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The Physics Hypertextbook © 1998–2013 Glenn Elert |
No condition is permanent.
relativistic momentum
| p = | mv |
| √(1 − v2/c2) |
relativistic energy
| E = | mc2 |
| √(1 − v2/c2) |
binomial expansion (or taylor series)
| E = mc2 | ⎛ ⎝ |
1 + | 1 | v2 | + | 3 | v4 | + | 5 | v6 | + | 35 | v8 | + | 63 | v10 | + … | ⎞ ⎠ |
|||||
| 2 | c2 | 8 | c4 | 16 | c6 | 128 | c8 | 256 | c10 |
the first term is the rest energy
E = mc2
the second term is the classical formula for kinetic energy
| K = m | 1 | v2 |
| 2 |
the higher order terms are corrections that become more and more noticeable as the speed approaches the speed of light
relativistic mass
| m' = | m |
| √(1 − v2/c2) |
for massed particles
E2 = p2c2 + (mc2)2
for massless particles
E = pc
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The Physics Hypertextbook © 1998–2013 Glenn Elert |
No condition is permanent.