The gravitational force of attraction between two students sitting at their desks in physics class is 2.34 ✕ 10^-8 N. If one student has a mass of 45.0 kg and the other student has a mass of 61.6 kg, how far apart are the students sitting?
the letter are what again
G is Universal gravitational constant
In these SCI units it is about
6.67 * 10-11 m^3 /(kg s^2)
M is one mass in kg
m is other mass in kg
d is distance between the centers of gravity of the two masses
F is gravitational force in Newtons
hmm this would make the answer
Well, I must say, those students must have some extraordinary gravitational pull to require such precise calculations! But fear not, for Clown Bot is here to help!
To find the distance between the students, we need to use Newton's law of universal gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where F is the force of attraction, 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, and r is the distance between them.
Now, let's plug in the given values and solve for r:
2.34 ✕ 10^-8 N = (6.67430 × 10^-11 N m^2 / kg^2) * (45.0 kg) * (61.6 kg) / r^2
To make things a bit easier, let me simplify that equation for you:
2.34 ✕ 10^-8 N = (41136.84 N m^2 / kg^2) / r^2
Let's cancel out the units and solve for r:
r^2 = (41136.84 N m^2 / kg^2) / (2.34 ✕ 10^-8 N)
r^2 ≈ 1.76 ✕ 10^15 m^2
Taking the square root, we get:
r ≈ 1.33 ✕ 10^8 m
So, according to my calculations, these two students are sitting approximately 133 million meters apart!
Now, I have to warn you, that's quite a distance for a physics class! The teacher might need binoculars! But hey, at least they won't be able to copy each other's homework easily!
To find the distance between the two students sitting, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two students (given as 2.34 × 10^-8 N),
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2),
m1 and m2 are the masses of the two students (45.0 kg and 61.6 kg, respectively),
and r is the distance between the two students (which we need to find).
Rearranging the equation to solve for r:
r = sqrt((G * m1 * m2) / F)
Now we can substitute the given values into the equation:
r = sqrt((6.67430 × 10^-11 m^3/kg/s^2 * 45.0 kg * 61.6 kg) / (2.34 × 10^-8 N))
Calculating this equation, we get:
r ≈ 2.094 meters
Therefore, the students are sitting approximately 2.094 meters apart.
well, you know that
F = GMm/d^2
so, d^2 = GMm/F
Now just plug in your numbers.