The gravitational force of attraction between two students sitting at their desks in physics class is 2.23 ✕ 10-8 N. If one student has a mass of 52.0 kg and the other student has a mass of 57.4 kg, how far apart are the students sitting?
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To find the distance between the two students sitting at their desks, we can use the formula for the gravitational force of attraction:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force of attraction (2.23 ✕ 10^-8 N),
G is the gravitational constant (approximately 6.67 ✕ 10^-11 N·m^2/kg^2),
m1 and m2 are the masses of the two students (52.0 kg and 57.4 kg, respectively), and
r is the distance between the two students (which we need to find).
Rearranging the formula, we have:
r^2 = G * (m1 * m2) / F
Now, let's substitute the given values into the equation:
r^2 = (6.67 ✕ 10^-11 N·m^2/kg^2) * (52.0 kg * 57.4 kg) / (2.23 ✕ 10^-8 N)
Let's calculate the right side of the equation:
r^2 = (6.67 ✕ 10^-11 N·m^2/kg^2) * (2984.8 kg^2) / (2.23 ✕ 10^-8 N)
≈ 8.9437441 ✕ 10^-6 m^2
To solve for r, take the square root of both sides of the equation:
r ≈ √(8.9437441 ✕ 10^-6 m^2)
≈ 9.458 meters
Therefore, the students are sitting approximately 9.458 meters apart from each other.