# Radiation Pressure causing acceleration

A vertically pulsed laser fires a 800 MW pulse
of 220 ns duration at a small 8 mg pellet at
rest. The pulse hits the mass squarely in the
center of its bottom side.
The speed of light is 3 × 108 m/s and the
acceleration of gravity is 9.8 m/s2.

If the radiation is completely absorbed
without other effects, what is the maximum
height the mass reaches?
Answer in units of μm.

Pressure*Area = Force = ma
F = dp/dt
p = E/c

I'm not even sure where to start. I guess I need to figure out the relation between Power and energy to get the momentum. From that I can get the force and then acceleration, etc...

Any hints would be appreciated

## Answers and Replies

Do you have any idea what the number should be? I gave it a try and my best attempt, from working out the net force on the pellet and the resulting acceleration then working out the distance kinematically. However, the h I get is very small due to the (comparatively) large mass and very short pulse time.

I'd like to know my answer was in the ballpark before I describe it so that I can help with confidence.

Cheers

sylas
Science Advisor
A vertically pulsed laser fires a 800 MW pulse
of 220 ns duration at a small 8 mg pellet at
rest. The pulse hits the mass squarely in the
center of its bottom side.
The speed of light is 3 × 108 m/s and the
acceleration of gravity is 9.8 m/s2.

If the radiation is completely absorbed
without other effects, what is the maximum
height the mass reaches?
Answer in units of μm.

Pressure*Area = Force = ma
F = dp/dt
p = E/c

I'm not even sure where to start. I guess I need to figure out the relation between Power and energy to get the momentum. From that I can get the force and then acceleration, etc...

Any hints would be appreciated

There's a very simple relation between energy and momentum for light -- which you have given above anyway. You can use that without worrying about forces.

Power is just energy per unit time. If you really want forces, then note that force is momentum per unit time... so for light, the relation between power and force of a light beam is the same as the relation between energy and momentum of a light pulse.

Cheers -- sylas