Question

Suppose you fell into an accretion disk that swept you into a supermassive black hole. On your way down, the disk radiates 10 % of your mass-energy, E=mc2.

1) Assume that your mass is 54.5 kg. Calculate how much radiative energy will be produced by the accretion disk as a result of your fall into the black hole.

Express your answer using two significant figures.

E= ..................... J

2) Calculate approximately how long a 100-watt light bulb would have to burn to radiate this same amount of energy.

Express your answer using two significant figures.

t= ..................... yr

Answer 1

1) E= mc²

the disk radiates 10 % of your mass-energy the mass is 54.5x(10/100) = 5.45 kg.

E = (5.45 kg)x (3x10⁸ m/s) = 4.9x10¹⁷ J

2) 1 Joule = 1 watt per second

t = (4.9x10¹⁷ J)/100 watt = 4.9 x 10¹⁵ s = 1.553x10⁸ Years