Question

Part A

How fast must an object travel for its total energy to be 10 % more than its rest energy?

Express your answer using two significant figures.

Part B

How fast must an object travel for its total energy to 90 % more than its rest energy?

Express your answer using two significant figures.

Answer 1

Total energy = 1.10 (rest energy)

rest energy + kinetic energy = 1.10 (rest energy)

kinetic energy = 0.10 (rest energy)

( - 1) mc² = 0.10 m c²

= 1.10

1/sqrt (1 - (V/c)²) = 1.10

1/sqrt (1 - (V/(3 x 10⁸))²) = 1.10

V = 1.3 x 10⁸ m/s

B)

Total energy = 1.90 (rest energy)

rest energy + kinetic energy = 1.90 (rest energy)

kinetic energy = 0.90 (rest energy)

( - 1) mc² = 0.90 m c²

= 1.90

1/sqrt (1 - (V/c)²) = 1.90

1/sqrt (1 - (V/(3 x 10⁸))²) = 1.90

V = 2.6 x 10⁸ m/s