August 31, 2016: Free Fall Lab; Determination of g and Analyzing data

Anthony Betancourt
Lab Partner: Josh Fofrich

Professor Wolf

Lab Performed: 08/31/2016

Free Fall Lab

Part 1

Purpose: This experiment is to demonstrate a free falling object, determining the value of g, and to study the motion with the aid of an apparatus. 

Procedure

1.     Pull a piece of the conductive tape through the bottom of the apparatus all the way top keeping the paper “tight” with the weighted clip. 

2.     Turn on power supply to electromagnet.  Use caution once apparatus is energized and do not touch any energized parts. 

3.     Prepare wooden/metal cylinder for free fall by placing it under the electromagnet near top of apparatus so it hangs. 

4.     Turn on power to the spark generator.

5.     Hold down sparker switch on spark generator (generator sparks at 60 Hz leaving a dot on the paper as it falls).

6.     While holding down the sparker button turn off the power source for the electromagnet.  Cylinder will fall once power is turned off to electromagnet. 

7.     Turn off power to the spark generator. 

8.     Tear off paper strip and place on table top alongside a meter stick.  Place the 0-cm mark on a dot and record the position of each dot measured from the 0-cm mark. 

9.     Once each dot is measured, open up Microsoft Excel and input measured values and create a graph with trend line including R-value and equation of the line. 

Theory

Utilizing the measured points on the tape, which account for each second of free fall for the wooden cylinder, an Excel spreadsheet can be made.  Once a reasonable number of data point are uploaded into Excel, the scatter plot of data can be used to obtain a trend line and consequently derive the theoretical value of g. 

Measured Data

Graphs

(graph comparing mid-interval time with mid-interval speed)

(graph comparing distance and time)

Analysis

1.     The velocity in the middle of a time interval is the same as the average velocity for that same time interval.  For example, the time interval from 0.017 second to 0.050 seconds:

o  

o   Equation from speed vs. Time graph trend line:

2.     Acceleration due to gravity can be calculated by finding the area under the graph for speed vs. time.

3.     In order to find the acceleration using a position vs. time graph, you must pick a point on the curve and find the 1^st derivative in order to find the velocity.  Then you take the second derivative of the function to find the acceleration at that point.

Conclusion

            Given the relative accuracy of this experiment, the systematic errors in the procedures hinder from obtaining a more precise value of g.  These defects could be resultant of poor measuring equipment, no taking into account any air resistance from the object falling, any friction from the cylinder making contact with the apparatus, and also the amount of data points entered into the spread sheet. 

·     

The experimental value of g should be within 10% of the accepted value.  Luckily, the measurements taken along with the number of data points that were recorded in the spreadsheet were able to establish a good amount of data for the trend line graph.  The more data points input into the computer, the more accurate the experimental value of g will be.  Along with more data points also utilizing more precise measuring equipment can lead to greater accuracy.

Part 2: Errors and Uncertainty

           

1.     Every lab group’s value of g differed with one being well below the accepted value.  Most of the experimental values were just under the accepted value except one being the actual accepted value. Subsequently, finding the exact value of g will vary from group to group because one group might have more or less data point collected from the tape measurements. 

2.     Our group’s value of g ended up being the exact same as the accepted value. 

3.     Most of the class’s values were under the accepted value for g. 

4.     Our value might differ from the rest of the class due to the amount of data points we input into the excel spreadsheet, the accuracy of the measurements taken from the tape, or also accuracy of the apparatus.  Systematic errors involved in the use of measurement instruments, equipment usage, and amount of data collected.  Random errors being those that occur when human interaction occurs, such as the actual measuring of the tape, and calculating uncertainty with the class averages. 

5.     This lab focused on the ability for individuals to work with others and run an experiment together in a timely manner with the ultimate goal of proving one method of obtaining an experimental value of g.  Some key ideas focus on data acquisition and making use of the measuring tools available to you.  Also, the use of standard deviation in calculating how replicable an experiment is to derive an expected value.  One lesson learned is the proper method of formally writing lab reports and documenting data to prove your result.