Homework Statement
A free particle (de Broglie wave) may be represented by the wave-function
\psi(x)=Aeikx
Show that this is an eigenstate of the momentum operator \hat{p}=-\hbar\frac{\delta}{\deltax}
Homework Equations
\hat{p}un(x)=anun(x)
an is the eigenvalue
un(x) is the corresponding...
Homework Statement
Designers of electrical circuits often take the maximum amplitude of the radiated electric field (at a large distance r) produced by an alternating current I0 flowing in a loop of area A cm2 to be given by
E=\frac{2.6AI0f2}{r}\muVm-1
where f is the frequency in MHz...
Homework Statement
A tunnel is bored through the centre of the Earth from Liverpool to New Zealand and a travel pod is dropped into it. The gravitational force on the pod is proportional to its distance from the centre of the Earth and so it undergoes simple harmonic motion described by...
Homework Statement
Write down an equation to describre a wave \psi(x,t) with all of the following properties
a) It is travelling in the negative x direction
b) It has a phase velocity of 2000ms-1
c) It has a frequency of 100kHz
d)It has an amplitude of 3 units
e) \psi(0,0)= 2 units...
Homework Statement
The ionisation energy of a single hydrogen atom is 13.6 eV. The application of Bohr quantisation to the hydrogen atom results in the stationary states having discrete energies given in terms of a positive integer n according to
E=-RB/n2
where RB is the Rydberg...
(b) The frequency of sound waves received by a detector when both source and detector move
relative to the air is:
f=f0[u(+ or -)vd/u(+ or -)vs] . Two trains are approaching each other at a level
crossing and blow their whistles at a frequency of 500 Hz. Train 1 is travelling at 20% of the...
Homework Statement
Question 1
(a) The displacement of a transverse wave on a string is described by:
y(x, t) = 0.01 sin(4x + 200t + \pi), where all quantities are expressed in SI units.
i) Determine values (with appropriate units) for the period, wavelength, and phase
velocity of the wave...
Homework Statement
The potential caused by an array of charges in a region of space can be described by the equation V(x,y,z)=2x+xy+y2-xz2 volts, where all distances are measured in metres. If a charge of 2 mC is moved from the position r1=(1,2,0)m to r2=(3,1,0), calculate the resulting change...
Homework Statement
During a collision between two initially uncharged polystyrene balls of radius 2 mm, some electrons are transferred from one of the balls to the other. In what direction does the resulting electrostatic force between the balls act?
The magnitude of the force between the...
Homework Statement
Assuming that the orbits of the Earth, and of Jupiter, around the Sun are circular and given that Jupiter orbits with a radius 5.2 times that of the Earth, calculate the orbital period of Jupiter around the Sun.
Homework Equations
T2=(4(pi)2/(G*M))*r3
The Attempt...
Homework Statement
Two bodies approach each other with the same speed of 2 m/s and collide head-on in an
inelastic collision. The mass of one body is m, the other has mass 3m. After the collision, the
lighter body has rebounded to travel back along its original trajectory with speed 1 m/s.
(i)...
Homework Statement
A box is held on a rough plank inclined at an angle of 60° to the horizontal. The box is
released from rest and slides down the plank with a constant acceleration of 5 m/s2. Calculate
the coefficient of kinetic friction between the box and the plank.
Homework...
Homework Statement
A crate resting on a rough plane is found to be on the verge of sliding when the plane is inclined at an angle of 40 degrees to the horizontal. Calculate the coefficient of static friction between the crate and plane. [
Homework Equations
f(s)<_(Mu(s))N
<_ is meant to...
Homework Statement
A projectile of mass 0.1 kg travelling horizontally through the air with speed v(t) experiences
a drag force DT (t) whose magnitude is given by:
D (t ) 0.001 [v (t )] 2
At one instant, the projectile’s speed is measured to be 100 m/s. Calculate the speed of the...