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:
[tex]\Delta W = \Delta U_{g}[/tex] (1)
Where:
[tex]\Delta W[/tex] - Work.
[tex]\Delta U_{g}[/tex] - Gravitational potential energy.
The work is equal to the following formula:
[tex]\Delta W = n\cdot \rho \cdot V \cdot g \cdot \Delta h[/tex] (2)
Where:
[tex]n[/tex] - Number of bottles, dimensionless.
[tex]\rho[/tex] - Density of water, measured in kilograms per cubic meter.
[tex]V[/tex] - Volume, measured in cubic meters.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]\Delta h[/tex] - Vertical displacement, measured in meters.
If we know that [tex]n = 100[/tex], [tex]\rho = 1000\,\frac{kg}{m^{3}}[/tex], [tex]V = 0.02\,m^{3}[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta h = 1\,m[/tex], then the work done is:
[tex]\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)[/tex]
[tex]\Delta W = 19614\,J[/tex]
The work done by picking up 100 20-L bottles and raising it vertically 1 meter is 19614 joules.
