Special Relativity Energy Problem a little confused

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Homework Help Overview

The problem involves calculating the increase in Earth's mass due to the energy received from sunlight over the course of one day, given the intensity of sunlight at Earth's location.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss how to calculate the total energy received by Earth in one day based on the intensity of sunlight. Questions arise regarding the use of cross-sectional area and the assumptions about radiation incidence.

Discussion Status

Some participants have provided guidance on calculating the energy received, while others are exploring the implications of using cross-sectional area and the geometry of the Earth in their calculations. Multiple interpretations of the problem setup are being considered.

Contextual Notes

Participants are working within the constraints of the problem statement and the provided equations, questioning the assumptions about energy distribution and the geometry involved in the calculations.

Engineergirl2
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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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