Answer:
Approximately [tex]1.0\times 10^{3}\; \rm kg[/tex] (assuming that [tex]g = 9.8\; \rm m \cdot s^{-2}[/tex].)
Explanation:
Consider an object of mass [tex]m[/tex] and (relative) height [tex]h[/tex].
The gravitational potential energy (GPE) of this object would be [tex]{\rm GPE} = m \cdot g \cdot h[/tex] (where [tex]g[/tex] denotes the gravitational field strength. Typically,[tex]g = 9.8\; \rm N \cdot kg^{-1}[/tex] near the surface of the earth.)
For the shipping crate in this question:
Rearrange the equation [tex]{\rm GPE} = m \cdot g \cdot h[/tex] to find an equation for [tex]m[/tex]:
[tex]\begin{aligned}m &= \frac{{\rm GPE}}{g \cdot h} \\ &= \frac{266,\!375\; \rm J}{9.8\; \rm N \cdot kg^{-1} \times 26\; \rm m}\\ &= \frac{266,\!375\; \rm N \cdot m}{9.8\; \rm N \cdot kg^{-1} \times 26\; \rm m} \\ &\approx 1.0\times 10^{3}\; \rm kg\end{aligned}[/tex].
Hence, the mass of this shipping crate is approximately [tex]1.0\times 10^{3}\; \rm kg[/tex].
