First slide

Conservation of mechanical energy

Question

A body is projected vertically downwards with an initial velocity from a height of 10m on to a horizontal floor. During the impact it losses 50% of its energy and rebounds to the same height. The velocity of projection is $(g = 9.8 m s^{- 2})$

Moderate

A

$14 m s^{- 1}$
B

$28 m s^{- 1}$
C

$9.8 m s^{- 1}$
D

$19.6 m s^{- 1}$

Solution

$\begin{array}{l} E_{f} = \frac{1}{2} E_{i} \\ m g h = \frac{1}{2} [\frac{1}{2} m v^{2} + m g h] \\ 2 m g h = \frac{1}{2} m v^{2} + mgh \\ v = \sqrt{2 \times 9.8 \times 10} = 14 {ms}^{- 1} \end{array}$

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