The gravitational force of attraction between two students sitting at their desks in physics class is 2.30 x 10-8 N. If one student has a mass of 45.0 kg and the other has a mass of 55.0 kg, how far apart are the students sitting? Round your answer to the nearest tenth of a meter.
We can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two students, and r is the distance between them.
Plugging in the given values, we get:
2.30 x 10^-8 N = (6.67 x 10^-11 N*m^2/kg^2) * (45.0 kg * 55.0 kg) / r^2
Solving for r, we get:
r = sqrt((6.67 x 10^-11 N*m^2/kg^2) * (45.0 kg * 55.0 kg) / (2.30 x 10^-8 N)) = 0.63 m
Therefore, the students are sitting about 0.6 meters (or 63 centimeters) apart.
To determine the distance between the two students, we can use Newton's law of universal gravitation, which is given by the formula:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force of attraction,
G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two students, and
r is the distance between the students.
Plugging in the given values:
F = 2.30 x 10^-8 N,
m1 = 45.0 kg,
m2 = 55.0 kg, and
G = 6.67430 x 10^-11 N m^2 / kg^2,
we can rearrange the formula to solve for r:
r^2 = G * (m1 * m2) / F
r^2 = (6.67430 x 10^-11 N m^2 / kg^2) * (45.0 kg * 55.0 kg) / (2.30 x 10^-8 N)
Now, we can calculate r:
r^2 = 7282.826087 m^2
Taking the square root of both sides, we get:
r ≈ 85.3 m (rounded to the nearest tenth of a meter)
Therefore, the students are approximately 85.3 meters apart.