Question

From the law of universal gravitation, the following gravitational forces have been calculated: Earth and large ball = 0.882 N, Earth and small ball = 0.049 N, Large ball and feather = 2.41 x 10⁻¹⁴ N. Use the formula for the law of universal gravitation to calculate the gravitational force between the large ball and the small ball. Assume the distance between them is 0.5 m. The mass of the objects are: Small ball = 5.0 x 10⁻³ kg, Large ball = 9.0 x 10⁻² kg, Feather = 1.0 x 10⁻³ kg. Show your work and give the answer with the correct units.

Answer 1

The gravitational force between the large ball and the small ball, using Newton's Universal Law of Gravitation and given values for mass and distance, is calculated to be 6.01 × 10-9 Newtons.

Step-by-step explanation:

The student is asked to use Newton's Universal Law of Gravitation to calculate the gravitational force between the large and small balls. According to the formula F = Gm1m2/r2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of two objects.

Given that the gravitational constant (G) is 6.674 × 10-11 N·m²/kg², the mass of the small ball (m1) is 5.0 × 10-3 kg, the mass of the large ball (m2) is 9.0 × 10-2 kg, and the distance (r) is 0.5 m, we can calculate the gravitational force between them:

F = (6.674 × 10-11 N·m²/kg²) × (5.0 × 10-3 kg) × (9.0 × 10-2 kg) / (0.5 m)2

After calculating, we find that the gravitational force F is :

F = 6.01 × 10-9 N

Therefore, the gravitational force between the large ball and the small ball, when separated by a distance of 0.5 m, is 6.01 × 10-9 Newtons.