When an object of mass m moves with a velocity v that is

Question

Question: When an object of mass m moves with a velocity v that is small compared to the velocity of light, c, its energy is given approximately by

E ≈ (1/2)mv²

If v is comparable in size to c, then the energy must be computed by the exact formula

E = mc²(1/√(1 - v²/c²) - 1)

(a) Plot a graph of both functions for E against v for 0 ≤ v ≤ 5 · 108 and 0 ≤ E ≤ 5 · 1017. Take m = 1 kg and c = 3 · 108 m/sec. Explain how you can predict from the exact formula the position of the vertical asymptote.

(b) What do the graphs tell you about the approximation? For what values of v does the first formula give a good approximation to E?