Two metal spheres, each weighing 24.0 kg are placed 0.0500 m apart. Calculate the magnitude of the gravitational force the two spheres exert on each other.
force= GM1*M2/distance^2
To calculate the magnitude of the gravitational force between the two metal spheres, we can use Newton's Law of Universal Gravitation. The formula is as follows:
F = (G * m1 * m2) / r^2
Where:
- F is the magnitude of the gravitational force
- G is the gravitational constant (6.67430 x 10^-11 N*m^2/kg^2)
- m1 and m2 are the masses of the two spheres
- r is the distance between the two spheres
In this case, the masses of both spheres are given as 24.0 kg each, and the distance between them is 0.0500 m.
Plugging these values into the formula, we get:
F = (6.67430 x 10^-11 N*m^2/kg^2) * (24.0 kg) * (24.0 kg) / (0.0500 m)^2
Calculating the numerator, (24.0 kg) * (24.0 kg) = 576 kg^2.
Next, we calculate the denominator, (0.0500 m)^2 = 0.0025 m^2.
Finally, substituting these values into the equation, we have:
F = (6.67430 x 10^-11 N*m^2/kg^2) * 576 kg^2 / 0.0025 m^2
F = (6.67430 x 10^-11) * 576 / 0.0025 N
F ≈ 1.529 x 10^-8 N
Therefore, the magnitude of the gravitational force the two spheres exert on each other is approximately 1.529 x 10^-8 N.