# Conservation of Energy and Momentum

#### Glass

1. Homework Statement
I have a 1g object on a frictionless surface being hit with light of a frequency 632nm (directly parrallel to the surface and the object absorbs all the light). How many photons did the object absorb by the time it's moving at 1mm/s?

2. Homework Equations

3. The Attempt at a Solution
Well I worked it out two different ways and I got two different answers:

My first attempt is via conservation of energy:
n*h*c/lambda + m*c^2 = gamma*m*c^2
where
n is the number of photons
h is planck's constant
c is the speed of light
lambda is the wavelength
m is the mass of the object
gamma is the 1/sqrt(1-v^2/c^2)
Then I solved for n.

My second attempt is via conservation of momentum:
n*h/lambda = gamma*m*v
Then I solved for n.

In both cases I got different answers. So I'm not sure what's wrong.

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#### Dick

Homework Helper
Trust conservation of momentum before you trust a naive conservation of energy calc. The collision is inelastic.

#### Glass

Ok thanks. But what happened to the energy? Did it radiate as heat or something?

#### Dick

Homework Helper
Some of it could have been converted into electrical energy if the surface is connected to a power grid. Conservation can't tell you where it went. But yes, most likely answer is heat.

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