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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?
Homework Equations
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.