Bill has a mass of 66.9 kg. Jane has a mass of 58.8 kg. If they are seated 2.2 m apart, how much gravitational force attracts them?
To calculate the gravitational force between Bill and Jane, we can use Newton's law of universal gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67 * 10^-11 N * m^2/kg^2),
m1 and m2 are the masses of the two objects,
r is the distance between the centers of their masses.
Let's plug in the given values:
m1 = 66.9 kg (Bill's mass)
m2 = 58.8 kg (Jane's mass)
r = 2.2 m (distance between them)
G = 6.67 × 10^-11 N * m^2/kg^2
Substituting these values into the formula, we can calculate the gravitational force:
F = (6.67 × 10^-11 N * m^2/kg^2 * 66.9 kg * 58.8 kg) / (2.2 m)^2
Simplifying further:
F = (6.67 × 10^-11 N * m^2/kg^2 * 66.9 kg * 58.8 kg) / (4.84 m^2)
Calculating the numerator:
6.67 × 10^-11 N * m^2/kg^2 * 66.9 kg * 58.8 kg = 2.77 × 10^-7 N * m^2
Now, let's substitute this value back into the equation:
F = (2.77 × 10^-7 N * m^2) / (4.84 m^2)
Calculating the final result:
F ≈ 5.72 × 10^-8 N
Therefore, the gravitational force attracting Bill and Jane is approximately 5.72 × 10^-8 Newtons.