A laser beam is used to levitate a metal disk against the force of Earth\'s grav
ID: 1623551 • Letter: A
Question
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 at lights, 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. (b) If the disk has mass 13 g and radius 0.05 m, find the necessary light intensity. (c) Give two reasons why using light pressure as propulsion near Earth's surface it impractical.Explanation / Answer
(a)
The intensity of laser beam is I,
Eenergy of laser falling on area A in time t is,
U = IAt
The momentum of the laser beam falling on the disk is,
P = U/c, since the light is reflected perfectly, the change in momentum is,
P = 2P = 2U/c = (2/c)IAt
So force on the disk is,
F = P/t = (2/c)IAt/t
or, F = (2/c)IA
This force balances the gravitation force on disk, so,
F = mg
or, (2/c)IA = mg
or, I = (mgc)/(2A)
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(b)
we have I = mgc/2A
or, I = [(13X10-3kg)(9.8 m/s2)(3X108 m/s)]/2[3.14X(0.05m)2]
or, I = 2.43X109 W/m2
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(c)
We saw above that to lift just a 13 g disk we need the enormous intensity of I = 2.43X109 W/m2. So the enormous energy requirement is a big impediment.
Also, the energy absorbed by the surface of a practical device would raise its temperature to high level which would be difficult to handle. This is because no material is perfect reflector.
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