Protons with kinetic energy of 1 GeV in a narrow beam are diffracted by Oxygen nuclei. The first minimum is observed at an angle of 8.5 degree. Calculate the radius of the Oxygen nuclei.
The Doppler effect is the change in the frequency of a wave caused by a
moving source or observer. Let's assume a source produces sound wave with the
speed v and frequency f0.
(a) When the source moves toward a stationary observer with speed vs,
what is the frequency of the sound heard by the observer?
(b) When the observer moves toward the stationary source with speed vo,
what is the frequency of the sound heard by observer?
(c) For a light wave with frequency f and speed c, show that the classical
Doppler effect violates special relativity. Use special relativity to derive
the frequency of the light wave when the source is moving toward observer with
the speed vs.
In a deuterium-tritium (D - T) nuclear reaction, 17.6 MeV of energy is
released. You are given a laser-fusion fuel pellet of mass 5 mg which is
composed of equal parts (by mass) of deuterium and tritium.
(a) If half the deuterium and an equal number of tritium nuclei participate in
D - T fusion, how much total energy (in Joules) is released?
(b) At what rate must pellets be fueled in a power plant with 3 GW thermal
power output?
(c) What amount of fuel would be needed to run the plant for 1 year? Compare
with the 3.6 megatons of coal needed to fuel a comparable coal-burning power
plant.
The potential energy of a mass m as a function of position x is given by U(x) = ax2 + bx + c, with a, b, c positive constants.
(a) Find the equilibrium position of the mass.
(b) If the mass is released from rest at x = 0 at t = 0, find its position as a
function of time assuming no resistive force is present. What is the maximum
kinetic energy of the mass?
(c) If the mass is subject to a drag force Fd = -γv, (with γ2
<< 8am) and is released from rest at x = 0 at t = 0, find the time when the
amplitude of the motion is ¼ of the initial amplitude.