Two cars each have a mass of 1050 kg. If the gravitational force between them is 2.27 10-7 N, how far apart are they? G = 6.67 × 10-11 N⋅(m/kg)2A.18 mB.33 mC.5.6 mD.21 m
Question
Two cars each have a mass of 1050 kg. If the gravitational force between them is 2.27 10-7 N, how far apart are they? G = 6.67 × 10-11 N⋅(m/kg)2A.18 mB.33 mC.5.6 mD.21 m
Solution
The gravitational force between two objects can be calculated using the formula:
F = G * (m1 * m2) / r^2
where: F is the gravitational force, G is the gravitational constant (6.67 × 10^-11 N(m/kg)^2), m1 and m2 are the masses of the objects, and r is the distance between the centers of the two objects.
We can rearrange the formula to solve for r:
r = sqrt((G * m1 * m2) / F)
Substituting the given values:
r = sqrt((6.67 × 10^-11 N(m/kg)^2 * 1050 kg * 1050 kg) / 2.27 * 10^-7 N)
r = sqrt((7.396025 * 10^-5 kg^2*m^2/N) / 2.27 * 10^-7 N)
r = sqrt(0.3257 m^2)
r = 0.5708 m
So, the two cars are approximately 0.57 meters apart. This is closest to option C, 5.6 m, if we assume the question meant to ask for the distance in meters.
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