A laser that produces a spot of light that is 1.10 mm in diameter is shone perpe

Question

A laser that produces a spot of light that is 1.10 mm in diameter is shone perpendicularly on the center of a thin, perfectly reflecting circular (2 mm in diameter) aluminum plate mounted vertically on a flat piece of cork that floats on the surface of the water in a large beaker. The mass of this "sailboat" is 0.14 g, and it travels 1.5 mm in 75.0 s. Assuming that the laser power is constant in the region where the sailboat is located during its motion, what is the power of the laser? (Neglect air resistance and the viscosity of water.) 0.0112 W 4 0.0112 W 0.0116 W 0.0113 W

Explanation / Answer

E = h , where E = energy of each photon of the laser and = frequecncy of the laser

E = Pc, whre P = momentum of each photon and c = speed of light

or P = E/c

Let power of the laser be W then, W = nE/t = nPc/t, where n is the number of photons

or W/c = nP/t

So W/c is the momentum of light falling per unit time on the plate. Or, in other words it is the force imaprted to the plate when the light falls on the plate. But since the light bounces back after collision and doesn't get absorbed the net force imparted will be 2W/c.

Not the sailboat travels 1.5mm in 75 seconds.

As S = ut + (1/2)at2, where u = initial velocity = 0, a = acceelration, S = distance travelled,

Now S = 0 + (1/2)at2

or a = 2S/t2

Force on the sialboat = F = ma = m(2S/t2)

But net force imparted by the laser is 2W/c, So,

2W/c = m(2S/t2)

or W = mcS/t2

or W = (0.14X10-3kg)(3X108m/s)(1.5X10-3m)/(75s)2

or W = 0.0112Watt is the answer.

This concludes the answer. Check the answer and let me know if it's correct. If you need anymore clarification I will be happy to oblige....

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