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Question

A 150-W lightbulb emits 5% of its energy as electromagnetic radiation. What is the radiation pressure on an absorbing sphere of radius 10 m that surrounds the bulb?

Solution

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Identify the unknown:\underline{\text{Identify the unknown:}}

The radiation pressure on absorbing sphere

List the Knowns:\underline{\text{List the Knowns:}}

Power: P=150×5100=7.5  WP=150 \times \dfrac{5}{100}= 7.5 \;\mathrm{W}

Distance: r=10  mr= 10 \;\mathrm{m}

Set Up the Problem:\underline{\text{Set Up the Problem:}}

The intensity:

I=P4πr2=7.54π×(10)2=5.99×103  W/m2I=\dfrac{P}{4 \pi r^2}=\dfrac{7.5}{4 \pi \times (10)^2} = 5.99 \times 10^{-3} \;\mathrm{W/m^2}

Radiation pressure on perfect absorber:

Prad=IcP_{rad}=\dfrac{I}{c}

Solve the Problem:\underline{\text{Solve the Problem:}}

Prad=5.99×1033×108=1.997×1011  N/m2P_{rad}=\dfrac{5.99 \times 10^{-3}}{3 \times 10^8}=\boxed{1.997 \times 10^{-11} \;\mathrm{N/m^2}}

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