- #1

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Suppose that an object of rest mass m

_{0}travels to the right with speed v

_{1}.

A photon of frequency f also travels to the right and hits the object. The photon is fully absorbed by the object and then the object travels to the right with the (unknown) speed v

_{2}after collision.

Now, the total energy should be same before collision as after collision.

Also the total momentum should be same before collision as after collision.

I expressed these two conservation laws by two equations:

$$\frac{m_0 c^2}{\sqrt{1-\left(\frac{v_1}{c}\right){}^2}}+h f=\frac{m_0 c^2}{\sqrt{1-\left(\frac{v_2}{c}\right){}^2}}$$

$$\frac{m_0 v_1}{\sqrt{1-\left(\frac{v_1}{c}\right){}^2}}+\frac{h f}{c}=\frac{m_0 v_2}{\sqrt{1-\left(\frac{v_2}{c}\right){}^2}}$$

But since there is only one unknown variable - the speed v

_{2}of the object after collision - the two equations cannot hold both.

So to compute the speed v

_{2}either I choose first equation or second equation, but the two computed values of v

_{2}would be different for each equation.

The question is, what am I doing wrong?