2) We can model the earth as a solid spherical conductor of radius RE surrounded by a concentric spherical conducting shell with inner radius Ri , and outer radius Ro, which is the ionosphere. The earth has charge +Q, while the ionosphere has zero net charge. Write all answers in terms of Q, RE, Ri , Ro, and 0.

For parts (a) through (c), what is the surface charge density on

(a) the outer surface of the inner sphere of radius RE?

(b) the inner surface on the spherical shell at radius Ri?

(c) the outer surface of the spherical shell at radius Ro?

For parts (d) through (g), determine the electric field E(r) everywhere in space:

(d) r < RE

(e) RE < r < Ri

(f) Ri < r < Ro

(g) r > Ro

(h) Calculate the energy of the system.

(i) Determine the potential at the center given that the potential is zero at r = ∞.

(j) Find the capacitance of the earth-ionosphere system assuming that the ionosphere has net charge −Q instead of zero.

Application 1: Complete the following brief calculations regarding intensity and intensity level:

a) If the intensity level of source A is 30dB larger than the intensity level of source B, the intensity of A is how many time large than the intensity of B?

b ) If there are two sound sources, L1 = 85 dB and L2 = 80 dB, what is the total sound intensity level? Write answer to the nearest tenth.

c) If there are two identical sound sources, L1 = L2 = 85 dB, what is the total sound intensity level? Write exact answer.

d) If there are two sound sources, L1 = 80.0 dB and L2 = 50.0 dB, what is the total sound intensity level? Write answer to the nearest tenth.

Show that the law of conservation of linear momentum is valid in ALL inertial frame.

Physics problem

Assume that you did the experiment described below, and obtained the given results.

P1- You had a spring with a rest length of 27.5 cm. You let the spring hang from a stand, so that one of its ends was attached to the stand, while the other end was free. You then let loads of different masses hang from the free end of the spring. The loads’ masses were 500 g, 1000 g, 1500 g, 2000 g, and 2500 g. These loads, when hanging, caused the spring’s length to change (from 27.5 cm) to 32.5 cm, 42.2 cm, 51.5 cm, 61 cm, and 70.5 cm respectively. Finally, you converted each mass to kilograms, then multiplied by 9.8 to find the corresponding weight in Newtons.

1. Process the data from P1 as follows.

a. Complete the multiplication of each mass (in kilograms) by 9.8, to obtain the corresponding weight in newtons.

b. For each load, find the spring’s elongation, by subtracting the rest length from the new length, due to the spring’s stretching. That is, 32.5 cm - 27.5 cm for the 500-g load, 42.2 cm - 27.5 cm for the 1000-g load, and so on. Then convert each elongation from centimeters (cm) to meters (m).

c. Plot the load’s weight (in newtons) versus the spring’s elongation (in meters). The elongations should be on the x-axis, and the weights on the y-axis. You have 5 points to plot.

d. Draw the line of best fit, and determine its slope. This slope, which is expressed in newtons per meter (N/m), is called the Spring Constant, and is denoted by the letter K. The determination of the Spring Constant is the whole point of this lab.

Match the following energy graphs for a jumping object with their proper labels:

I.

II.

III.

Kinetic Energy vs. Time ( I, II, or III)   

Gravitational Potential Energy vs. Time   (I, II, or III)

Total Energy vs. Time (I, II, or III)

Do all metal show the expected Hall effect? If not what is the reason?

Consider a de-excitation of Hydrogen from an excited state n = 3 to the ground state n = 1. The transition to a lower energy state will cause the atom to emit a photon. Due to momentum conservation, the atom will have a small recoil velocity. Determine an expression of the recoil velocity of the hydrogen atom, and compute its numerical value. Do not leave ΔE or the photon frequency f in your answer! Note that the atom is non-relativistic.

While the human eye responds to light with wavelengths up to about 750 nm, it is hard to distinguish the color of different wavelengths between 650 and 700 nm. Why?

Software Learning Curve

Corporate executives for a national company are considering implementing new software that will make their business run more efficiently, thereby saving the company a substantial amount of money in the long run. Two competing systems are being reviewed. Software A is the latest version of the software the company currently uses and many of the functions operate similarly to the current version. The software company claims the latest version will increase productivity by 20%. Software B is a completely different system, so it will take longer to learn, but its manufacturers claim it performs at 150% of its leading competitor (the software currently in use by this company).

Before committing to either product, the executives tested the competing software for four weeks in two of their offices. The first office installed software A, which proved easy for the employees to learn as expected. After one week, productivity was already 107.59% compared to previous levels; after two weeks it had jumped to 117.80%. A learning curve model A\left(t\right)=M-Ce^{-kt}A(t)=M−Ce−ktcan be used to represent the productivity at this office t weeks after the new software is installed, where M is the maximum level of productivity with the software. Use the given data to construct the specific learning curve for software A. Based on this model, how productive were the employees of this office when using this new software without any training (i.e., when the new software was first installed)?

The second office installed software B, which required lengthy training for most of the employees. Prior to training the employees could not use this software at all, so the initial productivity was zero in this trial. After four weeks of training and practice using the new software, many of the employees were still struggling and productivity was only 57.18%, of the previous output for this office. Use the given data, including the manufacturer’s performance claim, to construct a learning curve function B\left(t\right)B(t) for software B. How many weeks will it take for this office to reach its previous level of productivity?

Construct a table of values for both A\left(t\right)A(t) and B\left(t\right)B(t) for the first 12 weeks. Solve algebraically to obtain a precise estimate of the number of weeks after installing new software until productivity at the two offices would be equal.

Question#3

Use the given data to construct the specific learning curve function A\left(t\right)=M-Ce^{-kt}A(t)=M−Ce −kt for software A. Identify the values for each parameter below, giving M and C as integers and rounding k to the nearest hundredth.

M = Question Blank type your answer... ; C = Question Blank type your answer... ; k = Question Blank type your answer...

The resolution of microscopy limits by the diffraction barrier; however, super-resolution microscopy is capable of imaging below the diffraction limit. Explain the basic principle of any super-resolution using your own words how it is possible to resolve below the diffraction limit.

8) 3 kg mass moving with 10 m/s in the x-direction hits a 5 kg mass at rest. After the collision 3 kg is deflected by 30 degree while the 5 kg is deflected by 45 degrees. a) Draw a diagram for the initial and final motion including the directions of the velocities b) Find the final velocities of each mass c) Determine if the collision is elastic or not. d) Qualitatively, show the direction of the impulse (or the Force) on 3kg due to 5kg mass.  

A beam of homogenous x-rays with a wavelength of 0.0900Å is incident on a carbon scatterer. The scattered rays are observed at an angle of 54° with the direction of the incident beam. Find

1. The wavelength of the scattered rays,

2. The energies of the incident and scattered photons

3. The momenta of the incident and scattered photons

4. The energy, velocity, momentum, and angle of the recoil electron

Two positive charges of 2e-10 C are placed on the x axis at distances +40 cm and -40 cm from the origin, respectively. A third positive charge of 3e-11 C can be moved along the y axis. At what value of y the electrostatic force on the third charge is maximal?

Describe the techniques of total internal reflection fluorescence (TIRF) microscopy, and give an example of its application in life science. Most TIRF in vivo studies investigate membrane complexes; why is this? Can TIRF be applied to monitoring the nucleus of cells?