Relativistic Momentum and Energy

1. Relativistic Momentum and Energy

2. Relativistic Momemtum • First, we need to define a special type of mass, called rest mass • Rest mass, m0, is the mass of the object when it is at rest relative to us, • Then relativistic momentum is defined as

3. Simple Force As v approaches c, the acceleration approaches zero

4. Mass Increase • If time and length are affected by special relativity, then the mass is affected as well. • Note as v approaches 0, m ~ m0 • As v approaches c, m approaches inifinity

5. Relativistic Work and Energy • Observations about KE: • Under a Taylor series expansion with v<<c, KE is approximated by ½ mv2 • The expression is essentially the difference between mc2and m0c2. As v becomes small, K approaches 0 (as we expect)

6. Relativistic Energy • The total energy, E, of a free particle then is the sum of the kinetic energy, K, and the particle’s rest energy, m0c2. • E=K+m0c2 • E=mc2-m0c2+m0c2 • Thus, Einstein’s most famous formula E=mc2

7. Relating Energy and Momentum • If p=0, then E=m0c2 • If m0=0, then E= pc

8. Newton Versus Einstein • Newton was not wrong; just incomplete