The largest sea turtle found in the United States had a mass of 860.24 kg. If the gravitational potential energy associated with the turtle as it was being lifted onto a ship was 20,320.7 J, how high above the water was the turtle when it was lifted?

Question

Mathematics

Randy Sanford

1 October, 15:44

The largest sea turtle found in the United States had a mass of 860.24 kg. If the gravitational potential energy associated with the turtle as it was being lifted onto a ship was 20,320.7 J, how high above the water was the turtle when it was lifted?

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Colby Krueger · Answer 1

2.4080 meters.

Remember that the definition of work is force over distance. And that the gravitational potential energy that the turtle has will exactly match the work performed in lifting it. So have the following variables

Mass = 860.24 kg

Work = 20320.7 J = 20320.7 kg*m^2/s^2

Gravitational acceleration = 9.81 m/s^2

And we wish to get an answer in meters. So we need to multiply and divide the three numbers we have with all their related units and derive an answer with the unit of m. We can cancel out most of the units by dividing the work by the gravitational acceleration, so

20320.7 kg*m^2/s^2 / 9.81 m/s^2 = 2071.427 kg*m

Now we can cancel out the kg unit by dividing by the mass of the turtle. So

2071.427 kg*m / 860.24 kg = 2.407964 m

Rounding to 5 significant figures gives 2.4080 meters.