Working with Spreadsheets

Introduction
The purpose of this lab was to get familiar with Microsoft Excel spreadsheets. Speadsheets are an effective way to handle massive amounts of data efficiently, so it is good to know how to manipulate data in order to acheive the results needed.


Calculations
The calculations in this lab were done in Excel. Excel has commands that facilitate the calculations. Instead of doing every calculation by hand or by calculator the calculations are done in Excel. Excel has a language similar to conventional math. + adds, - subtracts, * multiplys, / divides. there are other commands that employ more complex tasks such as taking the average of a data sample. Values can be assigned to cells and then those cells can be used just like any other numbers. For this lab we used the formula f(x)=Asin(Bx+C).

A= 5
B= 3
C= (pi/3)

f(x)=Asin(Bx+C)
f(x)=5sin(3x+(pi/3)).

Here (x) was a list of values ranging from 0.1 to 10 radians (100 total)

This was just to get familiar with the program.

We used Excel to analyze data from graphical analysis of the position of a freely falling object. So our constants had to include the acceleration of gravity, the initial velocity, initial position, and time increment.

g= 9.8(m/s^2)
Vo= 50(m/s)
Xo=1000(m)
t= 0.2(s)

X=Xo+Vo(t)+(1/2)g(t^2)
X=1000(m)+ 50(m/s)(t)+ (1/2)(9.8m/s^2)(t)
X=1000(m)+ 50(m/s)(0.2 s)+ (1/2)(9.8m/s^2)(0.2^2 s)
X=1009.804 (m)

Data

Data for f(x)=Asin(Bx+C)

Data for X=Xo+Vo(t)+(1/2)g(t^2)

Position of free falling object graph. Here the A = gravity,  B = initial velocity,  C = initial position.

A = acceleration of gravity (-4.9*2)= -9.8 (m/s^2)

 B = initial velocity 50 (m/s)

C = initial position 1000 (m)

Formulas for X=Xo+Vo(t)+(1/2)g(t^2)

Conclusions
Excel is an excellent way to analyze massive amounts of data. We would have spent hours calculating all 100 equations but with Excel we did it in a fraction of the time. First we got familar with the concept of assigning values to cells and formulas in Excel with the equation f(x)=Asin(Bx+C) and assigned values for the constants in specific cells, the values of x were 0-10 with increments of 0.1. Then we took a data sample from Graphical Analysis of the Position of a falling object. For this data sample we used X=Xo+Vo(t)+(1/2)g(t^2) to find the position. The constants were g= 9.8(m/s^2), Vo= 50(m/s), Xo=1000(m), and t= 0.2(s). The time was taken in increments of 0.2 seconds from 0-20 seconds. The reults were then put into Graphical analysis to make a plot. The resuts were consistent with the trajectory of an object in free fall.

Acceleration of Gravity Edwin Gonzalez

Introduction

The purpose of this lab was to determine the acceleration of gravity for a freely falling object and to gain experience using the computer as a data collector. We used the computer to collect

some position (x) vs time (t) data for a ball tossed into the air. Since the

velocity of an object is equal to the slope of the position vs time curve, the computer can also construct the graph of velocity vs time by calculating the slope of position vs time at each point in time. We will use both the position vs. time graph and the velocity vs. time graph to find the free fall acceleration of the ball.

Data



Trial 1

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Trial 2

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Trial 3

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Trial 4

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Trial 5

 

Calculations

Position (m) vs Time (s)

Trial 1

x=At^2+Bt+C

x=(-4.863^2)+(7.7)t-(1.3)

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(2A-0.5*9.8)/ 0.5*9.8] x 100%

percent error = [((2*4.863)-9.8)/ 9.8)] x 100%

percent error = -2.04%

Trial 2

x=At^2+Bt+C

x=(-4.718^2)+(8.7)t-(2.2)

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(2A-9.8)/9.8] x 100%

percent error = [((2*4.718)-9.8)/ 9.8)] x 100%

percent error = -3.71%

Trial 3

x=At^2+Bt+C

x=(-4.703^2)+(7.7)t-(1.6)

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(2A-9.8)/9.8] x 100%

percent error = [((2*4.703)-9.8)/ 9.8)] x 100%

percent error = -4.02%

Trial 4

x=At^2+Bt+C

x=(-4.804^2)+(7.9)t-(1.8)

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(2A-9.8)/9.8] x 100%

percent error = [((2*4.804)-9.8)/ 9.8)] x 100%

percent error = -1.95%

Trial 5

x=At^2+Bt+C

x=(-4.708^2)+(7.821)t-(1.496)

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(2A-9.8)/9.8] x 100%

percent error = [((2*4.708)-9.8)/ 9.8)] x 100%

percent error = -3.91%

Velocity (m/s^2) vs Time (s)

