The gravitational force between two students is 3.20 x 10^-8N if one student has a mass of 50,0kg and the other has a mass of 60.0kg, how far apart are the students sitting?
To find the distance between the students' sitting positions, 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 (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two students
r is the distance between the students
Given:
F = 3.20 x 10^-8 N
m1 = 50.0 kg
m2 = 60.0 kg
We need to solve for r.
Plugging in the values into the formula, we can rearrange it to solve for r:
r^2 = (G * m1 * m2) / F
r^2 = (6.67430 × 10^-11 N m^2/kg^2 * 50.0 kg * 60.0 kg) / (3.20 x 10^-8 N)
r^2 = 10.00625 m^2
Taking the square root of both sides, we find:
r = √10.00625
r ≈ 3.16 meters
Therefore, the students are sitting approximately 3.16 meters apart.
To determine the distance between the two students, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force between two objects,
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 objects,
and r is the distance between the centers of the two objects.
In this case, we are given the gravitational force (F = 3.20 x 10^-8 N), as well as the masses of the two students (m1 = 50.0 kg and m2 = 60.0 kg). We need to solve for r, the distance between the students.
Rearranging the formula, we have:
r = sqrt((G * m1 * m2) / F)
Now, let's plug in the values into the equation:
r = sqrt((6.67430 x 10^-11 N m^2 / kg^2 * 50.0 kg * 60.0 kg) / (3.20 x 10^-8 N))
After performing the calculations, the distance between the students would be approximately 3.54 meters.