Three very small spheres of mass 3.00 kg, 5.00 kg, and 3.00 kg are located on a straight line in space away from everything else. The first one is at a point between the other two, 13.0 cm to the right of the second and 24.0 cm to the left of the third. Compute the net gravitational force it exerts.
To compute the net gravitational force exerted by the three spheres, we need to calculate the gravitational force between each pair of spheres and then sum them up.
The gravitational force between two spheres can be calculated using Newton's Law of Universal Gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the spheres.
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2).
m1 and m2 are the masses of the spheres.
r is the distance between the centers of the spheres.
Let's calculate the forces step by step:
1. Force between the first and second sphere:
m1 = 3.00 kg
m2 = 5.00 kg
r1 = 13.0 cm = 0.13 m
F1 = (G * m1 * m2) / r1^2
2. Force between the first and third sphere:
m1 = 3.00 kg
m3 = 3.00 kg
r2 = 24.0 cm = 0.24 m
F2 = (G * m1 * m3) / r2^2
3. Force between the second and third sphere:
m2 = 5.00 kg
m3 = 3.00 kg
r3 = (r1 + r2) = 0.13 m + 0.24 m = 0.37 m
F3 = (G * m2 * m3) / r3^2
Finally, we can compute the net gravitational force by summing up the individual forces:
Net force = F1 + F2 + F3
Now, let's calculate the forces and find the net force.