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/s².]

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Solution

Step 1: Given data:
The vertical height to which the block is raised is h = 8 m.
Acceleration due to gravity is g = 10 m/s²
Energy spent is equivalent to the potential energy stored in the box P.E. = 64000 J.
Step 2: Formula used:
According to the formula,
Potential energy = mass x acceleration due to gravity x vertical height
P.E. = m x g x h
m = $\frac{P . E}{g x h}$
Where m is the mass of the box.
Step 3: Calculation:
Finding the mass of the box:
Substituting the known values,
m = $\frac{64000 J}{(10 m / s^{2}) x (8 m)}$ = $\frac{64000}{80}$ = 800 kg
Thus, the mass of the box is 800 kg.

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