42.2
15	27.2
16	52.4
17	58
18	63.8
19	68.7
20	76.1
21	82.6

Each mark represent 1/60th second. We input the data into the Microsoft Excel spread sheet. 

After we find the distance between each spark on the paper, 1/60th second apart, we input the formula into the spread sheet. Then we get a third column that has the distance per 1/60th second. This third column is the difference of distance.

Next, we make the fourth column titled "mid-interval time" by taking the original time plus 1/120. This gives the time for the middle of each 1/60 interval. Lastly, we produce the fifth column called "mid-interval speed" by diving the change in distance (∆x) by (∆t), 1/60 s.

We use the data to make two graphs. The first one is Mid-Interval Time vs Mid-Interval Speed and the other is Time vs Position graph.

Velocity/Time graph

position/ time graph

Questions/ Analysis:
1. Show that, for constant acceleration, the velocity in the middle of a time interval is the same as the average velocity for that time interval.

2. Describe how you can get the acceleration due to gravity from your velocity/ time graph. Compare your result with the accepted value.
The equation for the velocity/ time graph is y=939.74x+71.545. The figure 939.74x cm/sec^2 is the slope of this graph, which the acceleration, in this case, it is the gravity. 939.74 is measure in centimeter per second squared, when it is convert to meter, we get 9.4 m/sec^2. This is 5% less from the true value of gravity, 9.8 m/sec^2.
3. Describe how you can get the acceleration due to gravity from your position/ time graph. Compare your result with the accepted value.
The equation for the position/ time graph is y= 474.14x^2 + 69.661x +0.1514. When we take the derivative, we get y= 948.28x + 69.661. The gravity value we get is 948.28 cm/sec^2, which equals to 9.5 m/sec^2. This value is about 3 % less from the true value of gravity, 9.8 m/sec^2

Conclusions:
Assumptions of this lab
1. No friction (If there was friction, it would make the values smaller)
2. The sparks are exactly 1/60th second apart

Errors and Uncertainty



Toward the end of the lab, we take the gravity value from each group and analyze them. We make a excel spreadsheet to show the deviation from the mean. The way to get the deviation from the mean is by find the difference between the experimental values and the mean value. Squared the value and add every values together. Divide the sum of squared deviations by the number of data you have, in our case is 9. Then you take the square root of this number. Our standard deviation of the mean is 20.1.

According to the experimental data, the gravity is between 916cm/s^2-996cm/s^2, this is not a good experiment to find out the true value of gravity.

1.What pattern is there in the values of our values of g?
Our values of gravity are 9.4 m/s^2 and 9.5 m/s^2. The pattern is that they are close to each other.
2. How does our average value compare with the accepted values of g?
Our average value is 9.56 m/s^2, it is lower than the accepted value of gravity, 9.8 m/s^2.
3. What pattern is there in the class' values of g?
Class' values of gravity are smaller than the actual value of gravity.
4. What might account with any difference  between the average value of your measurements and those of the class? Which of these are systematic errors? Which are random errors?
5. Write a paragraph summarizing the point of this part of the lab. What were the key ideas? What were you supposed to get out of?
This experiment has a system error which reflects in the class's average value of gravity to be lower than 9.81. This system error is the assumptions that we make for the spark generator. We assume that there is no friction nor air resistance. They are system error because no matter how careful our measurement or calculation is, the values are always going to be inaccurate, the problem is the whole system, not individual technique.
The random error is reflect on individual technique. The gravity value of my group is 9.4 m/s^2. This value is toward the lower end of the class data. It might due to the technique of the operator who made the strip, it might be because of the condition of the spark generator at that moment, it might be we made some small mistake when measuring the marks. These factors are random, thus they are called random error.