How much energy would be required to accelerate a 77-kg professor from rest to 90% the speed of light? (c = 3.0 × 10⁸ m/s) A)1.6 × 10¹⁹ J B)2.1 × 10¹⁹ J C)9.0 × 10¹⁹ J D)2.8 × 10¹⁹ J E)3.5 × 10¹⁹ J

Question

Quizplus · Accepted Answer

The energy required is given by the equation: 
E = (gamma - 1)mc^2

where gamma = 1/sqrt(1-(v/c)^2) is the relativistic factor, m = 77 kg is the mass of the professor, and v = 0.9c is the final speed.

Plugging in the values, we get:

gamma = 2.29 
E = (2.29 - 1) * 77 kg * (3.0 × 10^8 m/s)^2 
E = 8.96 × 10^19 J

Rounding to two significant figures, we get:

E = 9.0 × 10^19 J

Therefore, the best choice is C.

How Much Energy Would Be Required to Accelerate a 77-Kg