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Lynna [10]
3 years ago
15

Someone plans to float a small, totally absorbing sphere 0.500 m above an isotropic point source of light,so that the upward rad

iation force from the light matches the downward gravitational force on the sphere. The sphere’s density is 19.0 g/cm3, and its radius is 2.00 mm. (a) What power would be required of the light source?
Physics
1 answer:
mote1985 [20]3 years ago
4 0

Answer:

468449163762.0812 W

Explanation:

m = Mass = \rhoV

V = Volume =\dfrac{4}{3}\pi r^3

r = Distance of sphere from isotropic point source of light = 0.5 m

R = Radius of sphere = 2 mm

\rho = Density = 19 g/cm³

c = Speed of light = 3\times 10^8\ m/s

A = Area = \pi R^2

I = Intensity = \dfrac{P}{4\pi r^2}

g = Acceleration due to gravity = 9.81 m/s²

Force due to radiation is given by

F=\dfrac{IA}{c}\\\Rightarrow F=\dfrac{\dfrac{P}{4\pi r^2}{\pi R^2}}{c}\\\Rightarrow F=\dfrac{PR^2}{4r^2c}

According to the question

F=mg\\\Rightarrow \dfrac{PR^2}{4r^2c}=\rho \dfrac{4}{3}\pi R^3g\\\Rightarrow P=\dfrac{16r^2\rho c\pi Rg}{3}\\\Rightarrow P=\dfrac{16\times 0.002\times 19000\times \pi\times 0.5^2\times 9.81\times 3\times 10^8}{3}\\\Rightarrow P=468449163762.0812\ W

The power required of the light source is 468449163762.0812 W

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Answer:

Efficiency = 30% = 0.3

Explanation:

The general formula for efficiency of a device is given as:

Efficiency = (Desired Output/ Input) * 100%

Here, in our case, we have a petrol engine as a device. So, we analyze it for the efficiency calculations. Here, we have:

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Now, we know that the desired output of a car or the purpose of a car is to provide Kinetic energy, while all other forms of energy such as heat and sound energies are produced as waste. And the chemical energy is provided to car as input, in form of fuel. Therefore,

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The force created by the teacher is 120 × 5 = 600N.

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The force created by the 50 kg student is 50 × 8 = 400N

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