A large box is raised to a vertical height of $8 m$ , when the energy spent is $64, 000 J$ . Calculate the mass of the box. [ Take $g = 10 m s^{- 2}$ ]

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Solution

Step 1: Given data:
Height, $h = 8 m$
Mass of water, $m = ?$ (To be calculated)
Acceleration due to gravity, $g = 10 m s^{- 2}$
Potential Energy, $P . E . = 64, 000 J$
Mathematical expression for potential energy:
$P o t e n t i a l E n e r g y = m a s s \times a c c e l e r a t i o n d u e t o g r a v i t y \times h e i g h t ∴ P . E . = m \times g \times h$
Step 2: By putting the values in the above expression, we get
$P . E . = m \times g \times h 64, 000 J = m \times 10 m / s^{2} \times 8 m ∴ m = \frac{64, 000}{10 \times 8} = 800 m$
Hence, mass of the box is $800 k g$ .

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