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# Energy

### 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

### Excited States of Non-Interacting Fermion and Bose Systems

See attached file.

### 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

### Charged spheres

1. A thin, spherical, conducting shell of radius R is mounted on an insulating support and charged to a potential of -125V. An electron is then fired directly toward the center of the shell, from point P at distance r from the center of the shell ( r>>R). What initial speed Vo is needed for the electron to just re

### minimum surface charge density on the plate to stop protons

Protons exit a high speed proton machine at a speed of 1.50 * 10^6 m/s. A device needs to stop the protons safely. Protons will embed themselves in a metal target, but protons traveling faster than 1.30 * 10^5 m/s emit dangerous x rays when they hit. The protons must be slowed down to an acceptable speed, then let them hit a

### A charged parallel plate capacitor with insertion of a dielectric slab.

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False. 1. Aft

### Momentum gain of an electron in an electric field.

See attached file for full problem description.

### Special Relativity - Energy Problems

A particle of mass 3.5 MeV/c2 and kinetic energy 4.5 MeV collides with a stationary particle of mass 0.5 MeV/c2 . After the collision, the particles stick together. (part 1 of 5) Find the total energy of the first particle before the collision. Answer in units of MeV. (part 2 of 5) Find the speed of the first particl

### For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy.

For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy. Prove that the first order energy correction vanishes for all n = odd integer excited state levels.

### Loop the loop speed

See attached file for full problem description. A small object, released from a height of 15m slides along the frictionless loop-the-loop with a diameter of 4.3m. What is its speed at the top of the loop?

### Measuring the speed of a bullet

You need to verify which gun fired a bullet in a police investigation with a very limited budget. There are two guns involved in a crime; both could fire bullets of the same kind of mass (0.1kg). One is an assault rifle which fires the bullet at speed of 300m/s; the other is a hand gun which fires the same bullet with speed of 2

A.) The filament of a light bulb has a temperature of 3.1 103 °C and radiates 70 watts of power. The emissivity of the filament is 0.38. Find the surface area of the filament. B.) A car parked in the sun absorbs energy at a rate of 550 watts per square meter of surface area. The car reaches a temperature at which it radiat

### Heat intensity

A dish of lasagna is being heated in a microwave oven. The effective area of the lasagna that is exposed to the microwaves is 1.6 10-2 m2. The mass of the lasagna is 0.26 kg, and its specific heat capacity is 3400 J/(kg°C). The temperature rises by 80.0°C in 7.0 minutes. What is the intensity of the microwaves in the oven?

### Possibility of Perpetual Motion Machine

Physicists say that it is impossible to create a perpetual motion machine, a machine whose own activity keeps it running perpetually. What energy principle precludes the possibility of a perpetual motion machine?

### Water skiing: determining height

A water skier lets go of the tow rope upon leaving the end of a jump ramp at a speed of 16.4 m/s. As the drawing indicates, the skier has a speed of 13.0 m/s at the highest point of the jump. Ignoring air resistance, determine the skier's height H above the top of the ramp at the highest point.

### Swinging Rod - Horizontal Axis through its Center

A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.550 kg clings to one end of the stick, and a mouse with mass 0.170 kg clings to the other end. The system is released from rest with the rod horizontal. If the animals can manage to hold on, what a

### Relativistic Electric Potential Difference

For this question you need to know that an electron accelerated through an electric potential difference of V volts acquires a kinetic energy of V eV. (This question is best done by not converting to joules, but by exploiting the fact that mec2 is given as 0.511 MeV). i) What is v/c for an electron? a) Striking the screen

### A Parallel Plate Air Capacitor

The plates of a parallel plate air capacitor are 1.2 nm apart and area of each plate is 20 x 10^-4 m^2. Find the capacitance. It is connected to a 40 V battery. (i) What is the charge on each plate? (ii) What is the energy stored in the capacitor? Repeat the calculations for the same capacitor with the air gap re

### Determine the Speed of the Gear Rack

The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of gyration k = 30 mm at their centers. If the rack is originally moving downward at 2 m/s, when s = 0, determine the speed of the rack when s = 600 mm. The gears are free to turn about their centers, A and B. (See attached file for fig. and

### A .15kg block of ice is placed on a horizontal table. It is pushed back compressing a spring .045m, and the spring's constant is 1900N/m. The spring's mass is negligible. The tabletop is 1.2m above the floor. When the spring is released, the block slides off the table and onto the floor. With negligible friction between the block and the table, what is the speed of the block when it hits the floor?

A .15kg block of ice is placed on a horizontal table. It is pushed back compressing a spring .045m, and the spring's constant is 1900N/m. The spring's mass is negligible. The tabletop is 1.2m above the floor. When the spring is released, the block slides off the table and onto the floor. With negligible friction between the

### Ferromagnet problem

See attached file for full problem description. Ferromagnet

### Electrostatic Energy and Capacitance

A capacitor has a charge of 30 uC (fancy u). The potential difference between the conductors is 400 is V. What is the capacitance?

### Electrostatic Potential Energy of a Distribution of Charges

Three point charges are on the x axis: q1 at the origin, q2 at x=3 m, and q3 at x= 6 m. Find the electrostatic potential energy for (a) q1=q2=q3=2uC (u is the fancy u sign); (b) q1=q2=2uC, and q3 -2uC; and (c) q1=q3 = 2uC, and q2= -2uC.

### Potential Energy of 2-Charge System

Two point charges of values +3.4 and +6.6 micro-coulombs, respectively, are separated by 0.20 m. What is the potential energy of this 2-charge system? (ke=9.00 x 10^9 Nm^2/C^2) EPE=kq1q2/r.

### Find the Total Energy, pc, βo, and γo for the Protons

The Cosmotron, which began operation in the early 1950's at Brookhaven National Laboratory, accelerated protons to kinetic energy of 3000 MeV. Find the total energy, pc, βo, and γo for these protons.

### Electrostatic Energy

A cylindrical capacitor consists of a long wire of radius R, and length L with a charge +Q and a concentric outer cylindrical shell of radius Rsub2, length L, and a charge -Q. (a) find the electric field and energy density at any point in space. b(b) how much energy resides in cylindrical shell between the conductors of radius

### Electrostatic energy: Parallel Plate Capacitor

A parallel plate capacitor with a plate area of 2 m^2 and a separation of 1.0 mm is charge to 100 V. (a) What is the electric field between the plates? (b) What is the energy per unit volume in the space between the plates? (c) Find the total energy by multiplying your answer from Part (b) by the total volume between plates. (d)