ITS FREE fall...

Purpose: The purpose of the lab is to find the constant of gravity by finding the change in distance in fixed time intervals of an object that is in free fall.

Equipment:

The apparatus in the picture is very simple. There is a weight that is on a wire that will drop from the top and go all the way to the bottom. There is a shocker that will send an electrical impulse to the falling weight every 60th of a second or .016666... seconds. A piece of paper will be between the falling weight and the source of the electrical impulse and a dot will be created at every point where the falling weight  was for each electrical impulse. In other words, the dots on the piece of paper measure the distance traveled by the weight for every 60th of a second.

Measuring the dots on the paper

Interpreting the data:

Data entered into Excel

The first column (position) in the Excel sheet is the distance (in centimeters) the first dot, which is assumed to be taken at the first electrical impulse or the first 60th of a second of the free fall of the object, is from the beginning of the piece of paper. The actual distance that was traveled isn't relevant but what is important is the change in position or delta x for each time interval. Having the change in position and the change in time gives the average velocity for that small interval. It is easy to see that there is a change in velocity when the values are placed one after another. A change in velocity in a fixed period of time gives us acceleration, however instead of creating a new column in the Excel program and writing a new equation to find the constant acceleration, making a graph of the velocity versus the mid time was easier and gives an average acceleration over the entire experiment. The mid time was used because it wouldn't make sense to say that there was a velocity at 0 seconds or when the object was at rest.

The equation displayed in the upper right hand corner of the is the y=mx+b version of the V(t)=gt+initailV. The only variable that is important of this particular graph is the constant g, which would be m in the equation displayed. The constant g determined is 974.8cm/s/s which is fairly close to the true value.





Conclusion:
There was only a single constant that was being determined and it was the experimental calue of g, 9.748m/s/s. When compared to the true value the percent error was -.53%, which means that there was minimal error. The most likely source of error for this was the fact that the falling weight was on a string, which could create possible tension that would prevent the weight from truly being in free fall.

Sincerely.

Swaggy C

Mass and Oscillation Period

Purpose:
The purpose of this lab was to develop an equation that showed the relationship between the mass of an object and the oscillation period of the object on an inertial balance clamped to the table.

Equipment used:

The picture is of the clamp and inertial balance set up, and the device that is at the end of the balance is the photogate instrument. With the setup, the oscillation period of the balance was timed by the photogate which uses a light sensor.

Logic behind the Numbers:

First an understanding of what data was actually collected is needed. The oscillation period of various weights on the tray of the balance were measured. The experiment started by measuring the oscillation of only the tray at the end of the balance then adding a 100 gram weight to the balance and measuring the oscillation of the balance again. This was repeated until 800 grams total were on the balance. 

The periods collected for each weight

There wouldn't be a reliable relationship if only the weight added was compared to the oscillation period, so the equation T = A(mass of object + mass of Tray)^n, where T is the period, A is a constant, and n is the order of the equation, had to be manipulated. The end result will be a graph of the natural log(T) versus the natural log(mass of the object and the mass of Tray).

Graph of  the natural log of the data collected

Expansion of text in box

The table of the value used for the graph

A parameter, which was an estimation at first, was used for the mass of the tray. When the parameter was changed, either increasing or decreasing the mass of the tray, the correlation of the best fit line change as well. The parameter was changed until the correlation was as close to 1 as it could be, .9991 was the closest that could be achieved for the set of data that was collected. Once the parameter, the mass of the tray, was adjusted, then the manipulated equation yielded the value for n and the value of the natural log(A), which are both constants. The mass of the tray = .251 kilograms, the natural log(A) = -.4159, and n = .5996. The new equation could now be used to find the mass of an object placed on the tray if the oscillation period is known.

Manipulated equation, isolating mass of object

Finding Unknown Masses:
Using the equipment and equation from above, the masses of two phones were found by measuring the oscillation periods when each phone is individually placed on the inertial balance. The first phone had an oscillation period of .3613 seconds and the mass calculated from the equation was .115 kilograms but when the phone was weighed the true mass was .118 kilograms. The second phone had an oscillation period of .3857 seconds and the mass calculated from the equation was .158 kilograms but when the phone was weighed the true mass was .164 kilograms.



Conclusion:
The percent error for the first phone was -2.54% and for the second phone the percent error was -3.66%. Both percent errors are fairly high considering the simplicity of the lab and the expected accuracy. The most probable cause of the error was the fact that multiple trials weren't performed for timing the oscillation period of each 100 gram weight increment. Since the data that would be used to create the equation was not very precise and accurate it created the high amount of error.

Sincerely,

Swaggy C