Solutions to Homework 7

1. Quarks form in groups of two or three, such that their total charge is an integer. The combinations are:
uuu (+2)
uud (+1)
udd (0)
ddd (-1)
and their anti-quark equivalents:
$\overline{uuu}$ (-2)
$\overline{uud}$ (-1)
$\overline{udd}$ (0)
$\overline{ddd}$ (+1)

Combinations of two:
$u\overline{u}$ (0)
$d\overline{d}$ (0)
$u\overline{d}$ (+1)
$d\overline{u}$ (-1)

2. In particle-antiparticle annihilation, all of the mass is converted to energy:
mass = 2 x 1.9 x 10³⁰ kg x 10¹¹ = 3.8 x 10⁴¹ Kg
E=mc² = (3.8 x 10⁴¹ kg) x (3 x 10⁸ m/s)² = 3.42 x 10⁵⁸ Joules

*this is more energy than the sun puts out in 10 billion billion years!- in one SECOND the sun produces 1000 times the annual energy budget for the USA. In other words, 10⁵⁸ Joules is inconceivably huge!*

3. 10 +/- 45
= 55 mph if they are traveling opposite directions
= 35 mph if they are traveling the same direction

If you use relativity: V=(u+v)/(1+uv/c²). But uv/c² is 2.73x10^-16. This is a VERY small number, so you can ignore it- only worry about relativity when u or v is close to the speed of light. Someone on a bike or in a car is safely out of this regime.