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A laser beam is used to levitate a metal disk against the force of earth's gravity.
(a) derive an equation giving the required intensity of light, i, in terms of the mass m of the disk, the gravitational acceleration g, the speed of light c, and the cross-sectional area of the disk a. assume the disk is perfectly reflecting and the beam is directed perpendicular to the disk. (do not substitute numerical values; use variables only.)
i =
(b) if the disk has mass 3.89 g and radius 2.40 cm, find the necessary light intensity.
(c) give two reasons why using light pressure as propulsion near earth's surface is impractical.

Sagot :

Jayilych4realidn

The necessary light intensity of the disk if the disk has mass 3.89 g and radius 2.40 cm is 6.483 x 10^12cd.

Calculations and Parameters:

a. Given that:

  • i= intensity of light
  • m= mass of disk
  • g= gravitational acceleration
  • c= speed of light
  • a= cross-sectional area of the disk

I = P/A

= Force x Speed/Area

Gravitational force, F= GM1M2/r^2

F= ma, F= mg

I= mg x c/q

That is,

i= mass x gravitational acceleration x speed/area

b.

Mass= 3.89g

Radius, r= 2.40cm

i=?

i= mg x c/a

Speed of light= 3.0 x 10^8 m/s

Area, a= /pi r^2

= 3.142 x (0.024)^2

= 3.142 x 0.000576

= 0.0018m^2.

i= 3.89 x 10 x 3.0 x 10^8/0.0018

i= 6.483 x 10^12cd.

c. Light has no mass, therefore, it lacks momentum and cannot exert pressure for propulsion of materials.

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