Determining Gravity With The Help of Technology and Physics; Jose Rodriguez; Lap partners: Kevin Nguyen and Kevin Tran; Lab Date: 3/1/2017

This experiment was composed of two parts and the students worked in groups of three to complete it.  The first part of this experiment was to try to prove that the accepted value for acceleration on Earth is 9.81m/s/s with the help of a simple apparatus, physics, and technology.  The second part honed into the errors and uncertainty section of an experiment; it required us to calculate each group's deviation of their experimental acceleration value from the class's mean average of experimental acceleration values, the class's standard deviation of the mean average, and the normal distribution of the class's experimental values of acceleration.

What we tried to measure was how much distance a free falling object (with no force but gravity imposed onto it) travels in consistent time intervals, and how much standard deviation each group's experimental acceleration values had from one another.  To accomplish this experiment, the use of an apparatus that is designed with a 1.5m falling distance, a free-falling object, a spark-generator, and a spark-sensitive tape provided the data that allowed us to generate computer graphs for distance vs time and velocity vs time that aided us in our pursuit to obtain a value for Earth's acceleration.  The logic behind this experiment was based on calculating the distance over a consistent time period of the falling object.  For instance, the spark-sensitive tape provided that information because we measured each gap and we knew that the spark-generator provided data for every 1/60th of a second.  Then, we will transfer that data onto the computer application Microsoft Excel to find the velocity of the object during its' fall at any time because the graph will display the slope-intercept equation of the velocity so we could obtain an experimental value of acceleration if we take the derivative of that equation.  Then, the second part of the experiment required us to calculate each group's deviation from the class's mean experimental acceleration value that lead to the standard deviation value of the class in whole to each group's experimental acceleration value to on another.

This experiment began with the professor's help because he assembled the apparatus so it was ready for use.  The apparatus was assembled by placing a (white-colored) spark-sensitive tape vertically on the main support beam, by placing a free-falling object in front of that tape at the top that was held in place by an electromagnet, and by connecting the power source to an outlet so that the spark-generator had power to produce an electrical charge.  Then, the professor flipped a switch so that the electromagnetic magnet disengaged and the object fell while a spark-generator marked its position every one-sixtieth of a second till it reached the bottom.  Next, we measured the distance between the marked sections with a meter stick (using the centimeter units) and recorded the data. Simultaneously, we set formulas on Excel to calculate time, distance, displacement, mid-interval time, and mid-interval speed to better aid in the graphing process and entered the distance we had measured as well as the time for every 1/60th of a second.  For the mid-interval time we used every 1/120th of a second and entered that value into Excel; the mid-interval speed was calculated as well.  Immediately after that, we created a distance over time graph and a mid-interval speed over mid-interval time graph which displayed the slope-intercept formulas that handed us our experimental acceleration value in the units of cm/s/s. Lastly, for the second part the professor asked all the groups for their experimental value and found the mean average, deviations of the class's mean average, and the standard deviation of each group's experimental value in respect to one another so we can debate whether or not the values were precise and therefore accurate.

This is a picture of the apparatus that was used to capture the distance vs time descent of the free-falling object.  Note that the professor is lifting the free-falling object so the electromagnet holds it at the top.
Also, the spark-generator power interface can be seen to the right of the apparatus; it is blue.

This is an image of the spark-sensitive tape with the meter stick laying along its side. The black dots on the white tape are where the spark-generator made its mark to capture the position of the free-falling object.  The distance between the black dots after the first mark is the distance we measured for the displacement of the object every 1/60th of a second.

Here one can see the data entry of the measured distance between the time interval of 1/60th of a second and mid-interval time of 1/120th of a second.  The mid-speed was calculated by entering a formula into Excel the divides the displacement over 1/60th of a second.

This is an image of the distance vs time graph and the equation for velocity in respect to time is seen in the middle of the image;the experimental acceleration value can be obtained by the derivative of this equation's slope.  Note also that the slope of the parabola is the velocity of the free-falling object.

This graph is composed of the speed on the y-axis vs the time on the x-axis and its' slope is our experimental value for acceleration.  The equation's slope that is visible in this slope-intercept format style equation is the free-falling object's acceleration at any time.

In conclusion, I assumed that we would automatically get the experimental value for Earth's accepted value for acceleration of 9.81m/s/s but that was not the reality because our experimental acceleration value was 9.58m/s/s. Also, I assumed that the speed between time intervals would be constant, but as one can see from a previous data picture it changed throughout the fall of the object so it was inconsistent. On the other hand, the pattern of the speed may be inconsistent because of other forces that were active on the free-falling object during the fall.  For example, it may be possible that there was some kind of friction applied on the object as it fell that we didn't anticipate before we began the experiment.  Or, possibly there was some kind of electrical resistance force applied onto the object when the spark-generator produced a spark to mark the object's position.  Although, a more logical reason for the discrepancy of the experimental value is that the meter stick that was used is not precise enough to make accurate measurements, or my eye sight may have failed when we measured the displacement value so the following calculations carried the error throughout the entire calculations. The meter stick has a standard deviation equal to +- 1/100th of a meter so it's not the most accurate tool that we could have used for the measurement for the displacement.  For example, if we had access to make some kind of laser measurement device I think we could have more accurate results.  The absolute difference of our calculated result to the accepted value of Earth's acceleration was 9.58m/s/s - 9.81m/s/s=-0.23m/s/s; the relative difference was (9.58m/s/s-9.81m/s/s / 9.81m/s/s) x 100% = -2.3%. Consequently, the graphs did give us equations for velocity and acceleration for the object at any given time and the velocity equation can be derived to obtain the acceleration value; as for the acceleration equation, its given slope is the experimental acceleration value.  As for the standard deviation of the mean average of the class, it was recorded as +- 6.1186m/s/s as seen in two pictures below.  The standard deviation value means that the class's group's average experimental values for acceleration were about 6.1186 units far from the average value in either a positive of negative direction.

This image proves that the magnitude of the speed for mid-interval is the same for the average speed for any displacement value for constant acceleration.  Note that this time interval is in between 2.3 - 3.8 seconds and that the average speed value matches the value for mid-interval speed at any time.  That can be seen in this picture.

This image illustrates the classes standard deviation value of 6.11860732m/s/s that can be calculated by taking the square root of 37.43735556 which is the average deviation value squared.  Also note that the class's mean average for our experimental acceleration value was 961.5m/s/s.