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Energy

Probability of a single-particle state being occupied.

For a system of fermions at room temperature, compute the probability of a single-particle state being occupied if its energy is (a) 1 eV less than mu. (b) 0.01 eV less than mu. (c) equal to mu. (d) 0.01 eV greater than mu. (e) 1 eV greater than mu.

Partition Function

Consider a hypothetical atom that has just two states: a ground state with energy zero and an excited state with energy 2 eV. Draw a graph of the partition function for this system as a function of temperature, and evaluate the partition function numerically at T = 300 K, 3000 K, 30,000 K, and 300,000 K.

Photoelectron Multiple Choice Problem

In an experiment different wavelengths of light, all able to eject photoelectrons, shine on a freshly prepared (oxide-free) zinc surface. Which statement is true? a. The number of photoelectrons emitted per second is independent of the intensity of the light for all the different wavelengths. b. The number of photoelectrons em

Calculating Potential, Kinetic, and Total Energies

You are at the top of a 500 meter tower and drop a 5-kg hammer. Calculate the potential and kinetic energies and total energy at the end of each second of free fall and at the moment of impact. Elasped D=5t2 V= a t PE = mgh KE =1/2 mv2 KE + PE mv Time m m/s

One dimensional infinite square well potential.

a) Show that the classical probability distribution function for a particle in a one dimensional infinite square well potential of length L is given by P(x) = 1/L b) Use the result from part (a) to find the expectation value for X and the expectation value for X^2 for a classical particle in such a well.

Pendulum and Spring Questions

____ 1. A simple pendulum, 2.0 m in length, is released with a push when the support string is at an angle of 25 deegree from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, what is its speed at the bottom of the swing? (g = 9.8 m/s2) a. 2.3 m/s b. 2.6 m/s c. 2.0 m/s d. 1.8 m/

energies at the end of each second of free fall

You are at the top of a 500 meter tower and drop a 5kg hammer. Calculate the potential and kinetic energies and total energy at the end of each second of free fall and at the moment of impact. t D=5t2 V=at PE=mgh KE=1/2mv2 Elapse Distance Do

The motion of spring when the length of string shortened

Consider a simple plane pendulum consisting of a mass m connected to a string of length L. After the pendulum is set in motion , the length of the string is shortened at a constant rate: dL/dt = -k The suspension point remains fixed. Compute the following: a) The Lagrangian and Hamiltonian functions b) Compare

Gravitational potential energy

Relative to the ground, what is the gravitational potential energy of a 55.0 kg person who is at the top of the Sears Tower, a height of 443 m above the ground?

Solar Intensity on a space flight

A possible means of space flight is to place a perfectly reflecting aluminized sheet into Earth's orbit and use the light from the Sun to push this solar sail. Suppose a sail of area 6.00 X 10^4 m^2 and mass 6000 kg is placed in orbit facing the sun. The solar intensity of 1380 W/m^2. a. What force is exerted on the sail?

Millikan experiment, Compton effect, photoelectric effect

1. In a Millikan oil drop experiment the terminal velocity of the droplet is observed to be vt = 1.5 mm/s. The density of the oil is = 830 kg/m3 and the viscosity of air is = 1.82 10-5 kg/m s. Use the following equations to find the values below. Calculate the droplet radius. µm (b) Calculate the mass of the drop

Conservative Forces and Potential Energy

How does on check a force to see if the force is conservative (using the curl)? Given a force how does one calculate the potential energy? Are the following forces conservative a) F(subx) = axz+bx+c, F(suby) = axz + bz, F(subz) = axy + by b) F(a vector) = e(sub r) a/r where a, b, c are constants and e(sub r) is

energy band structure of the material

1. A material is tested at 1 atmosphere and found to be an insulator. It is then very strongly compressed and found to have very much increased conductivity. Speculate on what changes may be happening to the energy band structure of the material.

Classical mechanics: Motion in two dimension.

1. A river flows due east at 1.00 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.0 m/s due north relative to the water. (a) What is the velocity of the boat relative to shore? (b) If the river is 280 m wide, how far downstream has the boat moved by the time it rea

Elastic Collision of Air-Track Glider

An air-track glider with an initial speed of 4.0 m/s has a head-on collision with another glider at rest that is three times as massive. What are the final speed and directions of the gliders if the collision is elastic? I believe the answer is V1 = -2.0 m/s and V2 = +2.0 m/s. I need to see each step and formula to solve this qu

Determining the elasticity of a collision

A steel ball is dropped from a height of 2.37 meters onto a flat stone slab. On rebounding, the sped of the ball is 3.94 m/s when it is 1.52 meters above the stone slab. Is the collision elastic?

What is the ratio of the masses of the two marbles?

A child playing marbles shoots a marble directly at another marble at rest. The first marble stops, and the second marble continues in a straight line with the same speed that the first marble had initially. What is the ratio of the masses of the two marbles? I need to see each step and formula to solve this question.

Speed of a falling egg

An egg falls from a nest at a height of 3.08 meters. What speed will it have when it is 0.5 meters from the ground? Neglect air friction. I need to see each step and formula to solve this question.

A block slides on a semicircular frictionless track.

A block slides on a semicircular frictionless track. If it starts from rest at position (A), what is its speed at the point marked (B)? A picture of the block and slide is attached as a jpeg file. I believe the answer is 3.7 m/s. I need to see each step and formula to solve this question.

What is the value of the spring constant k?

A 750-gram air-track glider slides along at a speed of 0.85 m/s until it hits a spring attached to the end of the very heavy track. The spring is compressed by 1.35 cm at the maximum compression. What is the value of the spring constant k? I need to see each step and formula to solve this question.

A 0.302-kg coffee mug rests on a table top 0.740 meters above the floor.

A 0.302-kg coffee mug rests on a table top 0.740 meters above the floor. A) What is the potential energy of the mug with respect to the floor? B) What is the potential energy with respect to the counter top 1.100 meters above the floor? I need to see each step and formula to solve this question.