Question

1) One plans to float a small, totally absorbing sphere at a distance of d above an isotrophic point source of light, such that the upward radiation force from the light balances with the downward gravitational force on the sphere. the density of the sphere is p and the radius of the sphere is r. What power of P by the light source to accomplish this?

Answer 1

given

distance of d

gravitational force on the sphere

density of the sphere is $\rho$

the radius of the sphere is r

power P = ?

the condition is using weight of the sphere is equal to force

using equation I = P / A_r

the pressure radiation P_R = P / c A_r

the pressure on the sphere can be written as P_R = F_R / A_s

F_R = P_R A_s

F_R = P A_s / c A_r  

W = F_r

m g = P A_s / c A_r  

P = m a c A_r / A_s

= $\rho$ V_s g 4 $\pi$ d² c / $\pi$ r²

= $\rho$ (4/3) $\pi$ r³ g 4 $\pi$ d² c / $\pi$ r²

P = 16 $\rho$ rg $\pi$ d² c / 3