## University Physics with Modern Physics (14th Edition)

a. $4.2\times10^9 kg$ per second. b. $4.7\times10^{20}s$.
a. Convert the energy produced in one second to its mass equivalent using $E=mc^2$. $$m=\frac{E}{c^2}=\frac{3.8\times10^{26}J}{(3.00\times10^8m/s)^2}=4.2\times10^9 kg$$ A kg of mass on Earth has a weight of about 2.2 lb, so this is about $(4.2\times10^9 kg)(\frac{2.2lb}{kg})(\frac{ton}{2000lb})=4.6\times10^6 tons$ b. The current mass of the sun is $1.99\times10^{30}kg$. At the rate we found, calculate the time required to burn up this mass. $$\frac{1.99\times10^{30}kg }{4.2\times10^9 kg/s}=4.7\times10^{20}s$$