- #1

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- Homework Statement
- Suppose a spherical particle of mass m and radius R in space absorbs light of intensity I for time t. (a) How much work does the radiation pressure do to accelerate the particle from rest in the given time it absorbs the light? (b) How much energy carried by the electromagnetic waves is absorbed by the particle over this time based on the radiant energy incident on the particle?

- Relevant Equations
- ##I = \frac{P}{A}##

##P = \frac{W}{t}##

##\rho = \frac{F}{A}##

a) ##\rho = \frac{I}{c} = \frac{F}{A}## for a perfect absorber

##F = ma## where ##a = \frac{c}{t}##

##\frac{I}{c} = \frac{mc}{tA}##

##I = \frac{I^2 tA}{mc^2} = \frac{P}{A}##

##P = \frac{I^2 tA^2}{mc^2} = \frac{W}{t}##

##W = \frac{I^2 t^2A^2}{mc^2}##

I am unsure what A is. I think it should be ##4\pi r^2##, but that doesn't generate the correct answer. The correct answer also has a 0.5 factor in the work equation which I don't know how they get.

##F = ma## where ##a = \frac{c}{t}##

##\frac{I}{c} = \frac{mc}{tA}##

##I = \frac{I^2 tA}{mc^2} = \frac{P}{A}##

##P = \frac{I^2 tA^2}{mc^2} = \frac{W}{t}##

##W = \frac{I^2 t^2A^2}{mc^2}##

I am unsure what A is. I think it should be ##4\pi r^2##, but that doesn't generate the correct answer. The correct answer also has a 0.5 factor in the work equation which I don't know how they get.