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launching a rocket from the space station

Rocket Propulsion. See attached file for full problem description. A rocket is fired from a space station that is 1000 miles above the surface of the Earth. We take the radius of the Earth to be 4000 miles, so r = 5000 miles. Suppose that the rocket is fired "horizontally". That is, suppose at the time the rocket is launched.

Maximum height of a spring

In problem 13.61(a), if the spring constant k is 30 N/m, and the collar C has 350-g, the maximum height above point B reached by the collar is: a. 0.198 m b. 0.291 m c. 0.306 m d. 0.148 m

Energy Conservation Calculation

A 1.0 kg block is shot up a 30* incline with an initial speed of 400cm/s. How far up the incline will the block go before sliding back down if the coefficient of kinetic friction between the block and the incline is 0.17? Use the principle of energy conservation in the analysis and solution.

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.

Quickest Path Down a Slide

See the attached file for full problem description, as there are a number of equations that cannot be expressed in plain text. Notes: The Solution uses a different constant of convenience: A) The b and the C of the provided question are related as b = 1/2C^2 B) It takes the negative y below zero, unlike the reversed direct

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/

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?

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

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