PHYS 4A/ Fall 2014; Free Fall Using a Spark Generator

Purpose: Using a spark generator and a spark-sensitive tape, marks are made on the tape to record the velocity of a falling object which is the analyzed to determine gravitational acceleration.

Spark Generator and Spark Tape Set up

The spark generator was connected to an object attached to a metal rod which allowed for 1.5m of free falling distance. Spark tape is put parallel to the metal rod along the 1.5m distance. The falling object was held at rest by an electromagnet before the experiment begins. When the object was released, the object creates sparks which mark the spark tape at a rate of 60 sparks/sec. The spark tape was then removed and taken for measurements. 

Spark tape and Meter Stick Set up

A meter stick with +/- 0.05m of uncertainty was used to measure the distance of each spark from the origin. This data was recorded and graphed in excel for analysis.

The data set below was created as a reference in order to make graphs that would display values for acceleration. Since sparks were created at a rate of 60 sparks/sec, time intervals were set at 1/60th of a second. The distance were also recorded per 1/60th of a second. The change in distance(m), x, was calculated. Time was then split into mid-intervals and the speeds during these intervals was also calculated. 

Velocity was graphed using Time vs Distance in order to verify that the data makes theoretical sense. This was verified as the graph showed an upwards curve due to a constant acceleration which was determined by taking the derivative of the x^2. Thus by taking the derivative of 484.59x^2, a value of 969.18m/s^2 was found. The R^2 value was 1 which showed that the curve had a direct correlation. Mid-interval Time vs Mid-interval Velocity was then graphed which gave us acceleration. The acceleration was given by taking the slope of the graph and was determined to be 970.03cm/s^2 or 9.70m/s^2. This value was approximately .11m/s^2 slower than the actual gravitational acceleration value. The two graphs gave similar accelerations of 9.70m/s^2 which is -1.12% from the actual value of acceleration. 

The values of gravitational acceleration were taken from the class and a class average was computed. This average was determined to be 9.51m/s^2 and standard deviation was used to determine a range. The standard deviation had a value of 12.27m/s^2 thus giving us the +/- value for our results.

The values that we found and the class average were both lower than the actual value. This may be due to friction along the metal rod as the object was in free fall. This friction could have slowed down the object and not allowed for full acceleration. The class average was 3.06% lower than the actual value compared to our experiment's 1.12%. This may be due to inconsistency in the equipment and the nature of the data recording as there were many different people taking data from different strips. This could add up to human error that may have affected the average. 

The experiment was a success as there was only a range of about 3% error between the data sets. The group acceleration was determined to be 9.70m/s^2 while the class average was 9.53m/s^2. These values were compared to the actual value of 9.81 m/s^2. The values were determined using excel and taking the derivative of the position vs time graph or the slope of the velocity vs time graph.