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:

  1. 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]

  2. 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]

  3. 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.

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Rewritten by : Barada