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Hamiltonians and Motion

A simple pendulum of length l and mass m is suspended from a point on the circumference of a thin massless disc of radius a that rotates with a constant angular velocity [(w)omega] about its central axis. Find the equation of the motion of the mass m.

Lagrangian of Particle Moving in Electromagnetic Field

An electromagnetic field is given by the potential: phi = 0 and A = ay(z-hat) + bt(x-hat) with a and b constant where 'x-hat?'z-hat?are unit vectors along the x and z directions respectively. a. Write the Lagrangian for a particle of charge q moving in this field. b. Identify any constants of the motion c. Write the

The Time and Amplitude of an Oscillator

An oscillator with a mass of 420g and a period of 0.800s has an amplitude that decreases by 2.30% during each complete oscillation. A) If the initial amplitude is 7.00cm, what will be the amplitude after 31.0 oscillations? B) At what time will the energy be reduced to 65.0% of its initial value?

Finding the Amount of Energy Absorbed by an Eardrum

A 54 dB sound wave strikes an eardrum whose area is 4.0 x 10-5 m^2. (a) How much energy (in watts) is absorbed by the eardrum per second? (b) At this rate, how long (in years) would it take your eardrum to receive a total energy of 1.0 J?

Simple Harmonic Motion Energy

A 0.53 kg mass vibrates according to the equation x = 0.49 cos 8.42t, where x is in meters, and t is in seconds. Determine the frequency in hertz. Determine the total energy in joules. Determine the kinetic energy and potential energy in joules when x = 0.26 m.

Gas mileage of car engine

When one gallon of gasoline is burned in a car engine, 1.19 x 10^8 J of internal energy is released. Suppose that 1.00 x 10^8 J of this energy flows directly into the surroundings (engine block and exhaust system) in the form of heat. If 6.0 x 10^5 J of work is required to make the car go one mile, how many miles can the car tr

Rate of change in water's temperature due to current.

Two square metal plates, each 0.1m on a side are parallel to each other and separated by distance 0.01m. the region between the plates is filled with water with conductivity 0.001 (ohm-meter)^(-1) If a potential difference is maintained between the plates, find the rate of change of temperature of the water.

Rate of production of heat

1. A certain sedentary person uses energy at an average rate of 123.29Watts. All of this energy has its ultimate origin in the sun. How much matter is converted to energy in the sun per day to supply this person? 2. If 1 kcal = 4.18 kJoule. What is the rate of energy production in kilowatts from a college student producing 1

Launching of satellite from Earth to Mars.

Assume the Earth has a circular orbit around the sun of radius and that Mars has a circular orbit around the sun of radius . To send a satellite to Mars that requires the least amount of energy the satellite is given an elliptical orbit whose perihelion corresponds to Earth's orbital distance and whose aphelion corresponds to

The Maximum Speed of Protons

Two protons are released from the res when they are 0.8nm apart. 1. What is the maximum speed they will reach? 2. When does this speed occur? 3. What is the maximum acceleration they will achieve? 4. When does this acceleration occur?

Physics - Sodium Light Wavelength and Energy

For a yellow sodium light emission, with a frequency of 5.09 x 1011 Hz a) What is the wavelength in nm? b) Calculate the energy of the light. (c = 3.00 x 108 m/s, h = 6.63 x 10-34 j-s, Rh = 2.18 x 10-18J)

Explanation of Energy Considertions in Motion

#1 A water slide is constructed so that right before the water you are moving horizontally and you fall a certain distance vertically and travel a certain distance horizontally. Given a certain amount of time (ignoring friction and air resistance). a) Find height from which you started at You are given how far person trav

Newton's laws of motion: Conservation of momentum

1) An astronaut loses contact with the hull of a space station and finds himself floating 16m from the station with zero velocity relative to it. Fortunately, he is carrying a 200W flashlight. Turning on the torch he uses it as a "light rocket? If he weighs 150kg, how long will it take to get back to the ship? Is there another w

Rotational motion and kinetic energy lost

PROBLEM 2: A playground whirl consists of a uniform disk of mass 10M and radius R. It is spinning at a rate of 2.0 rmp. A child mass M, originally at rest, steps on to the whirl. She does not slide back off. What is the final angular velocity of the whirl and the child (assuming the axis is frictionless)? What fractio

