Lab 2: Free Fall Lab: Determination of g (and learning a bit about Excel) and Some Statistics for Analyzing Data

Lab 2: Free Fall Lab: Determination of g (and learning a bit about Excel) and Some Statistics for Analyzing Data

Chris Ceron, Amy Chung, and John

The purpose of this lab was to examine the force of gravity in the absence of all other external forces in order to determine gravity's acceleration to be 9.8 m/s^2. 

Apparatus used to demonstrate the motion of a free falling body

Apparatus

The apparatus used in our experiment includes a 1.5 meter column and holds an electromagnet at the top of the column. When released, the electromagnet falls between two wires that transmit a spark from one wire to the next through the use of a spark generator. These sparks are created every 1/60 seconds, and were recorded by placing a spark sensitive tape in between the wire and the electromagnet. 

The black dots on the tape was created from the spark

Data

Once the apparatus was used and the sparks were recorded, we measured the distance in between each spark, starting with the spark that was created at the top of the column and following the direction of the fall.

Excel

We used Microsoft Excel to collect our data into organized columns:

Each column was used for the following:

• Column A - The time in between each spark (1/60 seconds)
• Column C - The distance between the initial spark at the top of the column and the rest of the                        sparks
• Column D - The space in between each spark (∆x)
• Column E - The mid-interval time of each spark. (The time in between each 1/60 second                              recorded in column A)
• Column F - The mid-interval speed of each spark (Calculated by dividing ∆x and the time in                       between each spark)

Graphs

After collecting all the data, we plotted two different graphs:

1. Mid-Interval Speed Graph - The graph of the mid-interval speed vs. mid-interval time. This graph shows the relationship of velocity vs time. As seen below, the velocity increased at a relatively constant rate, which also represents a constant acceleration. 


2. Distance Graph - The graph of distance vs. time. This graph shows that the distance gradually increases as the electromagnet continues to fall. 

On the mid-interval speed graph, we used a linear fit to create a line through the points plotted. We then displayed the equation of the line, which is displayed in the form y=mx+b. The acceleration of the electromagnet can be calculated by the slope of the line. The slope of the line is equal to m. Through our data, we found acceleration to be 969 centimeters, or 9.69 m/s².

Uncertainties 

Although our calculations were correct, there were other factors that were not taken into account. These factors contributed to the difference between the expected value of acceleration of the experimental value. Some of these factors include the friction created between the electromagnet and the wires as the electromagnet is falling, wind resistance, and uncertainties in the calculated quantities. Our absolute difference was calculated by the following:

Our absolute uncertainty is -1.12%