at what speed does the kinetic energy of an objest equal its rest mass energy?

Question

just curious!

Answer 1

The equation E = m c² includes both kinetic energy and rest energy. We can get the kinetic energy from

KE = E - m0 c².

Here, m0 is rest mass and m is relativistic mass, given by

m = m0 / sqrt(1 - v² / c²)

So we're looking for v such that

E - m0 c² = m0 c²
E = 2 m0 c²
m0 c² / sqrt(1 - v² / c²) = 2 m0 c²
1/2 = sqrt(1 - v² / c²)
1/4 = 1 - v² / c²
v / c = sqrt(3/4)
v = sqrt(3) c / 2

This is equal to about 0.87c or 2.6e8 km/sec.

Answer 2

Set mgh = mv^2/2 and solve for v.

Answer 3

thanks for 2 points and u can make that 10 by choosing it the best answer.

Answer 4

9.8 metres per second.