Power of laser beam pushing spaceship with reflecting mirror

[purduegrad]

a 10^4 kg spaceship with a perfectly reflecting mirror is pushed by a laser beam with an accel of .3% g ( Earth's gravity). what is the power of the laser beam? [note:intensity*A = power]


not sure what the perfectly reflecting means...but maybe someonce can help...

 

[nbo10]

depending on if a surface is reflecting or absorbing. light will inpart a different amount of momentum to the surface. It's a pretty straight forward problem. You do have to read the book some.

JMD

 

[Njorl]

By perfectly reflecting, the mirror causes twice the momentum of the light to be added to the spaceship. If it were perfectly absorbing, only 1x the momentum would be added.

Force = dp/dt = ma

Njorl

 

[Doc Al]

Here are some hints: Find the force exerted on the spaceship. Consider that light has momentum and energy. (What's the relationship between energy and momentum for light?) What is the change in momentum of the light when it reflects off the mirror? (Impulse = Ft)

A perfectly reflecting mirror reflects back all the incident light. No energy is lost. (The power of the reflected beam equals the power of the incident beam.)

 

[gnome]

Perfectly reflecting means that the ship doesn't absorb any of the energy of the beam, so the beam is reflected retaining all of its energy, & the ship ends up with twice as much momentum as the beam had.

I'll give you some pieces. See if you can put them together.

You have enough info to determine the force acting on the ship just using F=ma.

Now remember that pressure P = F/A (here, A is area)

The magnitude of the Poynting vector of an em wave is
|S| = (du/dt)/A (note that du/dt is power, S is the Poynting vector)

The last thing you need to know is that the pressure exerted by an em wave on a perfectly reflecting surface is
P = 2|S|/c (c being the speed of light)