Trial 1

y=mt+b

t = time

m = slope

b = y-intercept

y=9.885t+7.87

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(m-9.8)/9.8] x 100%

percent error = [(9.885-9.8)/ 9.8)] x 100%

percent error = 0.86%

Trial 2

y=mt+b

t = time

m = slope

b = y-intercept

y=9.892t+8.835

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(m-9.8)/9.8] x 100%

percent error = [(9.892-9.8)/ 9.8)] x 100%

percent error = 0.94%

Trial 3

y=mt+b

t = time

m = slope

b = y-intercept

y=9.306t+7.609

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(m-9.8)/9.8] x 100%

percent error = [(9.306-9.8)/ 9.8)] x 100%

percent error = -5.04%

Trial 4

y=mt+b

t = time

m = slope

b = y-intercept

y=9.886t+8.219

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(m-9.8)/9.8] x 100%

percent error = [(9.886-9.8)/ 9.8)] x 100%

percent error = 0.877%

Trial 5

y=mt+b

t = time

m = slope

b = y-intercept

y=9.449t+7.825

percent error = [(measured - actual)/(actual)] x 100%

percent error = [(m-9.8)/9.8] x 100%

percent error = [(9.449-9.8)/ 9.8)] x 100%

percent error = -3.58%

Results from Falling Body Experiment Trial gexp (2a)(m/s^2) % diff gexp (m)(m/s^2) % diff2 1 9.726 -2.04 -9.885 0.86 2 9.436 3.71 -9.892 0.93 3 9.406 -4.02 -9.306 -5.04 4 9.608 -1.95 -9.886 0.87 5 9.416 -3.91 -9.449 -3.58

Results from Falling Body Experiment
Trial	gexp (2a)(m/s^2)	% diff	gexp (m)(m/s^2)	% diff2
1	9.726	-2.04	-9.885	0.86
2	9.436	3.71	-9.892	0.93
3	9.406	-4.02	-9.306	-5.04
4	9.608	-1.95	-9.886	0.87
5	9.416	-3.91	-9.449	-3.58

Conclusions

In this lab we used logger pro software and logger pro interface to record the accelaration of gravity on a rubber ball. We simulated the ball falling on top of the motion detector with a wire basket on top of the motion detector (for protection) From this lab we concluded that the acceleration of gravity is 9.8(m/s^2) by taking  of the acceleration from the position vs time parabola graphs multiplied by 2, from the equation  by taking the average slopes of the velocity vs time graphs of y=mx+b where m = slope. The slope is the acceleration of gravity.

Graphical Analysis Edwin Gonzalez

Graphical Analysis

The purpose of this lab was to gain experience in drawing graphs and using graphing software. We used Windows based computer with Graphical Analysis software, Lab Pro interface, Logger Pro interface, Logger Pro software, a motion detector, a rubber ball, and a wire basket.

PART I

To get familiar with the graphical analysis software we made a graph with and equation of our choice. We chose [(X2)^5 *sin(3X2)] 

Part of getting familiar with the software was making graphs correctly. To make an effective graph/plot a title , x-axis lables, y-axis lables, and correct units are required. In the graph above our title is "Practice Graph", our y-axis is labled "y axis", our x-axis is labeled "x3". As we later noticed we did not label the correct units, thus making our graph totally ineffective.

PART II

We used to the ball to simulate a falling object. The motion detector was placed on the ground with the wire basket on top of it. The motion detector was connected to a Logger pro interface. Pro interface was connected to the computer where it was analyzed by the Logger Pro software. From there the information was transferred to the graphical analysis software, where the graph was made.

We recorded a trial and we obtained this following graph, which comprised of our data:

We applied a curve fit (quadratic fit) At^2+Bt+C and we came up with the equation: -7.175t^2+10.56t+ (-2.067) where t = time.

]

Dimensional Analysis

L=Lt^2 (t^2)

Unit Analysis

Meters = m/s^2 (s^2)

Conclusion

Our graph required 3 things. Those 3 things were A title, x-axis labels, y-axis labels, and units. On out first Practice Graph we failed to label units. On our Second graph, where we collected data from a free falling object, we failed to supply a title. As for the actual data, our results were off. The A in our equation was supposed to be roughly half of 9.8 form the acceleration due to gravity of 9.8 m/s^2. We had -7.175. we do not know why this happened. It is possible that we selected the wrong part of the data collection, not the ball falling or perhaps the ball was not in free fall and had another force on it that made it accelerate faster. Another source of error may have come from the equipment because it was our first time using motion detectors. In conclusion, we did get experience in using the graphical analysis software and logger pro equipment. We made mistakes and learned from them.