Question

Someone plans to float a small, totally absorbing sphere 0.518 m above an isotropic point source of light, so that the upward radiation force from the light matches the downward gravitational force on the sphere. The sphere's density is 22.2 g/cm3, and its radius is 2.12 mm. (a) What power would be required of the light source

Answer 1

Step-by-step explanation:

From the question we are told that

The height is
`h  =  0.518 \  m`

The sphere density is
`\rho =  22.2g/cm^3 =  (22.2 )/(1000)  *  1*10^(6) =  22200 kg/m^3`

The radius is
`r =  2.12 \  mm =0.00212 \ m`

Generally the power required is mathematically represented as

`P  =  (16 *  \pi *  \rho *  r *  g *  h^2 * c )/(3)`

substituting values

`P  =  (16 * 3.142 *  22200 *  0.00212 *  9.8 *  0.518^2 *  3.0*10^(8))/( 3)`

`P  = 6.22*10^(11) \  W`