A steel ball is dropped from a diving platform (with an initial velocity of zero). Using the approximate value of g = 10 m/s2 (a) Through what distance does the ball fall in the first 0.3 seconds of its flight? (b) How far does it fall in the first 4.9 seconds of its flight?

If charges Q₁=25nC is located at (0,0) and charge Q₂=-15nC is located at (2m,0). (a) Find the resultant force on a third charge Q₀=20nC located at (2m,2m), and (b) find the electric field due to the three charges at the point (1m,1m).

A quasiparticle of mass m is trapped by an extended crystal defect, which has a shape of a narrow, straight tube of length l. The quasiparticle hence is confined to move within this defect. Consider that the tube of this defect is sealed at both ends with potential V = 0 inside the tube. Treat the defect as a 1D infinite square well. Assume that this tube defect is placed at an angle Θ relative to the surface of the earth. The quasiparticle experiences the usual gravitational potential V = mgh. Calculate the lowest order change in the energy of the ground state due to the gravitational potential.

A hollow aluminum cylinder 15.5 cm deep has an internal capacity of 2.000 L at 22.0°C. It is completely filled with turpentine at 22.0°C. The turpentine and the aluminum cylinder are then slowly warmed together to 80.0°C. (The average linear expansion coefficient for aluminum is 24 ✕ 10−6°C−1, and the average volume expansion coefficient for turpentine is 9.0 ✕ 10−4°C−1.)

a) How much turpentine overflows?

b) What is the volume of turpentine remaining in the cylinder at 80.0°C? (Give your answer to at least four significant figures.)

c) If the combination with this amount of turpentine is then cooled back to 22.0°C, how far below the cylinder's rim does the turpentine's surface recede?

Give the VHDl code for your an 8-to-3 priority encoder using two 4-to-2 priority encoders and any additional necessary gates. Use port maps and code the structural behavior using logic gates not if else statements.

Calculate the commutators of angular momentum
(a) [x,L_x],[y,L_x],[z,L_x]

(b) [p_x,L_x],[p_y,L_x],[p_z,L_x]

A quasiparticle of mass m is trapped by an extended crystal defect, which has a shape of a narrow, straight tube of length l. The quasiparticle hence is confined to move within this defect. Consider that the tube of this defect is sealed at both ends with potential V = 0 inside the tube. Treat the defect as a 1D infinite square well. Assume that this tube defect is placed at an angle Θ relative to the surface of the earth. The quasiparticle experiences the usual gravitational potential V = mgh. Calculate the lowest order change in the energy of the ground state due to the gravitational potential.

An electron (in a hydrogen atom) in the n=5 state drops to the n=2 state by undergoing two successive downward jumps. What are all possible combinations of the resulting photon wavelengths?

While out on your 3rd floor apartment balcony, you notice someone drop a 8.0 kg ball from rest from the roof of the 5 story building across the street. You know that the two identical buildings are 34 m apart, and have floors that are 5.0 m tall. The first floor is at ground level.

m = 8.0 kg

d = 34 m

h = 5.0

(a) determine the magnitude of the angular momentum of the ball, in kilogram meters squared per second, as observed by you immediately after it is dropped.

(b) determine the magnitude of the angular momentum of the ball, in kilogram meters squared per second, as observed by you as it passes the floor of the 4th floor balcony of the other building.

(c) determine the magnitude of the angular momentum of the ball, in kilogram meters squared per second, as observed by you as it passes the floor of the 3th floor balcony of the other building (directly across from you).

(d) determine the magnitude of the angular momentum of the ball, in kilogram meters squared per second, as observed by you as it passes the floor of the 2th floor balcony of the other building.

(e) determine the magnitude of the angular momentum of the ball, in kilogram meters squared per second, as observed by you immediately before it hits the ground, at the bottom of the first floor..

Consider the situation of two particles which have equal but opposite charges, +Q and -Q. The particles have identical mass. Discuss the following situations in terms of their motion and the work done on them by the relevant field. Where relevant, also provide a short discussion of the implications of these effects on the properties of the charged particles. If necessary, include diagrams to illuminate your solution.

(a) For the positive charge, the charge is stationary, and it is placed in a uniform electric field directed to the right (the +x-direction).

(b) For the positive charge, the charge is moving upwards (the +y-direction), and it is placed in a uniform electric field directed to the right (the +x-direction).

(c) For the negative charge, the charge is initially stationary and it is placed in a uniform magnetic field directed to the right (the +x-direction).

(d) For the positive charge, the charge is moving upwards (in the +y-direction) at constant velocity, and it is placed in a uniform magnetic field directed to the right (the +x-direction).

List out at least two uses for an RC circuit and explain how the RC would affect the use.

Use a computer to make two plots of the Boltzmann, Fermi-Dirac, and Bose-Einstein distributions functions versus x=(LaTeX: \epsilon-\mu ϵ − μ )/kT. For one make both axes linear. For the other make the y-axis logarithmic, and indicate the x- and y- ranges where the distribution functions agree to better than one percent.

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.3cm. A second, parallel wire carrying a 2.6 A current intersects the x-axis at x=+2.3cm.

1. The Cosmic Microwave Background and Prizewinning Cosmology

(a) How can we see the CMB if the photons were released 14 billion years ago? Shouldn't those photons be billions of light years away by now?

(b) Who was awarded the 2006 Nobel Prize for Physics? What was the prize for-- what were the results, and how were they obtained?

(c) Why are these results from part (b) important?

You are given a new puppy as a birthday present and are eager to play with her. However, you soon come to realize that your new puppy has other plans. She decides to ransack your room and go after anything she can grasp in her mouth. One of the items is a rigid ball that has 5 grams of liquid ethanol in it from an experiment you did in class. The hot breath of the puppy vaporizes 50% of the ethanol to create an air-ethanol mixture at 50°C. After a few minutes, she releases the ball and the air-ethanol mixture comes to a new equilibrium state at 30°C. Taking the total pressure inside of the ball to be 1 atm, estimate the percent of ethanol that condenses at the final state. [HINT: Think carefully about how much ethanol is in the vapor state before the actual process starts. This is your starting amount.]