Problem 48
A tiny particle of density \(2000 . \mathrm{kg} / \mathrm{m}^{3}\) is at the same distance from the Sun as the Earth is \(\left(1.50 \cdot 10^{11} \mathrm{~m}\right)\). Assume that the particle is spherical and perfectly reflecting. What would its radius have to be for the outward radiation pressure on it to be \(1.00 \%\) of the inward gravitational attraction of the Sun? (Take the Sun's mass to be \(\left.2.00 \cdot 10^{30} \mathrm{~kg} .\right)\)
Problem 49
Silica aerogel, an extremely porous, thermally insulating material made of silica, has a density of \(1.00 \mathrm{mg} / \mathrm{cm}^{3}\). A thin circular slice of aerogel has a diameter of \(2.00 \mathrm{~mm}\) and a thickness of \(0.10 \mathrm{~mm}\). a) What is the weight of the aerogel slice (in newtons)? b) What is the intensity and radiation pressure of a \(5.00-\mathrm{mW}\) laser beam of diameter \(2.00 \mathrm{~mm}\) on the sample? c) How many \(5.00-\mathrm{mW}\) lasers with a beam diameter of \(2.00 \mathrm{~mm}\) would be needed to make the slice float in the Earth's gravitational field? Use \(g=9.81 \mathrm{~m} / \mathrm{s}^{2}\)
Problem 50
Two polarizers are out of alignment by \(30.0^{\circ} .\) If light of intensity \(1.00 \mathrm{~W} / \mathrm{m}^{2}\) and initially polarized halfway between the polarizing angles of the two filters passes through the two filters, what is the intensity of the transmitted light?
Problem 51
A 10.0 -mW vertically polarized laser beam passes through a polarizer whose polarizing angle is \(30.0^{\circ}\) from the horizontal. What is the power of the laser beam when it emerges from the polarizer?
Problem 52
Unpolarized light of intensity \(I_{0}\) is incident on a series of five polarizers, each rotated \(10.0^{\circ}\) from the preceding one. What fraction of the incident light will pass through the series?
Problem 54
A laser beam takes 50.0 ms to be reflected back from a totally reflecting sail on a spacecraft. How far away is the sail?
Problem 55
A house with a south-facing roof has photovoltaic panels on the roof. The photovoltaic panels have an efficiency of \(10.0 \%\) and occupy an area with dimensions \(3.00 \mathrm{~m}\) by \(8.00 \mathrm{~m} .\) The average solar radiation incident on the panels is \(300 . \mathrm{W} / \mathrm{m}^{2}\), averaged over all conditions for a year. How many kilowatt hours of electricity will the solar panels generate in a 30 -day month?
Problem 56
What is the radiation pressure due to Betelgeuse (which has a luminosity, or power output, 10,000 times that of the Sun) at a distance equal to that of Uranus's orbit from it?
Problem 58
What is the wavelength of the electromagnetic waves used for cell phone communications in the 850 -MHz band?
Problem 59
As shown in the figure, sunlight is coming straight down (negative \(z\) -direction) on a solar panel (of length \(L=1.40 \mathrm{~m}\) and width \(W=0.900 \mathrm{~m}\) ) on the Mars rover Spir- it. The amplitude of the electric field in the solar radiation is \(673 \mathrm{~V} / \mathrm{m}\) and is uniform (the radiation has the same amplitude everywhere). If the solar panel has an efficiency of \(18.0 \%\) in converting solar radiation into electrical power, how much average power can the panel generate?
