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# Energy

### Partition function, chemical potential, entropy, and free energy

Derive equations: S = -(&#8706;F/&#8706;T)_V, N = Nk [ln (V/N_vQ) + 5/2] - &#8706;F_int/&#8706;T and &#956; = (&#8706;F/&#8706;N)_T, V = -kT ln (VZ_int/N_vQ) for the entropy and chemical potential of an ideal gas.

### 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.

### Coupled Oscillators-eigenfrequencies and normal modes

Consider a system like the system in fig 2 except there are 3 equal masses M, and 4 springs all with equal spring constants K. with the system fixed at the ends. Find the eigenfrequencies and describe the normal modes for this system

### Generalized Lagrangian

See attached file for full problem description of this question on object of mass sliding frictionlessly.

### A Block of Mass Released from Rest at a Height

A block of mass m is released from rest at a height R above a horizontal surface. The acceleration due to gravity is g. The block slides along the inside of a frictionless circular hoop of radius R. A.Which expression would give the speed of the block at the bottom of the hoop and why? 1.v=mgR 2.v=mg/2R 3.v^2=g^2/R 4.v

### 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/

### Energy as function of temperature for Einstein solid.

As per the attachment, I understand what formula needs to be used, but I am unsure of what to do from this point. See attached file for full problem description.

### 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

### Lagrange dynamics of a rolling ball inside a hollow cylinder

A sphere of radius r is constrained to roll without slipping on the inner surface of the lower half of a hollow cylinder of inside radius R. Determine the following: a) the Lagrangian function. b) The equation of constraint c) Lagrange's equation of motion d) Frequency of SMALL oscillations

### Lagrange's Equation for a double pendulum

A double pendulum consists of two simple pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lengths of rigid, massless, rod and bobs of equal mass and if both pendula are confined to move in the same plane find Lagrange's equation of motion for the system...Do NOT assume small angles.

### Non-linear problems in oscillation

A mass, m, moves in one dimension and is subject to a constant force +F1 when x<0 and to a constant force -F1 when x>0. a) Describe the motion with a phase diagram b) Calculate the period of the motion in terms of: m, F1, and the amplitude A (disregard damping)

### Modern Physics: Determining Gravitational Potential Energy

When an 81.0 kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.00 x 10^3 J. By how much does the potential energy of an 18.0 kg child increase when the child climbs a normal staircase to the second floor?

### Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.

Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W.

### 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

### Normal modes of oscillation

AB and BC are two rods, smoothly jointed at B, and suspended from a smooth fixed support A. The rods AB and BC are each of length l. AB has mass m, BC has mass 3m/2. Calculate the periods of the normal modes of oscillation in the vertical plane.

### 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

### A particle is under the influence of a given force. To determine the potential energy.

A particle is under the influence of a force F = -kx+(kx^3)/a^3 where k and a are constants and k is positive. 1) Find U(x) the potential energy 2) What happens when E (total energy) = (1/4)ka^3

### There are ten questions involving two-dimensional motion, law of gravitation, simple harmonic motion, frictional force, circular motion and vectors.

(Please use g = 9.8 m/s^2). 1) Three balls are launched at the same speed from a one-story building. Ball 1 is launched vertically up, ball 2 is launched horizontally, ball 3 is launched straight down. Which ball has the greatest speed as they hit the ground? There will be 40 more problems, to be solved using a calculator, w

### 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.

### motion of a cookie jar on an incline

Show ALL your work, including the equations used to solve the problems. A cookie jar is moving up a 40º incline. At a point 55 cm from the bottom of the incline (measured along the incline), it has a speed of 1.4 m/s. The coefficient of kinetic friction between jar and incline is 0.15. a) How much farther up the incline

### Find Final Energy for Absorption of Photon by Electron

An electron in a 10.2 nm one dimensional box is excited from the ground state into a higher energy state by absorbing a photon of electromagnetic radiation with a wavelength of 1.369 10^-5 m. Determine the final energy state for this transition.

### 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

### Classical Mechanics.

1. A flea is able to jump straight up about 0.64 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100 story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle

### 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

### Elastic Collisions

A ball tossed upward with a speed of 4.27 m/s from 1.52 meters above the floor fall to the floor and bounces to a height of 2.38 meters. Is the collision with the floor elastic? I need to see each step and formula to solve this question.

### 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?