Answer Happy

#6 only (the data set for number 6 is provided)
Purpose: Write mathematical best fit equations that describe a variety of different curves. Recognize trends that are common to physical experimental data . Use Excel and Capstone software to plot data alongside best fit curves to compare models with actual data. Description: This exercise will prepare you for handling data and thinking like a scientist or an engineer. You will look at plots of data and use it to create mathematical expressions. A mathematical expression is an algebraic expression of the relationship between two or more variables. The expression is just one part of a physical model that describes a physical system. The other components of a complete physical model include diagrams, written & verbal descriptions, and graphical representations. For now, we will just focus on creating the graph and the mathematical expression for a given set of raw data. The expression lets us quantitatively describe the relationship between the experimental variables. We can subsequently use the mathematical expression to predict the value of a dependent variable D, for any value of the independent variable (. Linear Dml+b First, you should learn to recognize some of the most common relationships, shown below: Here the Greek letters represent free parameters, these can take on any value that best fits the data. By convention, we plot the dependent variable on the vertical axis, and the independent variable on the horizontal axis. This menu of common mathematical relationships is of course just a small sample from all of the possible relations that might exist given a particular experiment. It is important to be able to interpret a graphical relationship and express it in a written statement and by means of an algebraic expression. I (units) Square Root D = √I D (units) J Quadratic D=al²2 I (units) Exponential Decay D = μe D (units) Page (prais) 1 Inverse D = ² — I (units) Inverse Square D=72 of 2 ZOOM
Data Set 1 V(m₂) 0.2 1.0 2.0 4.0 Directions: For each of the data sets shown below, plot the data using Capstone or Excel, fit an appropriate curve from the list shown above, and write the best fit equation, using an equation editor in the style described below. Assume that the first column is the independent variable (horizontal axis), and the second columns is the dependent variable (vertical axis). 8.0 100 16.0 20.0 Data Set 4 t(s) 0.3 1.2 P(pa) 40.0 8.0 4.0 2.0 1.0 08 0.5 0.4 v(m/s) 10.0 20.0 30.0 40.0 50.0 2.7 4.8 7.5 10.8 60.0 147 700 19.2 80.0 Data Set 2 1 .2 .5 1 2 3 4 5 Data Set 5 r(m) 5 1.0 2.0 5.0 10.0 200 x(m) 03 .12 .75 3 12 27 48 75 F(N) 425 0 68.3 16.5 4.26 0.6/ 0.18 0042 Page < Data Set 3 A(mos) 1 2 5 1 2 3 4 5 x-3 t² W(lbs) 03 .12 .75 3 12 27 48 75 Data set 6-Given in the Canvas assignment page. 2 Import the data to Capstone from the csv fle The first column for data set 6 is time(s) and the second is current (A) Plot current (vertical) vs time (horizontal} Copy/paste each graph into Word and write the appropriate mathematical expression for each plot. Use the equation editor to write the equation. Remember to label axes with units and include units in the mathematical expressions for each coefficient / slope. Don't use y & x when you're writing the function, use the symbols for the experimental variables that you're fitting For each set of data, provide a written qualitative relation between the two variables, and identify the type of relationship between the variables in choosing from the examples of each shown above. When we write the formula that best describes our date, we should do so in the following way (always using an equation editor, and not relying on the output from Capstone software to write the expression for us.) Notice how we've done this the symbol for the vertical axis variable (x) is on the left (no unils) and then the of 2 ZOOM
2 1.09E-09 1.1111 3 1.26E-09 1.1111 4 1.60E-09 1.11109 5 2.29E-09 1.11107 6 3.67E-09 1.11105 7 6.42E-09 1.11099 8 1.19E-08 1.11088 9 2.29E-08 1.11065 10 4.50E-08 1.1102 11 8.90E-08 1.10929 12 1.77E-07 1.10748 13 3.53E-07 1.10388 14 7.06E-07 1.0967 15 1.41E-06 1.08248 16 2.82E-06 1.05459 17 5.64E-06 1.00095 18 1.13E-05 0.90164 19 2.25E-05 0.73119 20 4.51E-05 0.4786 21 9.02E-05 0.19664 22 0.00015 0.06212 23 0.00022 0.01143 24 0.00031 0.00082 25 0.00041 3.17E-05 26 0.0005 3.64E-06 27 #6 data-1