How Did the Author Derive the Relativistic Mass Formula?

[Mechdude]

Homework Statement

i was looking through an undergrad's original research and i wanted to get how he derived w\some formula, the paper is "Relativistic dynamics without conservation laws,B. Rothenstein1, Ş. Popescu2"
since its open access here is the page with the paper
http://www.jphysstu.org/archives/volume2issue1"
he gives two equations at about pg 7 eqn (47) and (48)
$$m = \frac{m_o}{\sqrt{1-u^2/c^2}}$$
$$m' = \frac{m_o}{\sqrt{1-u'^2/c^2}}$$

Homework Equations

he then mention this equation is used (eqn 17)
$$u = u' \frac{ \sqrt{(cos(\theta') + v/u')^2 + (1- v^2/c^2) sin^2(\theta') }} {\frac {cos \left( \theta' \right) u'v}{{c}^{2}}+1}$$and this is also relevant
$$u = \frac{u' +v}{1 + u'v/c^2}$$

The Attempt at a Solution

iv tried direct substitution but i can not get his relation between m and m' , which he states as ,
$$m = \frac{m' + vm' u_x /c^2 }{\sqrt{1- v^2/c^2}}$$

the farthest i get is this,$$\frac{m'\,\sqrt{{c}^{2}-{u'}^{2}}}{\sqrt{{c}^{2}-\frac{{\left( v+u'\right) }^{2}}{{\left( 1-\frac{u'}{{c}^{2}}\right) }^{2}}}}$$

 

[mark726]

your first step in responding to this forum post would be to carefully read the paper in question and try to understand the author's derivation. You can also try to replicate the author's steps and equations in your own calculations to see if you can arrive at the same results.

In this case, it seems like the author is using a combination of equations (17) and (48) to derive the final equation for m. You can start by writing out the equations and manipulating them algebraically to see if you can get to the author's final equation. It may also be helpful to make substitutions for the variables in the equations, such as replacing u' with (u' + v)/(1 + u'v/c^2) as given in equation (17).

If you are still having trouble understanding the derivation or replicating the results, you can reach out to the author or other experts in the field for clarification or assistance. It is also important to remember that scientific research can be complex and it may take time and effort to fully understand a particular paper or concept. Keep persevering and seeking out resources and support to help you better understand the material.