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• Users: RyanP
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1. ### Pi meson decay (relativistic momentum)

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.
2. ### Pi meson decay (relativistic momentum)

The momentum of the neutrino is equal and opposite to the momentum of the muon - should I solve for the speed of the muon?
3. ### Pi meson decay (relativistic momentum)

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...
4. ### Doppler shift derivation from Lorentz Transformations

That makes sense, thanks.
5. ### Doppler shift derivation from Lorentz Transformations

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...
6. ### General Lorentz Transformations

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)...
7. ### Special Relativity: Rotated Michelson Interferometer

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...
8. ### Q factor of an AM radio RLC circuit

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...
9. ### Q factor of an AM radio RLC circuit

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...
10. ### RC Circuit with a voltage source

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...
11. ### Off center hole in a current-carrying wire - magnetic field?

Oops - it actually comes out to 3*10^-3 tesla (30 gauss). That makes more sense
12. ### Off center hole in a current-carrying wire - magnetic field?

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...
13. ### Off center hole in a current-carrying wire - magnetic field?

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...
14. ### Coaxial metal cylinders

Ok, maybe instead I'll do J(r) = current (constant) / area (function of r). In this case I just get J(r) = V*sigma/(r*ln(b/a)). Does this sound right?
15. ### Coaxial metal cylinders

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...
16. ### Battery driven winch

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] /...
17. ### Battery driven winch

How could I figure out the voltage across the winch without knowing its resistance?
18. ### Battery driven winch

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...
19. ### Battery driven winch

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...