Professor Henry Greenside Physics 264L Professor Henry Greenside Monday 2015-08-30 1

Names of Students 2

Install Socrative app on your cellphone http://www.socrative.com/ 3

Polling Question One arcsecond 1’’ is a unit of time one degree 1/60 of one degree 1/3600 of one degree a smaller angle Answer: D one degree is divided into 60 arc minutes, one arc minute is divided into 60 arc seconds so 1 arcsecond = 1’’ = (1/3600) of one degree, this is a tiny angle! 4

Bradley’s Stellar Aberration Data 5

Polling Question As a photon from a remote star approaches the Sun, the photon’s speed v stays constant increases decreases Speed stays constant with speed c the speed of light 6

Polling Question As a photon with frequency f from a remote star approaches the Sun, it frequency f stays constant increases decreases Answer is B, frequency increases, representing a gain in energy of the photon. But as discussed in class, the Earth’s gravitational field is so weak that the change in frequency is quite tiny, e.g., if the photon drops a distance of 100 m in height, its change in energy would be determined by: h Delta{f} = m g H = (hf/c^2) g H or Delta{f}/f = g H/c^2 which is of order 10^-16, a very tiny shift. 7

Polling Question A point object with mass m is attached to an ideal spring with spring constant k, and the mass moves back and forth with amplitude A on a frictionless horizontal surface. If T1 is the period of the motion according to Newtonian mechanics and T2 is the period of the motion according to special relativity then T1 = T2 T1 > T2 T1 < T2 Answer C: the period of the oscillator when including special relativity is longer than the Newtonian case. The reason is that the inertial mass in the relativistic case is always a little larger than in the non-relativistic case, so a given amount of pulling by the spring leads to a smaller acceleration (a=F/m), so the block is always moving a bit more slowly, which means that the period has to be longer (time to go back and forth through one oscillation). 8

Polling Question If a point particle with mass m moves with speed v with respect to some observer, then the kinetic energy KE of that particle is given by (1/2) m(v) v2 = (1/2) m0 g v2. True False Answer: false The correct formula for the kinetic energy is m_0 c^2 (gamma – 1), it is the mass-energy minus the rest-energy. This has the same mathematical form for v/c << 1 but a quite different mathematical form otherwise. 9

Polling Question = f > f < f A rigid vertical rod of length L=1 m has a sound emitter with frequency f on the bottom and a microphone at the top. If the rod is dropped from the top of the Duke chapel, the microphone will measure a frequency f’ that is = f > f < f Does your conclusion change if the rod is rotated 180 degrees so the sound emitter is on the top of the rod, microphone at the bottom? 10

Michelson-Morley Interferometer 11

LIGO Gravity Wave Detector Based on Interferometry Interesting lesson for engineering students: many physics questions motivate people to build engineering devices that no engineer would otherwise build, too expensive, no market. So get a PhD in Physics if you want a chance to build insanely difficult and interesting devices… 12