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san4es73 [151]
2 years ago
6

Determine the gravitational potential energy, in kJ, of 3 m3 of liquid water at an elevation of 40 m above the surface of Earth.

The acceleration of gravity is constant at 9.7 m/s2 and the density of the water is uniform at 1000 kg/m3. Determine the change in gravitational potential energy if the elevation decreases by 10 m.
Physics
1 answer:
melomori [17]2 years ago
4 0

Explanation:

We will calculate the gravitational potential energy as follows.

                 P.E_{1} = mgz_{1}

       P.E_{1} = (\rho V)gz_{1}    

                    = 1000 kg/m^{3} \times 3 m^{3} \times 9.7 \times 40 m

                    = 1164000 J

or,                = 1164 kJ         (as 1 kJ = 1000 J)

Now, we will calculate the change in potential energy as follows.

             \Delta P.E = mg(z_{2} - z_{1})

                         = \rho \times V \times g (z_{2} - z_{1})

                         = 1000 \times 3 \times 9.7 (10 - 40)m

                         = -873000 J

or,                      = -873 kJ

Thus, we can conclude that change in  gravitational potential energy is -873 kJ.

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Dimensional analysis is where you just look at the units and see how they fit within each other.

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