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Firlakuza [10]
3 years ago
8

Consider a perfectly reflecting mirror oriented so that solar radiation of intensity i is incident upon, and perpendicular to, t

he reflective surface of the mirror. if the mirror has surface area a, what is frad, the magnitude of the average force due to the radiation pressure of the sunlight on the mirror
Physics
2 answers:
podryga [215]3 years ago
4 0
The answer is Frad<span> = 2IA/c.</span>
yKpoI14uk [10]3 years ago
4 0

To solve this problem we need to know the following:

the mass of the sun, Msun, 2.0 * 10^30 kg

the intensity of sunlight as a function of the distance R from the sun,

Isun(R) = 3.2 * 10^25 * 1/R2 (W/m2), and

the gravitational constant G = 6.67 * 10^-11 m3/(kg⋅s2)

Suppose that the mirror described in Part A is initially at rest a distance R away from the sun.

What is the critical value of area density for the mirror at which the radiation pressure exactly cancels out the gravitational attraction from the sun?

Using the formula from Part A, find the force due to solar radiation:

Fr = 2IA/c

And compare to the force due to gravity:

Fg = G * m1 * m2 / R2

Fr = Fg

2IA/c = G * m1 * m2 / R2

Substitute in for I and the mass of the sun:

2 * (3.2 * 10^25 * 1/R2) * A / c = G * (2.0*10^30) * m2 / R2

The R2s cancel:

2 * (3.2 * 10^25) * A / c = G * (2.0 * 10^30) * m2

Now solve for m/A (where m = m2, the mass of the solar sail):

m/A = 2 * (3.2 * 10^25) / (c * G * (2.0*10^30))

m/A = 2 * (3.2 * 10^25) / ((3.0 * 10^8) * (6.67 * 10^-11) * (2.0 * 10^30))

mass/area = 0.00160 kg/m2

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The total consumption of electrical energy in the United States is about 1.0 1019 joules per year.
dexar [7]

Answer:

a) 316880878140.2895 Joules

b) 1056.26 Joules

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Explanation:

Energy consumption

E=\frac{P}{t}\\\Rightarrow E=\frac{1\times 10^{19}}{365.25\times 24\times 60\times 60}\\\Rightarrow E=316880878140.2895\ W

Average rate of electrical energy consumption is 316880878140.2895 Joules

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E=\frac{316880878140.2895}{300\times 10^6}\\\Rightarrow E=1056.26\ J

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Converting to km²

372801033.10622=\frac{372801033.10622}{1000\times 1000}=372.80103310622\ km^2

Area required to collect the electrical energy used in the United States is 372.80103310622 km²

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