- #1
azerbajdzan
- 15
- 0
Hello,
Suppose that an object of rest mass m0 travels to the right with speed v1.
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 v2 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 v2 of the object after collision - the two equations cannot hold both.
So to compute the speed v2 either I choose first equation or second equation, but the two computed values of v2 would be different for each equation.
The question is, what am I doing wrong?
Suppose that an object of rest mass m0 travels to the right with speed v1.
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 v2 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 v2 of the object after collision - the two equations cannot hold both.
So to compute the speed v2 either I choose first equation or second equation, but the two computed values of v2 would be different for each equation.
The question is, what am I doing wrong?