what is the distance between centers of a baseball of mass 0.145 kg and a bowling ball of mass 5.5 kg, such that the gravitational force between them is 1.3 * 10^6N
To calculate the distance between the centers of two objects given the gravitational force between them, you can use Newton's law of universal gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximated as 6.67430 x 10^-11 N * (m/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're given the gravitational force (F) between the baseball and the bowling ball, which is 1.3 * 10^6 N, and the masses of the two objects (m1 = 0.145 kg and m2 = 5.5 kg).
To find the distance (r), we rearrange the formula:
r = sqrt((G * m1 * m2) / F)
Now we can substitute in the given values and solve for r:
r = sqrt((6.67430 x 10^-11 N * (m/kg)^2 * 0.145 kg * 5.5 kg) / (1.3 * 10^6 N))
Simplifying further:
r = sqrt(0.52086475) ≈ 0.721 meters
Therefore, the distance between the centers of the baseball and the bowling ball is approximately 0.721 meters.