Question

A shipping crate to be transported by cargo ship is raised 26 m above the dock. If its GPE

is 266,375 J, what is the crate's mass?

Answer 1

Approximately
`1.0* 10^(3)\; \rm kg` (assuming that
`g = 9.8\; \rm m \cdot s^(-2)`.)

Step-by-step explanation:

Consider an object of mass
`m` and (relative) height
`h`.

The gravitational potential energy (GPE) of this object would be
`{\rm GPE} = m \cdot g \cdot h` (where
`g` denotes the gravitational field strength. Typically,
`g = 9.8\; \rm N \cdot kg^(-1)` near the surface of the earth.)

For the shipping crate in this question:

• 
  `{\rm GPE} = 266,\!375\; \rm J`,
• 
  `g = 9.8\; \rm N \cdot kg^(-1)` (near the surface of the earth,) and
• 
  `h = 26\; \rm m`.

Rearrange the equation
`{\rm GPE} = m \cdot g \cdot h` to find an equation for
`m`:

`\begin{aligned}m &= \frac{{\rm GPE}}{g \cdot h} \\ &= (266,\!375\; \rm J)/(9.8\; \rm N \cdot kg^(-1) * 26\; \rm m)\\ &= (266,\!375\; \rm N \cdot m)/(9.8\; \rm N \cdot kg^(-1) * 26\; \rm m) \\ &\approx 1.0* 10^(3)\; \rm kg\end{aligned}`.

Hence, the mass of this shipping crate is approximately
`1.0* 10^(3)\; \rm kg`.