Two balls, each with a mass of 0.803 kg,
exert a gravitational force of 8.27 × 10
−11
N
on each other.
How far apart are the balls? The value
of the universal gravitational constant is
6.673 × 10
−11
N m2
/kg
2
.
Answer in units of
meters (m).
To find the distance between the two balls, we can use the equation for the gravitational force between two objects:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force,
G is the universal gravitational constant (6.673 × 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 the two objects.
Rearranging the equation to solve for r, we have:
r = sqrt((G * m1 * m2) / F)
Plugging in the given values:
m1 = m2 = 0.803 kg
F = 8.27 × 10^-11 N
G = 6.673 × 10^-11 N m^2/kg^2
We can substitute these values into the equation to find the distance between the balls:
r = sqrt((6.673 × 10^-11 N m^2/kg^2 * 0.803 kg * 0.803 kg) / (8.27 × 10^-11 N))
Simplifying the expression:
r = sqrt(3.217 x 10^-21 m^3/kg^2) / (8.27 x 10^-11 N))
Taking the square root of the numerator and dividing by the denominator:
r = sqrt(3.217 x 10^-21) / 8.27 × 10^-11
Using a calculator:
r ≈ 7.02 × 10^-6 m
Therefore, the distance between the two balls is approximately 7.02 × 10^-6 meters (m).