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Mass and Energy

Example: At the Earth’s distance from the sun, the intensity of the sunlight is about $1.4\cdot 10^3 \frac{w}{m^3}$ knowing that the radius of the earth’s orbit is $1.4\cdot 10^{11}$ m determine the approximate amount of mass lost by the sun as energy is being converted from the mass. Give the amount of $\frac{kg}{s}$ .

Draw a Picture	Knowns	Unknown
	R= $1.5\cdot10^{11}$ I= $1.4\cdot10^3 \frac{W}{m^2}$	m=___\frac{Kg}{s}

Make a shell or sphere around the sun. Make the shell have the same radius as the orbit of the earth. This helps you find the total power output of the sun
Area of a sphere (surface area) A= $4\piR^2$ = $4\codt\pi\cdot(1.5\cdot10^{11}m)$
A=2.827 $\cdot10^{23}m^2$
P=AI= $2.827\cdot10^{23}m^{2}\cdot1.4\cdot 10^3 \frac{2}{m^2}$
P=3.958 $\cdot10^{26}$ W
Make a note of the units of power W= $\frac{energy}{time}$
Convert energy to mass using E=mc $^2$ => Solve for mass
$\frac{E}{c^2}=m$
$c=3\cdot10^8 \frac{m}{s}$
$E=3.958\cdot10^{26}$ J
$\frac{3.958\cdot10^{26}J}{(3\cdot10^8 \frac{m}{s})^2}=4.398\cdot10^9 \frac{kg}{s}$
M= $4.398\cdot10^9 \frac{kg}{s}$