Gravity and superpostion of two spheres

In summary, the conversation discusses a problem involving a lead sphere with a hollowed-out center and a smaller sphere placed at a distance from the center of the lead sphere. The task is to calculate the gravitational force between the two spheres. The conversation also includes discussions about inconsistencies in the given mass and density of the spheres and the need to recalculate the density based on the given size and mass. There is also mention of using an HP 300s+ calculator and checking calculations for accuracy.
  • #1
J-dizzal
394
6

Homework Statement


The figure shows a spherical hollow inside a lead sphere of radius R = 4.6 m; the surface of the hollow passes through the center of the sphere and “touches” the right side of the sphere. The mass of the sphere before hollowing was M = 245 kg. With what gravitational force does the hollowed-out lead sphere attract a small sphere of mass m = 20 kg that lies at a distance d = 14 m from the center of the lead sphere, on the straight line connecting the centers of the spheres and of the hollow?
20150719_171355_zps0voqohjg.jpg

Homework Equations

The Attempt at a Solution


20150719_194518_zpscns6hjbm.jpg


when i find the mass of the "hollowed out" sphere its much larger than the larger sphere. I don't know how else to approach this problem.
 
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  • #2
The mass of the sphere is inconsistent with its given diameter and the density of lead. I would ignore the given "lead" and calculate the density based on the given size and mass.
 
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  • #3
mfb said:
The mass of the sphere is inconsistent with its given diameter and the density of lead. I would ignore the given "lead" and calculate the density based on the given size and mass.
I updated my original photo with my calculations. Would the total force be the force of the full sphere minus the force of the "hollow" sphere? F=F1-F2? I got the wrong answer not sure where i went wrong.
 
  • #4
Your volume and density calculations don't look right to me. Can you recheck them?
 
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  • #5
gneill said:
Your volume and density calculations don't look right to me. Can you recheck them?
Thank you! I am having problem getting adjusted to an hp 300s+, I often have to double check its picking up all the buttons i press.
 
  • #6
J-dizzal said:
I updated my original photo with my calculations. Would the total force be the force of the full sphere minus the force of the "hollow" sphere? F=F1-F2?
Right (if you take both F1 and F2 to be positive).
A quick check: is your mass ratio 1 to 8?
The ratio of forces should be a bit smaller than that (1 to 7.something or 6.something) as the smaller sphere is a bit closer. If that is not true, something is wrong.
 

1. What is the formula for calculating the gravitational force between two spheres?

The formula for calculating the gravitational force between two spheres is F = G * (m1 * m2)/d^2, where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two spheres, and d is the distance between their centers.

2. How does the distance between two spheres affect the gravitational force between them?

The gravitational force between two spheres is inversely proportional to the square of the distance between their centers. This means that as the distance between the spheres increases, the gravitational force decreases.

3. Can the superposition principle be applied to the gravitational force between two spheres?

Yes, the superposition principle can be applied to the gravitational force between two spheres. This means that the total force between two spheres is equal to the vector sum of the individual forces between each pair of masses.

4. How does the mass of a sphere affect the gravitational force between two spheres?

The gravitational force between two spheres is directly proportional to the product of their masses. This means that as the mass of one or both spheres increases, the gravitational force between them also increases.

5. What is the difference between the gravitational force between two spheres and the gravitational force between two point masses?

The gravitational force between two spheres takes into account the size and distribution of the masses, while the gravitational force between two point masses assumes that the masses are infinitely small and assume a point-like shape. In most cases, the difference in the calculated forces is negligible, but in cases where the sizes of the masses are significant, the gravitational force between two spheres will be more accurate.

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