Ended up with a quadratic equation for v (speed of the muon), in terms of both masses and c. Brute-forced it with the quadratic formula and got the right answer.
Homework Statement
A charged π meson (rest mass = 273me) decays into a neutrino (zero rest mass) and a μ meson (rest mass = 207me). Find the kinetic energies of the neutrino and the mu meson.
Homework Equations
E = moγc2
K = mo(γ-1)c2
v = pc2/E
p = moγv
The Attempt at a Solution
In the rest...
Homework Statement
Show how one can obtain the Doppler transformation for the frequency of a receding
source just using the Lorentz transformations for the energy (where E=h).
Homework Equations
Relativistic transformations for momentum and energy:
E = γ(E' + vp'x)
pc/E = v/c = β
The Attempt...
Homework Statement
We normally assume that the origins of two inertial frames coincide at t=t'=0. This way we find:
t' = γ(t - vx/c2)
x' = γ(x-vt)
Suppose instead that when t=T the origin of S' (which is moving along the x-x' axis with speed v relative to S) has abscissa x=X (neglect y and z)...
Homework Statement
The aether-wind theory of the Michelson-Morley experiment was discussed in class
for the special case where the arms of the interferometer (each of equal length L) are
parallel and perpendicular to the wind. In this problem we consider the general case
for an angular setting...
I also found this formula:
I = Io / [1 + Q^2 (w^2 - wo^2) / (w * wo)] where wo is the resonant frequency. With this formula I got Q = 23.8. I'm very confused now...
Homework Statement
Suppose you want to use a series RLC circuit to tune in your favorite AM radio station which broadcasts at a frequency of 1.20 MHz. You would like to avoid the obnoxious easy listening station which broadcasts at 1.10 MHz, right next to the one you like. In order to achieve...
Homework Statement
A voltage source E_0 cos ωt is connected in series with a resistor R and a capacitor C. Write down the differential equation expressing Kirchhoff’s law. Then guess an exponential form for the current, and take the real part of your solution to find the actual current...
I tried this again soon after posting with a slightly different strategy:
I put B in terms of current density, so B(r) = mu*J*r/2. J = 900/(pi * [0.04^2 - 0.02^2]) = 750,000/pi. Thus I treat the small cut out as J=-750,000/pi.
B due to the big cylinder = 0 since r=0. B due to the small...
Homework Statement
A long copper rod 8 cm in diameter has an off-center cylindrical hole 4 cm in diameter down its full length. This conductor carries a current of 900 amps flowing in the direction “into the paper.” What is the direction, and strength in tesla, of the magnetic field at the...
Homework Statement
[/B]
Two long, coaxial metal cylinders are separated by a material of conductivity sigma and dielectric constant epsilon. The radius of the inner cylinder is a, the radius of outer cylinder is b, and the length of both is L.
Suppose that the inner conductor is held at a...
I tried the max power transfer theorem and revised parts (b) and (c) (I don't think part a changes since it's just an energy calculation):
b. Max power: R_internal = R_load.
For a standard D cell, R_load = 1 ohm. Power dissipated by the load = I^2 * R_load = R_load * ([V_source] /...
Doesn't the voltage delivered by the battery remain constant? As in, "the chemistry of the batteries will produce the same amount of energy and will maintain the same EMF regardless of the current drawn from the battery."
Reference...
Homework Statement
A standard D cell can supply 10mA at 1.5 volts for about 300 hours. An alkaline D cell can do about the same. Assume - 2 - that the chemistry of the batteries will produce the same amount of energy and will maintain the same EMF regardless of the current drawn from the...