Mass and Energy Suppose your internship is to ship a jack-in-the box to every person on earth. Should you ship them open or closed? You find that when you close them, them they are easier to pack, but a little harder to accelerate! In other words, they have more_______

Mass and relativity What is mass, as you learned in physics 105? mass measures resistance to changing the velocity That idea is true in relativity (although we might have to redefine acceleration when v is close to the speed of light)

Mass, energy and Einstein Einstein: all “internal” forms of energy of an object (all energy that is not kinetic energy of the center of mass) make up some of the mass! e.g. spring or electrostatic potential energy, chemical, nuclear bonding energy, KE of vibration, rotation. It’s only noticeable with big energy changes as in nuclear physics. So mass is not conserved in general, because we can add or take away energy from an object!

P1. Which (otherwise identical) car is a tiny bit harder to accelerate (with the same force)? a hot railroad car a cool railroad car

Mass, energy and Einstein Rest energy of an object: Because mass can be turned into energy, and vice-versa, we assign an energy to an object with its center of mass not moving. Then we can require that total energy be conserved! Mass units 1 eV/c2 = 1.602x10-19 J /(2.998 x108 m/s)2 = 1.783 x10-36 kg   Atomic mass unit (1/12 of carbon atom mass) 1 u = 1.6605×10−27 kg = 931.494 MeV/c²

Relativistic energy and momentum Each object with its center of mass moving at speed v vs an observer has its own g, and that observer sees a momentum for that particle of and a total energy of Each object has a “rest energy” of , so the kinetic energy is

Speed limit in our universe It takes infinite energy (and momentum) for an object with mass to get to the speed of light.

P2. If a particle of mass m moves at v = 0 P2. If a particle of mass m moves at v = 0.95 c, what is the kinetic energy? ______ mc2 A. 0.53 B. 1.3 C. 2.0 D. 2.2 E. 3.2 P3. How much momentum does it have? ____ mc A. 0.5 B. 1.2 C. 1.9 D. 2.1 E. 3.0

P4. How much energy must you add to a particle of at v = 0 P4. How much energy must you add to a particle of at v = 0.95 to get the speed to 0.999c? ______ mc2 A. 2.5 B. 5.4 C. 11 D. 19 E. 22 P5. If I double the speed of a particle from 0.2c to 0.4c, the momentum ______ A. doubles B. increases less than double C. increases more than double.

Mr. Thompkins in Wonderland Read here

Conservation of momentum: classical won’t work An unstable nucleus at rest explodes into pieces with masses M, and 3M. The larger piece is seen traveling to the right at speed 0.9c. How fast is the small piece going?

Let’s use relativity! An unstable nucleus at rest explodes into pieces with masses 20 GeV/c2, and 60 GeV/c2 . The larger piece is seen traveling to the right at speed 0.9c. How fast is the small piece going?

Let’s use relativity! An unstable nucleus at rest explodes into pieces with masses 20 GeV/c2, and 60 GeV/c2 . The larger piece is seen traveling to the right at speed 0.9c. What was the mass of the original nucleus?

What about particles without mass? Pretty simple:

Electron-positron annihilation We can sometimes turn mass completely into E/M energy: The photons conserve mass/energy and momentum!

Electron-positron annihilation Suppose the electron is as rest, and the positron has a total energy of three rest masses. What are the two energies of the photons? Which photon has the highest energy? upward downward can be the same

Twin paradox One twin goes to a far planet with g =3, turns around and then comes home after 20 yrs as she measures it. Her sister is much older than she is. But why? From each point of view, the other moved away and came back Resolution of paradox: What is it about one’s experience that is fundamentally different from the other’s? Something she would notice even with her eyes closed. Acceleration!