Three very small spheres are located along a straight line in space far away from everything else. The first one (with a mass of 2.59 kg) is at a point between the other two, 10.50 cm to the right of the second one (with a mass of 5.03 kg), and 20.40 cm to the left of the third one (with a mass of 6.03 kg). Calculate the magnitude of the net gravitational force it experiences.
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To calculate the magnitude of the net gravitational force experienced by the first sphere, we need to find the individual gravitational forces between it and the other two spheres and then sum them up.
The formula to calculate the gravitational force between two objects is given by Newton's Law of Universal Gravitation:
F = G * ((m1 * m2) / r^2)
where F is the gravitational force, G is the gravitational constant (approximately 6.674 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Let's calculate the force between the first sphere and the second sphere:
m1 = 2.59 kg
m2 = 5.03 kg
r = 10.50 cm = 0.1050 m
F1-2 = G * ((m1 * m2) / r^2)
Now let's calculate the force between the first sphere and the third sphere:
m1 = 2.59 kg
m3 = 6.03 kg
r = 20.40 cm = 0.2040 m
F1-3 = G * ((m1 * m3) / r^2)
Finally, we can calculate the net gravitational force by summing up the individual forces:
F_net = F1-2 + F1-3
With these values, we can calculate the magnitude of the net gravitational force experienced by the first sphere.