Final answer:
The distance from the center of Earth at which a 12 kg object has a weight of 15 N is approximately 6.46 million meters.
Step-by-step explanation:
The weight of an object is given by the equation:
Weight = mass * gravitational acceleration
Given that the weight of the 12 kg object is 15 N, we can use this equation to find the gravitational acceleration:
15 N = 12 kg * g
Solving for g:
g = 15 N / 12 kg = 1.25 m/s^2
We can now use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by:
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 objects, and r is the distance between their centers.
In this case, one of the masses is the mass of the Earth (5.971x10^24 kg) and the other mass is the 12 kg object. We can rearrange the equation to solve for r:
r = sqrt(G * m1 * m2 / F)
Plugging in the values:
r = sqrt((6.67x10^-11 Nm^2/kg^2) * (5.971x10^24 kg) * (12 kg) / 15 N) = 6.46x10^6 m
Therefore, the distance from the center of the Earth at which the 12 kg object has a weight of 15 N is approximately 6.46 million meters.