An object with a mass of 200.0 kg is 500.0 km above the surface of the Earth. The magnitude of the force of gravity on the 200.0 kg mass is (G = 6.67 × 10^-11 N m²/kg², the radius of the Earth is 6.38 × 10⁶ m, and the mass of the Earth is 5.98 × 10²⁴ kg) A) 2.02 × 10³ N. B) 1.69 × 10³ N. C) 1.42 × 10³ N. D) 1.28 × 10³ N. E) 1.05 × 10³ N.

Question

Quizplus · Accepted Answer

The force of gravity on the object can be calculated using the formula:

F = G * (m1 * m2) / r^2

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 is the mass of the object (200.0 kg), m2 is the mass of the Earth (5.98 × 10^24 kg), and r is the distance from the center of the Earth to the object (radius of the Earth + height of object above the surface of the Earth):
r = 6.38 × 10^6 m + 5.00 × 10^5 m = 6.88 × 10^6 m

Substituting these values into the formula:
F = (6.67 × 10^-11 N m^2/kg^2) * (200.0 kg) * (5.98 × 10^24 kg) / (6.88 × 10^6 m)^2
F = 1.69 × 10^13 N

Therefore, the magnitude of the force of gravity on the 200.0 kg mass is 1.69 × 10^13 N. The correct answer is B).

An Object with a Mass of 200