Question

Chapter 33, Problem 026 In the figure, a laser beam of power 3.85 W and diameter 2.60 mm is directed upward at one circular face (of diameter d < 2.60 mm) of a perfectly reflecting cylinder. The cylinder is levitated because the upward radiation force matches the downward gravitational force. If the cylinder's density is 1.71 g/cm', what is its height H? Number Units the tolerance is +/-5% Click If you would like to show Work for this question: Open Show Work

Answer 1

Density * (Pi * r^2) * G * H = (2 * power) / C

G = 9.8 m/s^2
C = Speed of Light = 2.998E8 m/s

You are given:

Power = 3.85 W, Therefore 2*Power = 7.70 Watts
Diameter = 2.60 mm = 2.6E-3 meters
Therefore, Radius = 1.3E-3 meters
Density = 1.71 g/cm^3 = 1710 kg/m^3

Now, we plug in what we know:

1710 * (Pi * 1.3E-3^2) * 9.8 * H = 7.70 / 2.998E8

This gives us an H of 2.886E-7 meters...Answer.

IF You need your answer in mm, so multiply your answer by 1000, giving you 2.88E-4 mm. ....Answer.