Multiple-Choice Homework Problem 14.6 The Planetary Society\'s light sail, that

Question

Multiple-Choice Homework Problem 14.6 The Planetary Society's light sail, that we discussed in lecture, has a mass of 100kg and a sail area of 600m^2. We found a very boring acceleration for sunlight in near-earth orbit. To make the sail accelerate faster we shine lasers on it from earth. Assume the laser completely illuminate the sail area, all 600 m^2, and that the sail is perfectly reflecting. What must the intensity of the light be at the sail to produce an acceleration of g = 9.81 m/s^2? Don't forget the 2 for perfectly reflecting. Select One of the Following: 1.2 times 10^8 W/m^2 2.0 times 10^7 W/m^2 4.9 times 10^8 W/m^2 2.5 times 10^8 W/m^2

Explanation / Answer

d) 2.45*10^8 W/m^2

Force required to get the required acceleration, F = m*a

= 100*9.81

= 981 N

so, radiation pressure required, P = F/A

= 981/600

= 16.35 N/m^2

but we know,
for perfectly reflecting surface.

radiation pressure, P = 2*I/c

I = P*c/2

= 1.635*3*10^8/2

= 2.45*10^8 W/m^2 <<<<<<<<----------Answer

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