Question

A rock with a mass of 16 kilograms is put aboard an airplane in New York City and flown to Boston. How much work does the gravitational field of the earth do on the rock

Answer 1

The work done by the gravitational field of the earth on the rock is 9.998 x 10⁸ J.

The given parameter include:

the mass of the object, m₁ = 16 kg

Note: the mass of the earth, m₂ = 5.972 x 10²⁴ kg

• The work done by the gravitational field of the earth is given as;

Work done = gravitational force (F) x radius of the earth (R)

$Work \ done = \frac{Gm_1m_2}{R^2} \times R\\\\Work \ done = \frac{Gm_1m_2}{R} \\\\where;\\\\R \ is \ the \ radius \ of \ the \ earth = 6,378 \ km = 6,378,000 \ m\\\\G \ is \ the \ universal \ gravitation \ constant = 6.674 \times 10^{-11} Nm^2/kg^2\ \\\\Work \ done = \frac{(6.674 \times 10^{-11} ) \times (5.972\times 10^{24}) \times (16)}{6,378,000 } \\\\Work \ done = 9.998 \times 10^{8} \ J$

Therefore, the work done by the gravitational field of the earth on the rock is 9.998 x 10⁸ J.

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