Answer :
To calculate the work done to lift water, we need to use the formula for gravitational work, which is given by:
[tex]\text{Work} = \text{Force} \times \text{Distance}[/tex]
In this context, the force is the weight of the water, which can be calculated using the formula:
[tex]\text{Force} = \text{Mass} \times \text{Gravity}[/tex]
Where:
- The mass of the water can be found by multiplying its volume by the density of water. Typically, the density of water is approximately 1000 kg/m³.
- Gravity is approximately 9.81 m/s² on Earth.
Step-by-step calculation:
Find the mass of the water:
The volume of water given is 5 cubic meters. Thus, the mass [tex]m[/tex] is:
[tex]m = \text{Volume} \times \text{Density} = 5 \, \text{m}^3 \times 1000 \, \text{kg/m}^3 = 5000 \, \text{kg}[/tex]Calculate the force:
[tex]\text{Force} = \text{Mass} \times \text{Gravity} = 5000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 49050 \, \text{N}[/tex]
Compute the work done:
We need to lift this mass to a height of 10 meters.
[tex]\text{Work} = \text{Force} \times \text{Distance} = 49050 \, \text{N} \times 10 \, \text{m} = 490500 \, \text{J}[/tex]
Therefore, the magnitude of the work needed to lift 5 cubic meters of water to a height of 10 meters is 490,500 joules.
