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What would be the distance

Problem:

Some point masses m₁ and m₂, located at a distance r =15 m from each other, are attracted to each other with a force of 13 N.
What would be the distance between these masses to attract each other with a force of 96 N?
Input your answer in N using scientific/exponential notation and 3 significant figures.

Solution:

Let's use the formula for the gravitational force between two point masses:

F = G * (m₁ * m₂) / r²
where:

F is the force between the two masses (in N)
G is the gravitational constant (6.67408 × 10⁻¹¹ N⋅m²/kg²)
m₁ and m₂ are the masses of the two objects (in kg)
r is the distance between the two objects (in m)
We can rearrange the formula to solve for r:

r = √(G * (m₁ * m₂) / F)
Plugging in the given values, we get:

r₁ = √(G * (m₁ * m₂) / F₁)
r₂ = √(G * (m₁ * m₂) / F₂)

We can see that the distance is reversely proportional to the square root of the force. Therefore, the new distance will be:

r₂ = r₁ * √(F₁ / F₂)
Plugging in the given values, we get:

r₂ = 15 m * √(13 N / 96 N)


Input to Google Search: 15 m * √(13 N / 96 N)

Google Search gives:
15 m * √((13 N) / (96 N)) =
5.51985054 meters
Therefore, the new distance between the two masses would be approximately 5.52 m.
Input to answer box 5.52E0

Gravitational Force Calculator

Enter the initial force (F₁) and the desired force (F₂) to calculate the new distance between two point masses.

Initial Force (F₁ in N):
Desired Force (F₂ in N):
Initial distance (r₁ in m):

New distance (r₂ in m):