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Wavefunctions and expectation values

For a particle in a 1-dimensional box confined between 0<x<a , the initial state of a particle is given by phi = phi_1 + 3phi_2 + 2phi_3 (all phi's are functions of x). a) Normalize this wave function. b) If no energy measurements are made what is the expectation value of energy of this state at a later time t? c)

Energy of a Thrill Seeking Cat

A thrill-seeking cat with mass 4.00 (rm kg) is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 (rm m), and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero

Gravitational Field of Ring Shaped Body

Consider the ring-shaped body of the figure (see attachment). A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane. Use F = -dU/dx to find the magnitude and direction of the force on the particle (using the variables G, M, m, x,

A girl springs from a trampoline with an initial upward velocity. At a given height above the trampoline, the girl grabs a box. What is the maximum height that the girl (with box) reaches?

A girl of mass m1= 60 kilograms springs from a trampoline with an initial upward velocity of v1= 8.0 meters per second. At height h= 2.0 meters above the trampoline, the girl grabs a box of mass m2 = 15 kilograms. For this problem, use g= 9.8 meters per second per second for the magnitude of the acceleration due to gravity. W

Elastic Collisions Calculation

That neighbor's pesky kid now has new missiles that make elastic collisions- He insists on throwing 25.0 g rocks at your new 2.25 kg light fixture hanging by a 26.0 cm wire from the ceiling of your porch. If each rock strikes the fixture traveling at 10.0 m/s, how high will the light fixture go after it is hit by one of these

Microstates and macrostates for an assembly of three particles

1. Enumerate all the microstates and macrostates for an assembly of three particles fixed in position with levels, 0, e, 2e, 3e, and a total energy of 3e. What is the least and what is the most probable distribution of energy? What is the average distribution of energy? 2. 1200 distinguishable particles are to be distributed

The mass of an electron is 9.11x10to the minus31 kg.

1. The mass of an electron is 9.11x10^-31 kg. The mass of one (negative) coulomb of electron (in kilograms) is equal to? 2. If a charge of 8.4 microcoloumbs is evenly distributed around a ring of radius 0.31m, the charge per unit length (in micro c/m) will be? 3. An engine takes in 4.7 calories of heat and discharges 3.5 c

heat lost from the steam pipe

2. A steam pipe is covered with 1.50cm thick insulating material of thermal conductivity 0.200 cal s"1 cm"1 °C"1. How much energy is lost per second when the steam is at 200°C and the surrounding air is at 20.0°C? The pipe has a circumference of 800cm and a length of 50.0m. Neglect losses through the ends of the pipe.

mechanical energy lost on the hill

A fun-loving 11.4 kg otter slides up a hill and then back down to the same place. she starts up at 5.75m/s and returns at 3.75m/s , how much mechanical energy did she lose on the hill? change of (E (mech))= ? J what happened to the energy?

box moving between two different springs

A 1.50 box moves back and forth on a horizontal frictionless surface between two different springs, as shown in the accompanying figure. The box is initially pressed against the stronger spring, compressing it 4.00 , and then is released from rest. By how much will the box compress the weaker spring? What is the max

kinetic energy of the cricket

It takes 4.186 of energy to raise the temperature of 1.00 of water by 1.00 degree. How fast would a 2.00 kg cricket have to jump to have that much kinetic energy? How fast would a 4.00 kg cricket have to jump to have the same amount of kinetic energy? v = ? m/s

Superball Collides With a Table. To determine change in momentum.

As shown in the figure (see attachment), a superball with mass m equal to 50 grams is dropped from a height of h1= 1.5 m. It collides with a table, then bounces up to a height of h2= 1.0 m. The duration of the collision (the time during which the superball is in contact with the table) is tc= 15 ms. In this problem, take the

Object with mass, initially at rest, explodes into two fragments

An object with mass m, initially at rest, explodes into two fragments, one with mass m_A and the other with mass m_B, where m_A + m_B = m. a). If energy Q is released in the explosion, how much kinetic energy does each fragment have immediately after the collision? Express your answers in terms of the variables m_A, m_B, an

Force and Direction on a Particle

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in the figure. The particle is released from rest at point A. a). What is the direction of the force on the particle when it is at point A? (Positive or Negativ

difference between the tensions in the string

A ball of mass m is attached to a string of length L. It is being swung in a vertical circle with enough speed so that the string remains taut throughout the ball's motion. Assume that the ball travels freely in this vertical circle with negligible loss of total mechanical energy. At the top and bottom of the vertical circle, th

Angular Momentum Equal Mass

Please see attached. 1. The two spheres of equal mass m are able to slide along the rotating horizontal black rod. If they are initially latched in position a distance r from the axis of rotation with the assembly rotating freely with an angular velocity of Wo. Determine the new angular velocity Wf after the spheres are rele

Choosing the Proper Electromagnetic Detector

Q. On a cold winter day, your employer sends you out to make some photographs of an inhabited house that can be used to determine where the house has poor heat-insulation. He offers you to take one of four tools. Which one do you pick: a radio telescope, an infrared camera, an off-the-shelf digital camera, or an UV camera? Just

Calculate the maximum velocity of slider

Please see attached...solve using energy equations, ie, potential, kinetic Calculate the maximum velocity of slider B if the system is released from rest with X = Y (the red line is a frictionless, mass less linkage of length .9 m ) Motion is in the vertical plane. Friction is negligible and the masses of A and B are equal

Spring Problem - Stored Energy

A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected

Springs and Slopes

A spring of constant k, compressed a distance x, is used to launch a mass m up a frictionless slope that makes an angle "theta" with the horizontal. Find an expression for the maximum distance along the slope that the mass moves after leaving the spring? How is the expression modified when you include kinetic friction in the pro

Two problems on capacitors.

1. A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 0.22 micro Farad capacitor. The capacitor is charged to 5.00V, then discharged through the resistor. The time for the potential difference across the plates to decrease to 0.800V is measured by a clock inside the game

Effective Mass of Electron in the Infinite Quantum Well

A one-dimensional quantum well of width 19 nm is created, and measurements show that the energy difference between the ground state and the first excited state is 0.19 eV. What is the effective mass of the electron in the well? Answer in units of kg.

Energy of an Electron in an Infinite Well

Part a Consider an electron in an infinite well of width 0.03 nm. Given : 1eV = 1.60218 × 10^-19 J hbar = 1.05457 × 10^-34 J s , What is the ground-state energy of the electron, in electron volts? Answer in units of keV. Part b What is the energy of the first excited state? Answer in units of keV.

Magnetic energy of solar flare

The problem reads as: "The magnetic field permeating a region of space represents stored energy. This energy is often quantified in terms of its density (magnetic energy per unit volume) given by B^2/(2*u) where u=4*pi X 10^(-7). Suppose an "X2" flare occurs within a volume of 10^12 km3 over a sunspot pair initially permeate

the kinetic energy of the electrons in the beam

A beam of electrons, each with the same kinetic energy, illuminates a pair of slits separated by a distance of 52 nm. The beam forms bright and dark fringes on a screen located a distance 2.3 m beyond the two slits. The arrangement is otherwise identical to that used in the optical two-slit interference experiment. The brigh