Two balls, each with a mass of 0.844 kg, exert a gravitational force of [tex]8.45 \times 10^{-11} \, \text{N}[/tex] on each other. How far apart are the balls?
The value of the universal gravitational constant is [tex]6.673 \times 10^{-11} \, \text{N m}^2/\text{kg}^2[/tex].
Answer (3)
The Universal Gravitation law is F=GMm/d^2 So: 8.45x10^-11=6,673x10^-11x0,844x0,844/d^2 d^2=1,78, so finale d=1,33m
The separation distance between the two balls, each with a mass of 0.844 kg and exerting a gravitational force of 8.45 × 10^(-11) N on each other, is approximately 2 micrometers.
The gravitational force between two masses is given by Newton's law of gravitation, expressed as F = G * m1 * m2 / r^2, where F is the gravitational force, G is the universal gravitational constant, m1 and m2 are the masses, and r is the separation distance between the masses.
In this case, both masses (m1 and m2) are 0.844 kg, and the gravitational force (F) is 8.45 × 10^(-11) N. The value of the universal gravitational constant (G) is 6.673 × 10^(-11) N m^2/kg^2.
Rearranging the formula to solve for the separation distance (r):
r = square root of (G * m1 * m2 / F)
Substituting the given values:
r = square root of ((6.673 × 10^(-11) N m^2/kg^2) * (0.844 kg) * (0.844 kg) / (8.45 × 10^(-11) N))
Calculating this expression gives the separation distance r.
r ≈ square root of (3.99 × 10^(-11) m^2)
r ≈ 2 × 10^(-6) m
Therefore, the two balls are approximately 2 × 10^(-6) meters or 2 micrometers apart.
Using Newton's law of gravitation, the distance between the two balls, each with a mass of 0.844 kg, is calculated to be approximately 0.75 meters, which is 750,500 micrometers apart.
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