blog 2

THE INTRO

In Physics, gravity often comes into play in our equations. The accepted rate of acceleration due to gravity is 9.8 m/(s^2). The purpose of this lab was to verify this by measuring it in the real world. And to a lesser, more practical extent, to learn how to use Microsoft Excel.

THE PROCEDURE

In order to measure the acceleration of an object due to gravity, we can measure to position of a falling object at set intervals of time. This is achieved by using a stand with an electromagnet at the top suspending a weight 1.86 m off of a catching device (figure 1). Attached to the weight is a length of spark sensitive paper which will be marked by a sparking device every 1/60th of a second. In the lab handout, the procedure for carrying out the data collection portion of this experiment is described as follows (figure 2)

                                     fig 2
                                                                                                  
                                                                                                            fig 1






In our lab, however, this portion of the experiment had already been done by other physics students, leaving only the task of inputting the data into excel and interpreting it. Using a meter stick, we measured the distance between each mark on the paper and the origin point and plotted it against the time. Next, using excel we measured the distance between each position and then divided each resulting value by 1/60th of a second to figure out the mid interval speed of each position. This mid interval speed was then plotted against time. The resulting chart and graph is seen in figure 3.

fig 3

As this graph shows the relationship of velocity and time, or v(t), the slope of this line is how quickly the velocity is changing over time, or acceleration. As the linear fit R squared is .998, we can be reasonably sure that v(t) is linear and so acceleration is constant. Meaning that we have achieved a result of acceleration due to gravity=9.38m/(s^2). 

We were not, however, the only group to perform this experement. Rather we were one of 8. After all the groups had collected and analyzed their data, we recorded all of the values for acceleration they had determined from this experiment and input them into a new excel file. We then set about figuring out the standard deviation and average value for acceleration from all 10 experiments using this equation for SD and average, respectively:

The actual calculations were done through excel giving us this chart:

As stated above, the average was 9.48 m/(s^2) and the standard deviation was 0.0871 m/(s^2). Meaning that assuming that the distribution is normal 68.4% of all results from this experement should fall within + or - 0.0871 m/(s^2) of 9.48 m/(s^2), and 95% should fall within + or - 0.1742 m/(s^2) of 9.48 m/(s^2). The curve would look like this if plotted:

CONCLUSIONS

That would mean that the actual value of 9.8 m/(s^2) of the acceleration due to gravity would be considered an outlier, falling 3.67 standard deviations from the average. This suggests that there is a systematic error in our experiment, most likely friction due to the wires that the weight slides between as it falls, slowing its decent and giving a falsely low reading for acceleration.