Determining Angle and Speed: Helium Example

A neutron collides elastically with a helium nucleus (at rest initially) whose mass is four times that of the neutron. The helium nucleus is observed to rebound at an angle of 43° from the neutron's initial direction. The neutron's initial speed is 6.6 x 10^5 m/s. Determine the angle at which the neutron rebounds, measured

Conservation of angular and linear momentum

(1) A particle of mass m at the end of a light string wraps itself about a fixed vertical cylinder of radius a. All the motion is in the horizontal plane. the angular velocity of the cord is w0 when the distance from the particle to the point of contact of the cylinder and string is b. find the angular velocity and tension in t

Four problems on rotational dynamics

1) How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.3 cm and a mass of 15.1 g. The laser scans at a constant tangential velocity of 1.26 m/s. Assume that the music is first detected at a radius of 20.3 mm from the center of the disk. Ignore the small circular ho

coefficient of kinetic friction between the block and table

A 0.510 kg wood block is firmly attached to a very light horizontal spring (k = 190 N/m). It is noted that the block-spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the tabl

Work done with torque and angular momentum

How much work is done by the motor in a CD player to make a CD spin, starting from rest? The CD has a diameter of 12.8 cm and a mass of 15.5 g. The laser scans at a constant tangential velocity of 1.16 m/s. If we assume that the music is first detected at a radius of 20.3 mm from the center of the disk. Ignore the small circular

Oscillation and escape velocity of a particle

The potential energy function of a particle of mass is V = cx/(x^2 + a^2), where c and a are positive constants. Sketch V as a function of x. Find the position of stable equilibrium, and the period of small oscillations about it. Given that the particle starts from this points with velocity v, find the ranges of values of v for

Mechanics: Kinetic & Potential Energy

A small circular object with mass m and radius r has a moment of inertia given by I=Bmr^2. The object rolls without sliping down a track. The track ends with a ramp with height R=2.5m that launches the object vertically. The object begins at a height H=6.0 m. To what maximum height will it rise after leaving the ramp if B=.40?

Spring : Energy Conservation

A spring fixed at one end is compressed from its relaxed position by a distance of 0.20 m. See the graph of the applied external force, Fx, versus the position, x, of the spring. (graph is attached) (a) Find the work done by the external force in compressing the spring 0.11 m starting from its relaxed position. (answer in Jou

Rydberg Constant for Beryllium

The beryllium (3) ion, Be 3+ is like the hydrogen atom in that it has a single electron. Its emission line spectrum is similar to that of hydrogen, except that the value of the Rydberg constant is different. The following lines were observed for a 'series' (i.e. all have the same value of nf) the Be 3+: 117.18 nm, 80.10nm, 68.35

kinetic energy in Lagrangian

Please see the attached file. I need an explanation of how one gets from the top equation (with v)s given by to the bottom equation where v is given by l*(theta)dot. I do not need an explanation of the double pendulum. Derive the kinetic energy equation of the double pendulum in Lagrangian.

Gravitational self-energy

** Please see the attached file for full problem statement ** Please show all work. Show that the gravitational self-energy (energy of assembly piecewise from infinity) of a uniform sphere of mass M and radius R is: U= -3/5 GM^2/R

Potential Energy and conservation of energy

Please see the attachment. 1.) The water slide shown below ends at a height of 1.50 m above the pool. If the person starts from rest at point A and lands in the water at point B, which has a horizontal distance L = 2.52 m from the base of the slide, what is the height h of the water slide? (Assume the water slide is frictionl

# problems in Quantum Mechanics

1. show that the commutator obeys: [A,B] = -[B,A] [A,B+C]=[A,B] + [A,C] [A,BC]=[A,B]C+B[A,C] [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0 Given the fundamental commutator relation between momentum and position [x,p] = ih show that: a. [x^n,p] = ihn*x^(n-1) b. [x,p^n] = ihn*p^(n-1) c. show that if f(x) can be expanded in polyno

Elastic and inelastic collision of two objects with arbitrary mass

An object A moving with velocity V collides with a stationary object B. After the Collision, A is moving with velocity (1/2)V and B with velocity (3/2)V. Find the ratio of their masses. If, instead of bouncing apart, the two bodies stick together after the collision, with what velocity would they then move?

The motion of two masses and three springs

I need some assistance for a 3 spring problem: horizontal configuration, frictionless surface. Spring constant is k for all three springs and mass = m for both weights ie configuration is: wall| spring - weigh t- spring - weight - spring |wall. Meed solution using eigenvalues and Lagrangian to obtain equations of motions.