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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)

Finding potential energy of conservative force

See attached file for full problem description. Previously it was considered a force of the form f = ixy + jcx^2 + kz^3, and found a value of "c" from the following list such that this was a conservative force. Note: there must really be extra 'constants' in front of each term, with magnitude 1 but the proper units (such as

Electric Energy Between Charged Spheres

Two hollow metal spheres are concentric with each other. The inner sphere has a radius of 0.1500 m and a potential of 85.0 V. The radius of the outer sphere is 0.1520 m and its potential is 82.0 V. If the region between the spheres is filled with Teflon, what is the electric energy contained in this space?

Rotational kinetic energy of a ball

A uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.50 m/s when it rolls off the edge and it falls towards the floor, 1.10 m below. What is the rotational kinetic energy of the ball just before it hits the floor? 0.506 J 0.732 J 1.05 J

Angular speed of pencil when it makes 30 degree angle with vertical

A pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil when it makes a 30.0 degree angle with the vertical? 3.56 rad/s 7.23 rad/s 1.83 rad/s 6.32 rad/s

Angular speed of a pencil

A pencil, 15.7 cm long, is released from a vertical position with the eraser end resting on a table. The eraser does not slip. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table? a) 13.7 rad/s b) 7.23 rad/s c) 24.5 rad/s d) 16.8 rad/s

Finding Electric Potential Difference

The potential at location A is 452 V. A positively charged particle is released there from rest and arrives at location B with a speed Vb. The potential at location C is 791 V, and when released from rest from this spot, the particle arrives at B with twice the speed it previously had, or 2vb. What is the potential at B?

Potential Energy Between Two Points

An electric force moves a charge of +1.80 x 10^-4 C from point A to point B and performs 5.80 x 10^-3 J of work on the charge. (a.) What is the difference (EPEa-EPEb) between the electric potential energies of the charge at the two points? (b.) What is the potential difference (Va-Vb) between the two points. (c.) Which point is

Determining Kinetic Energy: Example Problem

The moment of inertia of a uniform rod (about its center) is given by I = M/12. What is the kinetic energy of a 120-cm rod with a mass of 450 g rotating about its center at 3.60 rad/s? 0.350 J 4.20 J 0.700 J 2.10 J

Energy- Kinetic

A solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 3.5 rad/s. What is its kinetic energy? 0.18 J 0.092 J 1.05 J 0.53 J

Truck and Car Kinetic Energies

A truck has four times the mass of a car, however, the car is moving with twice the speed of the truck. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say which of the following? Kt= 4Kc Kt= 2Kc Kt= Kc Kt= 1/2Kc.

Energy Required to Cut Through a Log

A wood cutting saw is plugged into a source of 100 volt DC power. The current drawn by the machine as it cuts through a log is given by the following relationship: I(t) = 10sin(.31416 t) where t = seconds. It takes 10 seconds to cut through the log and the saw is stopped at the end of the cut so that another may be placed into

Classical Mechanics Homework

A block of mass m: I.62 kg slides down a frictionless incline (attached). The block is released a height h : 3.91m above the bottom of the loop. See attached for full problem description.

Bose-Einstein condensate of atoms in a potential well

This exercise is for a Bose-Einstein condensate of indistinguishable atoms which do not interact with each other and are in a 3-dimensional harmonic well. The system is described by the following Hamiltonian (see attached file). This exercise is for a Bose-Einstein condensate of indistinguishable atoms which do not interact w

potential energy and kinetic energy of the stone

A stone of mass 0.62kg is fired upwards at an angle to the ground and with a speed of 5.5 m s-1, as shown in the figure in the attachment. The figure shows the path of the stone until it strikes the ground at point C. Disregard air resistance. Take the acceleration, g, due to gravity to have a value of 9.8 m s-2. Calculate

Power and Energy

A perfectly insulated container contains 70 g of water and has a small heater immersed in water. The temperature of the water is 40 degrees Celsius, and the heater is connected to a 12V battery via a switch. When the heater is switched on, an electric current of 13A flows through its heating element and the temperature of the w

Electricity and Magnetism Problems

Problem A): Consider the railgun shown below: See attached file for full problem description. Consider a 1 kilogram projectile that is accelerated using a 10 meter long, 3 cm wide, railgun with a 1 million amp constant current pulse. 1) Derive an analytic expression for B everywhere in the plane between two infinitely

Simple harmonic motion

See attached file for full problem description. 1. Consider the four equivalent ways to represent simple harmonic motion in one dimension: To make sure you understand all of these, show that they are equivalent by proving the following implications: I-->II--> III--> IV. For each form, given an expression for the constants (C

Partition Function and Probability

Consider the lowest 3 energy levels of a hydrogen atom: Ground state energy : -13.6 eV degeneracy = 0 First excited state energy : -3.4 eV degeneracy = 4 Second excited state energy: -1.5 eV degeneracy = 9 Ignore higher states. a) Estimate the partition function Z for H-atom at 5800 K. Do not forget to t

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

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

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

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.