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DavidCantwell

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I am reading Resnick and Halliday's "Basic Concepts in Relativity" (ISBN: 0023993456) and have come to an impass about deriving equation 3-4a

\begin{equation}m = \gamma m_0\end{equation}

in the text. The authors wrote that the equation can be derived from the following equations

\begin{array}{cr}

M = m^{\prime} + m_0 & \\

Mu = m^{\prime} u^{\prime} & \\

u^{\prime} = 2u / (1+u^2/c^2)& \\

\end{array}

based on the attached figure. The derivation is left as an exercise (problem 18 pp 133). The problem is to derive m in the first equation above from the three equations below it, but I only keep coming up with

\begin{equation} \frac{m^{\prime}}{m_0} = \frac{1+u^2/c^2}{1-u^2/c^2} \end{equation}

which is an intermediate equation in Tolman's text that leads to the desired equation after substituting a transformation equation for γ into the rhs ratio (e.g. see the sometimes "colorful" thread at https://www.physicsforums.com/forumdisplay.php?f=70\&order=desc\&page=23). But this approach seems to deviate far afield of the three equations given, and it leaves me feeling like I am doing something wrong. What I mean is that I cannot complete the derivation without including the transformation for γ from Tolman, and it seems to me that the authors think I should. Can anyone tell me what I am doing wrong? Hints, recommendations, anything? I am stuck. Apparently the book is out of print, so I can provide more info if need be. Thnx for any help.

\begin{equation}m = \gamma m_0\end{equation}

in the text. The authors wrote that the equation can be derived from the following equations

\begin{array}{cr}

M = m^{\prime} + m_0 & \\

Mu = m^{\prime} u^{\prime} & \\

u^{\prime} = 2u / (1+u^2/c^2)& \\

\end{array}

based on the attached figure. The derivation is left as an exercise (problem 18 pp 133). The problem is to derive m in the first equation above from the three equations below it, but I only keep coming up with

\begin{equation} \frac{m^{\prime}}{m_0} = \frac{1+u^2/c^2}{1-u^2/c^2} \end{equation}

which is an intermediate equation in Tolman's text that leads to the desired equation after substituting a transformation equation for γ into the rhs ratio (e.g. see the sometimes "colorful" thread at https://www.physicsforums.com/forumdisplay.php?f=70\&order=desc\&page=23). But this approach seems to deviate far afield of the three equations given, and it leaves me feeling like I am doing something wrong. What I mean is that I cannot complete the derivation without including the transformation for γ from Tolman, and it seems to me that the authors think I should. Can anyone tell me what I am doing wrong? Hints, recommendations, anything? I am stuck. Apparently the book is out of print, so I can provide more info if need be. Thnx for any help.

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