What is a 3 way switch? Why do they come in pairs? How does it work?

1. - Let z equal the square root of −i. (a) Find Rez and Imz (real and imaginary parts of z). (b) Find real and imaginary parts for the square root of z ∗ . Don’t forget that every number (real or complex) has two square roots.

2. - Use the Euler Formula derived in Lecture to evaluate the real and imaginary parts of the complex wave function ψ(x) = 2e ikx for these 5 values of x: x = λ/2, λ/3, λ/4, 3λ + λ/5, 13λ/6 . You’ll have to recall the standard relation between wave vector and wavelength and evaluate some trig functions.

A 60.1-kg crate rests on a level floor at a shipping dock. The coefficients of static and kinetic friction are 0.515 and 0.406, respectively. What horizontal pushing force is required to (a) just start the crate moving and (b) slide the crate across the dock at a constant speed?

A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.51° from the horizontal. A donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 535-N force for a distance of 159 m by means of a rope that is parallel to the ground and makes an angle of 13.1° with the track. The coefficient of friction for the cart\'s wheels on the track is 0.0127. Take g = 9.81 m/s2.

a)Find the work that the donkey performs on the cart during this process.

b)Find the work that the force of gravity performs on the cart during the process.

c)Calculate the work done on the cart during the process by friction.

. You read in the newspaper that rocks from Mars have been found on Earth. Your friend says that

the rocks were shot off Mars by the large volcanoes there. You are skeptical so you decide to

calculate the magnitude of the velocity that volcanoes eject rocks from geological evidence. You

know the gravitational acceleration of objects falling near the surface of Mars is only 40% that on

the Earth. You can look up the height of Martian volcanoes and determine the distance rocks from

a volcano hit the ground from pictures of the Martian surface. If you assume the rocks farthest

from a volcano were ejected at an angle of 45 degrees, what is the magnitude of the rock's

velocity as a function of its distance from the volcano and the height of the volcano for the rock

furthest from the volcano?

In the figure, a small block of mass m = 0.121 kg slides down a frictionless surface from an initial height of h = 0.850 m and then sticks to a uniform vertical rod of mass M = 0.879 kg and length L = 1.83 m. The rod pivots about point O through an angle θ before momentarily stopping. Find θ (in degrees).

Two isolated, concentric, conducting spherical shells have radii R1 = 0.470 m and R2 = 1.00 m, uniform charges q1 = +1.50 μC and q2 = +2.00 μC, and negligible thicknesses. What is the magnitude of the electric field E at radial distance (a) r = 4.70 m, (b) r = 0.610 m, and (c) r = 0.220 m? With V = 0 at infinity, what is V at (d) r = 4.70 m, (e) r = 1.00 m, (f) r = 0.610 m, (g) r = 0.470 m, (h) r = 0.220 m, and (i) r = 0?

(a) Sketch the bond model and (b) the energy band model illustrating a broken Si-Si bond for each model. Label Ec and Ev for the energy band model.

PLEASE SHOW ALL STEPS and equations used.

Two identical strings are fixed on both ends. The first string is vibrating in its fundamental mode and it is observed that the other string begins to vibrate at its third harmonic, driven by the first string. What is the ratio of the tension of the second string to that of the first string.

This was answered else where but I don't understand the answers. If possible please draw a picture.

Two in?nitely large sheets are shown in the ?gure. Sheet 1 contains a charge density +?. Sheet 2 contains ??. Between the two sheets is an in?nitely large 0.25 mm thick conducting plate that contains zero net charge. (a) What is the charge density induced on each side of the conducting plate. Explain. (b) What is the value of the electric ?eld at points A and B. Explain. (c) Calculate the voltage between the two sheets. Explain.

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 2 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity.

Find the equation of motion x(t) if the mass is driven by an external force equal to f(t) = 20 cos(3t). (Use g = 32 ft/s2 for the acceleration due to gravity.)

A 2.25

Which of the following methods of generating electricity is the only one that does NOT rely on Faraday's law of electromagnetic induction?

A. Wind turbines

B. Nuclear power plant

C. A conventional fossil fuel power plant, burning coal, oil, or natural gas

D. Solar photovoltaics (solar panels)

E. Hydro-electric power plant

Briefly describe what a wavefunction is. Use the term “boundary condition” in your answer. State 2 properties of wavefunctions. Give 2 examples of physical systems that would be described by wavefunctions.

During launches, rockets often discard unneeded parts. A certain rocket starts from rest on the launch pad and accelerates upward at a steady 3.05 m/s^2 . When it is 260 m above the launch pad, it discards a used fuel canister by simply disconnecting it. Once it is disconnected, the only force acting on the canister is gravity (air resistance can be ignored).

A.   How high is the rocket when the canister hits the launch pad, assuming that the rocket does not change its acceleration?

B. What total distance did the canister travel between its release and its crash onto the launch pad? This includes the distance the canister travels while going up plus the distance it travels while falling back to the ground.

**** Please show work. Thanks!