Physics LAB Report

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PHYS 163 Lab #3 Graphing and Graphical Analysis Graphical Analysis Series Slope or Coefficient Steep Value Shallow Value  A 48.893 50.913 46.912 2.0005 B 0.3714 0.3999 0.3428 C 28.275 51.304 D 6.6034 9.6603 Intercept or Exponent -0.096 Type of Curve Shallow Value  -0.105 -0.087 -0.009 0.02855 -45.364 -63.022 -27.705 -17.6585 17.445 16.9295 -1.953 -2.41 -1.597 -0.4065 12.935 -1.63735 0.0443 0.0385 0.0341 0.0022 Graphical Analysis Results Series Steep Value Equation of Curve A Exponential y= 48.893*-0.096 B Power y= 0.3714*-45.364 C Linear y= 28.275*-1.953 D Exponential y= 6.6034*0.0443 PHYS 163 Lab #3 Graphing and Graphical Analysis Data Series A - Amplitude vs. Time t (s) A (cm)  0.00 0.01 50 1.00 0.01 45 2.00 0.01 40 3.00 0.01 36 4.00 0.01 33 5.00 0.01 30 6.00 0.01 27 7.00 0.01 25 8.00 0.01 23 9.00 0.01 21  3% 3% 3% 3% 3% 3% 3% 3% 3% 3% Data Series B - Velocity vs. Position x (cm) v (m/s)   234 8 38 8 329 8 80 8 424 8 112 8 592 8 177 8 712 8 216 8 811 8 259 8 944 8 303 8 Steep/Shallow data Asteep Ashallow 51.5 48.5 46.35 43.65 41.2 38.8 37.08 34.92 33.99 32.01 29.1 30.9 26.19 27.81 24.25 25.75 22.31 23.69 20.37 21.63 Data Series C - Force vs. Distance r (cm) F (N)  2.5 0.1 4.7 3.2 0.1 3.1 3.7 0.1 2.1 5.0 0.1 1.2 5.2 0.1 1.1 6.1 0.1 0.8 6.5 0.1 0.7 7.4 0.1 0.6 Steep/Shallow data vsteep vshallow 30 46 72 88 104 120 169 185 224 208 267 251 311 295 Data Series D - Acceleration vs. Time t (ms)  a (m/s2) 12 1 15 21 1 22 29 1 30 43 1 49 56 1 86 69 1 141 87 1 269 Data A 60 50 350 y = 0.3999x 300 y = 0.3428x 250 y = 0.3714x 40 200 30 150 y = 46.912e-0.087x 20 100 y = 48.893e-0.096x 10 50 y = 50.913e-0.105x 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 0 0 100 0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0 10.00 0 100 350 Data C 6 300 5 y = 9.6603e 250 4 y = 28.275x-1.953 3 200 y= 2 150 y = 17.445x-1.597 1 y = 12.935e 51.304x-2.41 0 100 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 50 0 0 10 e vs. Distance  0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 Steep/Shallow data Fsteep Fshallow 4.9 4.5 3.3 2.9 2.3 1.9 1.4 1 0.9 1.3 0.64 1.04 0.53 0.93 0.38 0.78 Steep/Shallow data asteep ashallow 10 20 17 27 25 35 44 54 91 81 146 136 274 264 eleration vs. Time  5 5 5 5 5 5 5 Data B y = 0.3999x - 63.022 y = 0.3428x - 27.705 y = 0.3714x - 45.364 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 Data D y = 6.6034e0.0443x y = 9.6603e0.0385x y = 12.935e0.0341x 10 20 30 40 50 60 70 80 90 100 21 #3 Graphing and Graphical Analysis Objectives The major objectives of this experiment are: 1. To understand graphs and graphical relationships. 2. To understand the use of error bars on graphs. 3. To recognize linear relationships, power relationships, and exponential relationships from the shape of the respective curves and to plot and de- termine the equations of such curves. Introduction and Theory Many experiments are of the type where one wishes to discover the re- lationship between a pair of quantities that depend on each other, either to verify a theoretical prediction or to help guide the development of a theory where none exists. Examples of related pairs of quantities are: the velocity vs. time of a mass falling in a gravitational field, the period of oscillation vs. mass for a mass-spring system undergoing simple harmonic motion, and the specific heat of a substance vs. its temperature. I. Functional Relationships There are many kinds of possible relationships y = f(x), but we will be concerned here with only three types: A. Linear Relationships. A relationship is linear when the independent variable, x, is related to the dependent variable, y, in the form | y = ax + b, (3.1) where a and b are constants. Example: A mass in free fall: v = vo - gt m/s. In this equation t is the independent variable, v the dependent variable, and vo and g are constants. 22 B. Power Relationships. Here the independent variable is related to the dependent variable as y = bxa (3.2) Example: The period of a simple pendulum is T = 24 V Lg, , or 2π T = VI seconds. g 2π In this equation L is the independent variable, T the dependent variable, and vo is a constant. Depending on the value of a, the graph of a power function will assume one of the three shapes shown in Fig. 3.1. a>1 1>a>0 a
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PHYS 163
Laboratory 3: Graphing and Graphical Analysis
Objectives
The purpose of this experiment was to understand graphs and graphical relationships as well
as the use of error bars on graphs. Also, to recognize linear relationships, power relationships,
and exponential relationships from the shape of the respective curves and to plot and
determine the equations of such curves.
Introduction and Theory
A majority of experiments are designed in a manner that one wishes to discover the
relationship between a pair of quantities that depend on each other, either to verify a
theoretical prediction or to help guide the development of a theory where none exists.
The following experiment involves plotting and analyzing the graphs of relation between
pairs of values. If two values are related to each other, the graph of the measurements from
several pairs of such values can be used to determine the type of relationship between these
values. Using such graph, I can clearly deduce one of the values if given the ot...


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