Laboratory #2 Free Fall Lab Determination of Gravity (Daniel Guzman)

Free Fall Lab Determination of Gravity

Daniel Guzman

James Okamura

Alejandro Rodriguez

March 1, 2017

Part #1

In this experiment one was trying to determine the acceleration due to gravity of a falling object that started from rest. In order to determine the acceleration due to gravity that the object was experiencing, one had to measure the position as it was falling down with respect to time. Once the position of the object was recorded one could find the change of position of the object, which is very important when finding the velocity at which the object was moving. Once one knew thee velocity of the falling object one could proceed and graph velocity vs time, and position vs time. When the graphs of position and velocity are graphed one can proceed and determine the equations of the line from, which could derive the acceleration due to gravity that the object was experiencing.

Description of the apparatus and experimental procedure
The apparatus used for this experiment consisted of a sturdy column, a 1.5 meter piece of paper, an electromagnet, a falling object and a spark generator. The object or falling body was held by an electromagnet , which helped the object to start from rest, once the object is falling down a spark generator starts to generate sparks every 1/60 of a second which are recorded on the 1.5 meter paper that is attached to the sturdy column.
Once the position of falling object is recorded on the 1.5 meter paper one would proceed, and make measurements of the dots that are in the paper, once the distance between the dots is measured one could proceed and record that data in excel spread sheets. One had to record in excel : the position with respect to time of the object, the mid time interval between each dot and then calculate the velocity in the time interval. Once this is done one could proceed and graph velocity  with respect to time and position with respect to time. Once this is accomplish one can determine the acceleration due to gravity from the equations of the lines.

Data Tables/ Graphs 

Graph of velocity vs time of the falling object. The equation of the line is displayed in the graph because is very important when finding the acceleration due to gravity of the object

Graph of position vs time of the falling object. The equation of the line is displayed because is very important at the moment of finding the acceleration due to gravity that the object was experiencing.

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 ho you can get the acceleration due to gravity from the velocity/ time graph. Compare the result with the accepted values?

Acceleration due to gravity can be obtained from the velocity vs time graph by taking the derivative of the equation of the line, which models the velocity vs time of the falling object.

3. Describe how you can get the acceleration due to gravity from your position vs time graph. Compare your results with the accepted value

As mentioned before the equation of the line is very important when one wants to find the acceleration due to gravity. In this particular case one would take the derivative of the equation of position with respect to time of the object. Once one has the velocity with respect to time one would take the derivative of the equation which will give one the acceleration due to gravity.

Part # 2 ( Analyzing the class data for g )

Data Table 

 Questions and analysis

1. what pattern if any if any is there in the values of our values of g?

The values obtained for gravity in our group were relatively far from the accepted value of gravity which is 9.82m/sec^2 which tells one that the systematic errors really influenced the results obtained. The results obtained for the gravity were in a range from 957 cm/sec^2 to 960 cm/sec^2, which once again tell one that the results obtained are far from the accepted value.

2. How does our average value compare with the accepted value?

The average value obtained for the acceleration due to gravity that our group got was 961.356 cm/sec^2 which, lets one infer that the value was far from the accepted value of gravity, which is 9.8m/ sec^2. Even though the percentage error between the accepted value and the average obtained is only 2.25% it is far from being precise.

3. What pattern if any is there in the class' values of g?

All the values obtained in the class for gravity were relatively far from the accepted value of gravity, which lets one infer that the systematic errors definitely affected the data and the results obtained. The only pattern that I found in the results obtained by the class is that all the results are within a range that goes from 950 cm/sec^2 to 969.7 cm/sec^2

4. What might account with any difference between the average value of your measurements and those of the class? Which are systematic errors? which are random errors?

The difference between of the average values that I obtained for gravity and the class's might come from different factors; for instance, the position of the falling object marked in the paper might have a very little variation, the differences can also come from the measurements made by each group of the distance that there is between each dot, because some groups or even my group rounded the measurements, which will generate a difference between the average values.

Some systematic errors in this particular experiment might come from the measuring devices such as the apparatus itself or the assumptions that one made. for instance, assuming that friction did not play an important role as the object is free falling. Another systematic errors could come from how the data was manipulated. for instance, a miscalculation might change some results, that will definitely alter the expected or final result. 

Some random errors can come from how the measurements between the dots were made because is almost impossible to make each measurement with the same precision as the last one. This random errors are errors that will be propagated or that will be inevitable, even if the best physicist would do the experiment    

5. Summary of the important part of this experiment. What were the key ideas? What were you supposed to get out of it?

The most important part of this experiment was to obtain the acceleration due to gravity that a falling object was experiencing as it is moving. However, to obtain the acceleration due to gravity one had to go through a series of steps that led one to obtain a valuable relatively close to the accepted one. For example, one had to graph velocity vs time and position vs time and from these graphs one had determine the value of the acceleration for the graph. This is a very interesting approach because one can find the acceleration of any object as long as one has the position with respect to time of the object. The interesting feature of these experiment was the numerical approach that one had to have in order to obtain the value for g because it leads one to follow a certain series of steps that eventually will lead one to achieve what one was looking for in the experiment.