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**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.