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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