Question

Using Excel

Question 2: An electromagnetic projectile launcher has been built. You are tasked with developing a model for the velocity of the projectile.

The launcher stores energy in a capacitor, which is charged to a voltage, Vi prior to launch. The capacitor discharges to 2,000 V, Vf during the launch. The velocity of the projectile is measured for several different voltages as shown in the table.

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

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

3. Determine the energy, Ewaste, which does not transfer from stored 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 the relationship     E = ½ CV2 where C is the capacitance (2 F) and V is the voltage. This is calculated from the various voltage values shown, and the units are Joules (J).      TKE = ½*mass*Velocity2   This velocity corresponds to the charge voltage actually used.

Finally, recall the Law of Conservation of Energy discussed in Lesson 2. Energy in any form remains constant (energy is neither created nor destroyed by changes form), so the total energy of this system must be unchanged. This means that independent of the form (electrical, kinetic, or wasted) the net change in energy must be zero!

                                    in simple terms:            Initial energy = Kinetic Energy + Final Energy + Wasted Energy

4. Show the fraction (percentage), Ewaste/Einitial for each launch.

5. Create a second scatter plot of the fraction loss vs Initial voltage. Include title, labels and other standard information to properly document the plot.

6. Using a trendline model, determine the polynomial which best describes the waste fraction as a function of initial voltage.

     (This is a perfect example of applying the curve fit "in a limited region"; is is not for all possible values 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

Answer 1

A(X) G BLY) Velocity (Y) Energy Ei D(Y) TKE E(Y) Ef FLY EW (Y) Ew/Ei 10000 9000 8000 7000 6000 12000 13000 14000 15000 762 598 456 334 232 1156 1386 1641 1919 1E8 8.709E6 8.1E7 5.364E6 6.4E7 3.119E6 4.9E7 1.6733E6 3.6E7807360 1.44E8 2.0045E7 1.69E8 2.881E7 1.96E8 4.0393E7 2.25E8 5.523E7 4E6 4E6 4E6 4E6 4E6 4E6 4E6 4E6 4E6 8.7291E7 7.1636E7 5.68817 4.332E7 3.119E7 1.1995E8 1.3619E8 1.516E8 1.6577E8 0.87291 0.8844 0.88877 0.88422 0.86646 0.83302 0.80586 0.77351 0.73676

I have calculate initial energy by formula v = 1 cy² here c= 2F hence U=V2 and total kinetice energy here M = 80 kg > [T = 1572 final energy of = I CVE² Where Wf is residual voltage VE is given 2000N hence Uf = 4 x 2X (200012 4X106 Joule and Energy wante Ew= U-Tuf

Ew/Ei Polynomial Fit of Sheet1 Ew/Ei 0.90 0.85 - y= Intercept + B 1x 1 + B2 x 2 + B3X3 + B4X4 3 0.80 - Equation Fractionlal LOSS Weight No Weighting Residual Sum of 5.13332E-7 Squares Adj. R-Square 0.99996 0.75 Intercept Value 0.29275 1.97903E-4 -2.30247E-8 1.1389 3E-12 -2.3334E-17 Standard Error 0.03096 1.29472E-5 1.98049E-9 1.27682E-13 3.02806E-18 EwEi B4 0.70 + 6000 8000 10000 16000 12000 14000 Initital voltage V