Special Relativity Energy Problem a little confused

AI Thread Summary
The discussion centers on calculating the increase in Earth's mass due to the energy received from sunlight, which is 1.5 kW/m^2. To find the total energy received in one day, the cross-sectional area of Earth must be considered, along with the intensity of sunlight. The change in kinetic energy is deemed negligible, allowing the use of the equation ΔE=Δmc^2 to determine mass increase. The expected result is an increase of approximately 1.83x10^5 kg per day. Understanding the integration over the hemispherical area and the angle of incidence is crucial for accurate calculations.
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Homework Statement


At Earth's location, the intensity of sunlight is 1.5kW/m^2. if no energy escaped earth, by how much would Earth's mass increase in 1 day?


Homework Equations


ΔE=Δmc^2+ΔKE
Rearth=6.378x10^3


The Attempt at a Solution


I know that the change in kinetic energy does not change, so that value can go to 0. But I'm not sure what exactly I'm supposed to start with. The answer is supposed to be 1.83x10^5kg/day. Any help would REALLY be appreciated.
 
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You need to calculate how much energy is received in 1 day by the entire Earth.
You know how much is received in one second (kW is energy per second) by 1 m^2 of the surface.
 
Do I use cross sectional area?
 
You can use the cross sectional area and assume the radiation is normal on it.
Integrating over the area of the (hemi-)sphere and taking into account the angle of incidence for each location will produce the same result.
 

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