Question

A distance of 2.00 mm separates two objects of equal mass. If the gravitational force between them is 0.0104 N, find the mass of each object.

Answer 1

To find the mass of each object, use the equation F = G * (m1 * m2) / r^2. Substitute the given values and solve for m1 and m2. Each object has a mass of approximately 0.079 kg.

Step-by-step explanation:

To find the mass of each object, we can use Newton's law of universal gravitation: F = G * (m1 * m2) / r^2, where F is the gravitational force, 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, the gravitational force is 0.0104 N and the distance is 2.00 mm (0.002 m). Plugging in these values, we can rearrange the equation to solve for the mass:

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

m1 = m2 = √((F * r^2) / G)

Substituting the given values:

m1 = m2 = √((0.0104 N * (0.002 m)^2) / (6.674 × 10^-11 N·m² kg²))

Simplifying the calculation:

m1 = m2 = √((4.16 × 10^-8 N·m^2) / (6.674 × 10^-11 N·m² kg²))

m1 = m2 = √(6.222 × 10^-3 kg)

m1 = m2 ≈ 0.079 kg

Therefore, each object has a mass of approximately 0.079 kg.

Answer 2

Given the distance r = 2/1000 m, the force between them F = 0.0104 N, the mass of the two object can be calculated using formula:

F = G(m1m2)/r^2 since the mass are equal F = G (m^2)/r^2

And where G = is the gravitational constant (6.67E-11 m3 s-2 kg-1)

The mass of the two objects are 24.96 kg