Question

You get a job delivering water. You calculate how much work is done picking up each 20 L bottle of

Answer 1

Answer:

The work done by picking up 100 20-L bottles and raising it vertically 1 meter is 19614 joules.

Explanation:

By the Work-Energy Theorem, the work needed to raise vertically 100 bottles of water is equal to the gravitational potential energy, units for work and energy are in joules:

$\Delta W = \Delta U_{g}$ (1)

Where:

$\Delta W$ - Work.

$\Delta U_{g}$ - Gravitational potential energy.

The work is equal to the following formula:

$\Delta W = n\cdot \rho \cdot V \cdot g \cdot \Delta h$ (2)

Where:

$n$ - Number of bottles, dimensionless.

$\rho$ - Density of water, measured in kilograms per cubic meter.

$V$ - Volume, measured in cubic meters.

$g$ - Gravitational acceleration, measured in meters per square second.

$\Delta h$ - Vertical displacement, measured in meters.

If we know that $n = 100$, $\rho = 1000\,\frac{kg}{m^{3}}$, $V = 0.02\,m^{3}$, $g = 9.807\,\frac{m}{s^{2}}$ and $\Delta h = 1\,m$, then the work done is:

$\Delta W = (100)\cdot \left(1000\,\frac{kg}{m^{3}} \right)\cdot (0.02\,m^{3})\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (1\,m)$

$\Delta W = 19614\,J$

The work done by picking up 100 20-L bottles and raising it vertically 1 meter is 19614 joules.