1. simplify

Simplify this :

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

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

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

$\displaystyle =\frac{M}{m}$

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

THanks ..

2. Originally Posted by alphabeta
Simplify this :

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

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

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

$\displaystyle =\frac{M}{m}$

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

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

You only can cancel the Mms if M = m.

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

You only can cancel the Mms if M = m.

sorry , it should be :
$\displaystyle \frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^ 2}$

4. Originally Posted by alphabeta
sorry , it should be :
$\displaystyle \frac{\frac{1}{2}mu^2}{\frac{1}{2}M(\frac{m}{M}u)^ 2}$
In this case your result is OK:

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