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)

A device used in radiation therapy for cancer contains 0.33 g of cobalt-60 (59.933 819 u). The half-life of this isotope is 5.27 yr. Determine the activity (in Bq) of the radioactive material.

If a coal-fired power plant burns 2 kg of coal to produce electricity, and the electricity is used to power an elevator motor that is 60% efficient, how high can the elevator and passengers be lifted up if their total mess is 1500 kg?

and then How many human workers using muscle power('energy servants") would be needed to lift the elevator up to the same height, if they had one minute to do so?

Assuming that one energy servant is 100w of energy and the coal power plant is 33% efficient. ANd 29MJ/kg in coal

Consider the gas phase dissociation of iodine I₂(g)↔2I(g)

A. Calculate the thermal wavelength of ^127I at T=298K.

B. Calculate the translational partition function of ¹²⁷I at T=298K. Assume P=1.00atm and V=24.4L.

C. Calculate the rotational partition function of I_2 at T=298K. Assume θ_rot=0.0537K

D. Calculate the vibrational partition function of I₂ atT=298K if teh vibrational temperature of I_2 is θ_vib=308K

E. Using the result from Part B, calculate the partition function of I. Assume the ground electronic state degeneracy of I is g₁=4.

F. Calculate the partition function of I_2. Assume g_1=1 and D_e=150.3kJ/mol

G. Calculate the equilibrium constant for the dissociation of I_2 at T=298K. Assume N=6.02*10^23.

H. Calculate ΔG^o for the dissociation of I₂ at T=298K.

I How accurate is this statistical calculation? For I(g) ΔG^o_f=70.2kJ/mol. For I₂(g) ΔG^o_f=19.3kJ/mol. Calculate ΔG^o__reac for the dissociation of I_2(g).

It's cold--check your tires.

When it gets cold, you have to add more air to car tires. If a 1.90×10⁻² m3m3  car tire at 299 KK  has an *absolute* pressure of only 213 kPa

How many moles of air do you have to add to increase its *absolute* pressure to 271 kPa? The temperature and volume of the tire remain constant.

A light source emitting radiation at 7.00∙1014 Hz is just capable of ejecting photoelectrons from Eiteneerium (Ei).

A. What can be done with the light to produce no photoelectrons? Explain conceptually in one sentence.

B. What is the effect of increasing intensity of this light?

C. What is the work function of Eiteneerium?

D. If the frequency of light is now doubled, what is the speed of the emitted electrons?

A car travelling at constant speed passes by a stationary pedestrian as the car driver sounds the horn. As the car approaches the pedestrian she hears the horn sounding at 50 Hz. Once the car has driven past her, she hears the horn sounding at 10 Hz. Calculate the frequency in Hz of the sound waves emitted by the car horn.

An apple with mass 0.4 kg is hanging at rest from the lower end of a light vertical rope. A dart of mass 0.1 kg is shot vertically upward, strikes the bottom of the apple, and remains embedded in it.

a) If the speed of the dart is 5 m/s just before it strikes the apple, what is the speed of the apple just after the collision?

b) How much energy was dissipated during the strike?

c) How high does the apple move upward because of its collision with the dart?

A particle (mass = 6.7 x 10-27 kg, charge = 3.2 x 10-19 C) moves along the positive x axis with a speed of 4.1 x 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 5.0 m into the field. What is the magnitude of the electric field (in N/C) ?

A teacher places a fluid substance, with a refractive index of 1.65, between two horizontal panes of flat glass (each of which has n = 1.50). He then illuminates the assembly from above with monochromatic light (λ = 670 nm). What is the minimum thickness (in nm) that the liquid layer must have, if the light is to be strongly reflected back toward its source?

Show that if the acceleration is always perpendicular to the speed, the speed is constant.

Explain briefly how Faraday’s law is used to produce electricity in a coal-fired power station?

Ampère's law in free space may be written as ∮ ? . ?? = ???

a) Write the equation in words, giving the meaning of each parameter.

b) Starting with the equation above obtain an expression for the law in differential form.

c) A long wire P carries a current ?. Use the law to show that the magnetic field at a radial distance r from the wire is ? = ??? / 2?? [3] [4] [4] Page 4 of 4 A second long wire Q is placed parallel to wire P, with the two wires separated by a perpendicular distance ?. The second wire also carries a current ? but in the opposite direction to the current in wire P.

d) Draw a diagram to illustrate the wires and the directions of the currents.

e) Show on the diagram the directions of the forces that the wires experience. Explain clearly the reason for these directions.

f) Show that the force per unit length on the wires is ??? ^2 / 2??

g) Power lines separated by a distance of 2.0 m carry a current of 180 A. Determine the force per unit length experienced by each wire.

Answer the following questions for an orbit with the following Position and Velocity vectors:

(R = 7626I + 4972J + 806K km, V = 0.626I - 0.690J - 6.160K km/s)

1. Determine the size of the size (semimajor axis) of this orbit.

2. Determine the shape (eccentricity) of this orbit.

3. Determine the inclination of this orbit.

4. Determine the right ascension of the ascending node for this orbit.

5. Determine the argument of the perigee for this orbit.

6. Determine the true anomaly for this orbit.