First slide

Conservation of mechanical energy

Question

In the figure $m_{1}$ and $m_{2}$ ( $< m_{1}$ ) are joined together by a pulley. When the mass $m_{1}$ is released from the height h above the floor , it strikes the floor with a speed

Moderate

A

$\sqrt{2 g h (\frac{m_{1} - m_{2}}{m_{1} + m_{2}})}$
B

$\sqrt{2 g h}$
C

$\sqrt{\frac{2 m_{2} g h}{m_{1} + m_{2}}}$
D

$\sqrt{\frac{2 m_{1} g h}{m_{1} + m_{2}}}$

Solution

$\begin{array}{l} E_{i} = E_{f} \Rightarrow i n i t i a l e n e r g y = E_{i} a n d f i n a l e n e r g y = E_{f} \\ 0 = m_{2} g h - m_{1} g h + \frac{1}{2} (m_{1} + m_{2}) v^{2} \\ ∴ v = \sqrt{2 g h (\frac{m_{1} - m_{2}}{m_{1} + m_{2}})} \end{array}$

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