Calculating Minimum Power for Perception of Radiation from a Point Source

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SUMMARY

The minimum power required for a point source of radiation to be perceived at a distance of 10 meters, given an intensity of 8 x 10-7 W/m2, is calculated using the formula P = I * A. The area A of a sphere is determined by the equation A = 4πr2, leading to a power output of 0.001 Watt, or 1.0 mW when expressed with appropriate significant digits. This calculation confirms the relationship between intensity, area, and power in radiation perception.

PREREQUISITES
  • Understanding of radiation intensity and power calculations
  • Familiarity with spherical geometry and area calculations
  • Basic knowledge of significant figures in scientific notation
  • Concept of point sources in physics
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  • Learn about the inverse square law in relation to point sources
  • Study significant figures and their importance in scientific calculations
  • Investigate the effects of distance on the perception of radiation
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Students and professionals in physics, particularly those studying radiation, acoustics, or any field involving point sources and intensity calculations.

jasmin_89
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Homework Statement
Power source of radiation
Relevant Equations
Is my solution correct?
Hallo, can anybody help me and check if i have the right result:

What is the minimum power P that a point source of radiation (I=8*10^(-7) W/m^2) at a distance of l=10 m from the listener must have in order to still be perceived? (Note: The emitted energy per area can be related to a spherical body with A=4 π r^2)

P=I*A
P=8*10^-7 (W/m^2)*4*pi *(10m)^2= 0,001 Watt
 
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Your result looks correct to me.

Small nitpick: If no other constraints are given I would probably write the result as 1.0⋅10-3 W or just 1.0 mW to better signal the number of significant digits in the result.
 
Ok, thank you :)
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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