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A stream of particles, each of mass m and having kinetic energy E, is collimated into a parallel beam of cross-sectional area A. The particles are incident normally on a smooth plane surface at rate n and they rebound elastically. Derive an expression for the pressure on the surface in terms of A, m, E and n. Explain why the pressure would be different if the surface were rough so that the particles rebounded at various angles.

An electric light bulb emits 20W of radiation uniformly in all directions. What is the maximum radiation pressure on a surface placed 2.0m away from the bulb? State the conditions under which this will occur?

Attempt:

[tex]E_k = 0.5mu^2 \Rightarrow u=\sqrt{2E/m}[/tex]

[tex]\text{Ft} = 2m\sqrt{2E/m}[/tex]

[tex]F = Ftn[/tex]

[tex]P= \dfrac{2mn\sqrt{2E/m}}{A}[/tex]

[tex]P = \dfrac{2n\sqrt{2EM}}{A}[/tex]

2nd part: incident momentum is added a factor of sin/cosine and therefore effective impulse decreases (blah blah blah..).

I don't know how to start the light bulb part. Does λ=h/p come into use? The wavelength of light covers a range of values; which should I choose? Can anyone please give me some hints? Thank you!

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# Homework Help: Year 12: Cambridge Physics Problem (Classical mechanics v. Light particle collision)

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