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Energy

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?

Motion of a charged sphere projected toward a stationary charged sphere

A small metal sphere, carrying a net charge of q1 = -2.50 micro-Coulombs, is held in a stationary position by insulating supports. A second small metal sphere, with a net charge of q2 = -7.60 micro-Coulombs and mass 1.80 g , is projected toward q1. When the two spheres are 0.800 m apart, q2 is moving toward q1 with a speed

Kinetic energy and loss of potential energy

1. What velocity does a 1-kg object have when its kinetic energy is 1 J? 2. A man skis down a slope 200 m high. If his velocity at the bottom of the slope is 20 m/s, What percentage of his potential energy was lost due to friction and air resistance?

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

Particle in a Changing Potential

A particle of mass m is in the ground state of a potential described by V(x) = 1/2mw^2x^2 when the equilibrium point of the potential is suddenly changed from x = 0 to x = s. Show that the probability that after this change the particle will be in the first excited state of the new potential is given by (please see the attach

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.

The Susceptibility of Paramagnetic Atoms

Show that the susceptibility of N spin - 1/2 paramagnetic atoms in a volume V does not depend on whether or not they are localized (i.e. is the same for distinguishable and indistinguishable statistics).