Question

Two identical isolated particles each of mass 2.00kg, are separated by a distance of 30.0 cm.what is the magnitude of the gravitational force exerted one particle on the other?

Answer 1

The gravitational force between two objects can be calculated using Newton's law of universal gravitation:

F = G * (m1 * m2) / r2

where:

F is the force between the masses,

G is the gravitational constant (6.674 x 10-11 N(m/kg)2),

m1 and m2 are the two masses, and

r is the distance between the centers of the two masses.

In this case, m1 = m2 = 2.00 kg and r = 30.0 cm = 0.30 m. Substituting these values into the equation gives:

F = (6.674 x 10-11 N(m/kg)2) * (2.00 kg * 2.00 kg) / (0.30 m)2

Solving this equation gives the magnitude of the gravitational force.

Step-by-step explanation:

The gravitational force is derived from Newton’s Second Law, F=ma, where F is the force of gravity in Newtons, m is the mass of the object in kilograms, and a is the acceleration due to gravity on Earth, 9.81 m/s2 . When the formula is used specifically to solve for the weight of an object, it appears as W=mg. Weight is always measured in force units Newtons, m is the mass of the object in kilograms, and g is the gravitational strength on the planet in N/kg or m/s2 (gEarth = 9.81 m/s2).

Answer 2

The magnitude of the gravitational force between the two identical particles, each with a mass of
`\(2.00 \, \text{kg}\)` and separated by
`\(30.0 \, \text{cm}\)`, is approximately
`\(8.89 \, \text{N}\).`

The gravitational force (F) between two masses (
`\(m_1\) and \(m_2\)`) separated by a distance (r) is given by Newton's law of gravitation:

`\[ F = (G \cdot m_1 \cdot m_2)/(r^2) \]`

Given two identical masses (
`\(m_1 = m_2 = 2.00 \, \text{kg}\)`) and a separation distance (
`\(r = 30.0 \, \text{cm} = 0.3 \, \text{m}\)`), we can substitute these values into the formula:

`\[ F = \frac{(6.67 * 10^(-11) \, \text{N}\cdot\text{m}^2/\text{kg}^2) \cdot (2.00 \, \text{kg})^2}{(0.3 \, \text{m})^2} \]`

Calculate the result:

`\[ F \approx 8.89 \, \text{N} \]`

The magnitude of the gravitational force exerted by one particle on the other is approximately
`\(8.89 \, \text{N}\).`