Using Excel

Question 2: An electromagnetic projectile launcher has beenbuilt. You are tasked with developing a model for the velocity ofthe projectile.

The launcher stores energy in a capacitor, which is charged to avoltage, Vi prior to launch. The capacitordischarges to 2,000 V, Vf during the launch. Thevelocity of the projectile is measured for several differentvoltages as shown in the table.

1. Create an Excel scatter chart with trendline for data set,selecting the best mathematical model type. Show the trendlineequation and goodness of fit R2 on the chart. Include title,labels, and other standard information to properly document theplot.

1. TKE, if the projectile is 30 kg for each launch and thecapacitor is 2 F (farad).   Note: Energy remaining storedin the capacitor is not wasted, and can be used in the next launch;this is the residual or final energy stored in the capacitor. Itmay be helpful to record this for each event. From the problemstatement, the residual voltage is 2000 V

1. Determine the energy, Ewaste, which does not transfer fromstored energy in the capacitor to kinetic energy

(Ewaste represents energy converted to heat, sound, light,etc.)

Hint: Energy stored in a capacitor is given by therelationship     E = ½ CV2 where C is thecapacitance (2 F) and V is the voltage. This is calculated from thevarious voltage values shown, and the units are Joules(J).      TKE =½*mass*Velocity2   This velocity corresponds to thecharge voltage actually used.

Finally, recall the Law of Conservation of Energy discussed inLesson 2. Energy in any form remains constant (energy is neithercreated nor destroyed by changes form), so the total energy of thissystem must be unchanged. This means that independent of the form(electrical, kinetic, or wasted) the net change in energy must bezero!

                                   in simpleterms:           Initial energy = Kinetic Energy + Final Energy + Wasted Energy

1. Show the fraction (percentage), Ewaste/Einitial for eachlaunch.

1. Create a second scatter plot of the fraction loss vs Initialvoltage. Include title, labels and other standard information toproperly document the plot.

1. Using a trendline model, determine the polynomial which bestdescribes the waste fraction as a function of initial voltage.

     (This is a perfect example of applyingthe curve fit \"in a limited region\"; is is not for all possiblevalues of voltage)

Vi [V]	Velocity [m/s]	Energy, Initial (J)	TKE (J)	Energy, Final (J)	Energy, Waste (J)	Ewaste/Einitial
10000	762
9000	598
8000	456
7000	334
6000	232
12000	1156
13000	1386
14000	1641
15000	1919