A highly reflective low-density cylinder is being held motionless in mid-air by

Question

A highly reflective low-density cylinder is being held motionless in mid-air by a laser beam that is directed vertically upward, and which reflects off one of the two circular faces of the cylinder. The beam is large enough that the entire face of the cylinder is uniformly illuminated. The cylinder has a height h, a cross-sectional area A, and a density of 100 kg/m3.

Find the height of the cylinder, if the intensity of the laser beam is 1.80 e107 W/m2. Assume that 100% of the light is reflected from the cylinder. Hint: sketch a free-body diagram of the cylinder, and apply Newton's second law.

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I tried to use the these equations, but can't seem to solve this problem.

I = Power/Area

Density = mass/Volume

F=ma

but I can't get one that works. I always get stuck on the radius portion.

Explanation / Answer

radiation pressure for total reflection is given by Pr = 2I/c
where I = intensity= power/area = Emax^2/(2uoC)
c = velocity of light = 3e8 m/s
so here now we apply pressrue = 2* 1.8*10^7/3e8

Pr = 0.12 Pa

but Presuure also = rgo gh

so rgo gh = 0.12

so h = 0.12/(100*9.8)

h = 0.122 mm

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