1. simplify

Simplify this :

$\frac{\frac{1}{2}mv^2}{\frac{1}{2}m(\frac{m^2u^2}{ M^2})}$

$=\frac{u^2}{\frac{m^2u^2}{M^2}}$

$=\frac{M^2}{m^2}$

$=\frac{M}{m}$

i doubt if i am correct (the last 2 steps) , is it possible to change this
$\frac{M^2}{m^2}$ to $\frac{M}{m}$

THanks ..

2. Originally Posted by alphabeta
Simplify this :

$\frac{\frac{1}{2}m{\color{red}v^2}}{\frac{1}{2}m(\ frac{m^2u^2}{M^2})}$

$=\frac{\color{red}u^2}{\frac{m^2u^2}{M^2}}$.......<<<<<<< are you sure?

$=\frac{M^2}{m^2}$

$=\frac{M}{m}$

i doubt if i am correct (the last 2 steps) , is it possible to change this
$\frac{M^2}{m^2}$ to $\frac{M}{m}$

THanks ..
$\frac{v^2}{\frac{m^2u^2}{M^2}} = \frac{M^2 \cdot v^2}{m^2u^2} = \left(\frac{M \cdot v}{m \cdot u} \right)^2$

You only can cancel the Mms if M = m.

3. Originally Posted by earboth
$\frac{v^2}{\frac{m^2u^2}{M^2}} = \frac{M^2 \cdot v^2}{m^2u^2} = \left(\frac{M \cdot v}{m \cdot u} \right)^2$

You only can cancel the Mms if M = m.

sorry , it should be :
$

\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^ 2}
$

4. Originally Posted by alphabeta
sorry , it should be :
$

\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^ 2}
$
In this case your result is OK:

$

\frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^ 2} = \frac{\frac{1}{2}m u^2}{\frac{1}{2}M \cdot \left(\frac{m^2}{M^2}\cdot u^2\right)} = \frac{\frac{1}{2}m u^2}{\frac{1}{2}m u^2 \cdot \frac{m}{M}} = \dfrac Mm
$