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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.

The Action of a Harmonic Oscillator

Consider the harmonic oscillator, for which the general solution is x(t) = A cos(wt) + B sin(wt) 1. Express the energy in terms of A and B and show it is time independent. 2. Choose A and B such that x(0)=x1 and x(T)=x2. 3. Write down the energy in terms of x1, x2 and T. 4. Calculate the action S for the trajectory conn

Magnetism - Why is a piece if iron attracted to either pole of a magnet? The magnetic poles of the earth are called geomagnetic poles. Is the north geomagnetic pole a north magnetic pole or a south magnetic pole? ...

Questions 19 Why is a piece if iron attracted to either pole of a magnet? Question 20 The magnetic poles of the earth are called geomagnetic poles. Is the north geomagnetic pole a north magnetic pole or a south magnetic pole? Question 29 When a wire loop is rotated in a magnetic field, the direction of the curren

Physics of a jump

What is the physics behind a jump, for example - snowboard jump, skateboard jump, kite boarding jump, and bike jump?

Elastic collision and speed of center of mass

Two titanium spheres approach each other head on with the same speed and collide elastically. After the collision one of the spheres whose mass is 300 g remains at rest (a) what is the mass of the other sphere? (b) What is the speed of the two-sphere center of mass if the initial speed of each sphere is 2.0 m/s?

Two blocks connected by cord and pulley system.

(Please see the attached file and solve problem number 3 only) Blocks A and B weigh 8 lb and 3 lb respectively and are connected by cord and pulley system and released from rest in the position shown with the spring undeformed (see attachment). Knowqing that the constant of the spring is k = 20 lb/ft, determine : a) the veloc

Electro-Magnetic Induction

See the attached file. A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a nonconducting cart (see attachment). The cart is placed on the inclined portion of a track and released from rest at position P1 at a height y above the horizontal portion of the track. It rolls with negligib

Consider a two level system (such as the orientation of the magnetic moments of protons in a magnetic field, e.g. NMR). Let the spacing between the two levels be delta that is, the lower level has an energy of 0 and the other an energy of delta. Evaluate the following quantities in terms of delta and T. a) the partition function b) the internal energy c) the entropy In the limit of large T, does the system in the previous problem conform with the equipartition principle? Should it?

Consider a two level system (such as the orientation of the magnetic moments of protons in a magnetic field, e.g. NMR). Let the spacing between the two levels be delta that is, the lower level has an energy of 0 and the other an energy of delta. Evaluate the following quantities in terms of delta and T. a) the partition functio

Solar Power: Photovoltaics

Need a breakdown of solar power and how it works. Need an explanation that is focused on how solar power can be harnessed in constructing a solar powered car.

Problems on rigid body dynamics.

Please solve problems 6/140 and 6/127 only. Refer attachment for fig. Problem 6/140 : The sheave of 400 mm radius has a mass of 50 kg and a radius of gyration of 300 mm. The sheave and its 100 kg load are suspended by the cable and the spring which has a stiffness of 1.5 kN/m. If the system is released from rest with the spri

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

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