September 5th, 2014 Lab 2: Free Fall- Determination of Gravity

Purpose: To use a spark generator to determine that a free falling object will accelerate at a rate of 9.8 m/s^2 .

Apparatus used:

 This is the top of our device. The electromagnet holds our object into place. Once it releases the object, the spark generator records the distance the object travels onto a strip of paper. It generates a spark every 1/60th of a second at 60 Hz.

The over all height of the Apparatus is 1.86 meters tall.

How we obtained our data: The apparatus above used a 60 Hz spark every 1/60th of a second. A spark sensitive tape would record the distance the object traveled at each time interval. (Photo below)

Spark Sensitive Tape next to a meter stick. Each dot is where the object was located at every time interval of 1/60 seconds.

What we did with this Data: We measured 15 dots and obtained the total distance it traveled from the top of the spark sensitive tape. We then created an excel worksheet which consisted of time, distance, the change of distance relative to time(Delta D), mid-interval time, and mid interval speed.

OUR DATA 

This information from the excel spread sheet was then used to make a POSITION VS TIME graph . Which is the photo below

Velocity V.Time Graph

Question for Analysis: Describe how you get the acceleration due to gravity from your velocity time graph? Your acceleration due to gravity can be found by obtaining the slope of the velocity versus time graph. Above is our velocity versus time graph. The slope on our graph is 939 cm/s^2. This converts to 9.39 m/s^2 which is not quite acceleration due to gravity.

Conclusion: Our efforts to conclude that acceleration due to gravity is equal to 9.8m/s^2 fell short. With our data we concluded that gravity was equal to 9.39 m/s^2 which is incorrect. 

• Using the formula for absolute difference (Experimental value-Accepted value) we determined that we were off by -.41m/s^s(9.39-9.8=-.41) 
• Using the formula for relative difference (Experimental value-Accepted value divided by accepted value times 100%) we determined that we were off by -4.1%

Reasons for error: What may have happened

• We measured or dots incorrectly
• The distance of the drop of the object (1.8 m) may have not be a long enough period. 
• We inserted the data or a formula incorrectly in our excel spread sheet.
• Human Error.
  
  Information obtained from group 1-9
  The closest to obtain g=9.8m/s^2 was group 6 who came up with 9.75. This graph shows that every group came up with a G that is lower than it should be which is known as a systematic error.