A laser beam of power P and diameter D is directed upward at one circular face (of diameter d < D) of a perfectly reflecting cylinder. The cylinder is levitated because the upward radiation force matches the downward gravitational force. If the cylinder's density is ρ, what is its height H? State your answer in terms of the given variables, using c and g if needed.
Intensity = P/A
F = 2IA/c <-- for totally reflecting surface
[tex]\rho[/tex] = m/V
F(gravity) = mg
The Attempt at a Solution
i set the two forces equal to each other because the cylinder is floating.
F(due to beam)=F(gravity)
F(due to beam) = 2IA/c
F(gravity)=[tex]\pi[/tex]*r^2*h*[tex]\rho[/tex])*g <-substituted density (constant rho) and volume ([tex]\pi[/tex]*r^2*h) for mass
**i think this is where i may be going wrong**
F(due to beam)= 2IA/c = 2P/c <-- substituted in the equation of intensity where I = P/A, power divided by area.
after this i solved for H and got, i also substituted r = d/2 because r was not a variable to use in this problem
2P/([tex]\pi[/tex]*(d/2)^2*h*[tex]\rho[/tex]*g*c) = H