Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of the gravitational force is 8.92 x 10-11 N.
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To find the distance between two billiard balls, given their masses and the magnitude of the gravitational force between them, you can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force,
G is the gravitational constant (which is approximately 6.67430 × 10-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects,
and r is the distance between the centers of the two objects.
In this case, you are given the masses of the two billiard balls (0.300 kg and 0.400 kg) and the magnitude of the gravitational force (8.92 x 10^-11 N). You need to find the distance between the two billiard balls (r).
Rearranging the equation, we can solve for r:
r = sqrt((G * m1 * m2) / F)
Plugging in the given values:
r = sqrt((6.67430 × 10^-11 N m^2/kg^2 * 0.300 kg * 0.400 kg) / (8.92 × 10^-11 N))
Calculating the equation:
r = sqrt(0.00080001439248 m²) / (8.92 × 10^-11 N))
Converting the scientific notation:
r = sqrt(8.9661031175 × 10^-6 m²) / (8.92 × 10^-11 N)
Taking the square root:
r = 0.00299420345 m / (8.92 × 10^-11 N)
Calculating the division:
r ≈ 3.36219739 × 10^10 m / N
Therefore, the distance between the two billiard balls is approximately 3.36 x 10^10 meters, or 33.6 billion kilometers.