Simple Net Gravitation problem

In summary, the question asks for the net gravitational force on one mass due to three other identical masses arranged in a square. The proper answer is 8.2 x 10^-3 N and to solve it, the vector sum of the three individual forces must be calculated, taking into account direction and superposition.
  • #1
godtripp
54
0
Here's the question.

"Four identical masses of 800 kg each are placed at the corners of a square whose side length is 10.0 cm. What is the net gravitational force on one of the masses due to the other three?"

for convenience, I replaced mass with "M" and the distance with "d"

So, I figure that Net Force is equal to the sum of the gravitational forces between the three masses.

So if we call the force between the vertical mass and horizontal mass F1 and F2 respectively then F1=F2

Calculating out F1 gives me F= (GM^2)/(d^2)

And by Pythagorean the distance to the horizontal mass is d[tex]\sqrt{2}[/tex]

so F3= (GM^2)/(2d^2)

So net force FN = 2F1+F3

or (5GM^2)/(2d^2).

However this is not the proper answer...


Proper answer is 8.2 x 10^-3 N

Can someone help me with this please? Thank you!
 
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  • #2
Hi godtripp,

godtripp said:
Here's the question.

"Four identical masses of 800 kg each are placed at the corners of a square whose side length is 10.0 cm. What is the net gravitational force on one of the masses due to the other three?"

for convenience, I replaced mass with "M" and the distance with "d"

So, I figure that Net Force is equal to the sum of the gravitational forces between the three masses.

Remember that here the net force is a vector sum, so it will be the vector sum of the three individual forces.

So if we call the force between the vertical mass and horizontal mass F1 and F2 respectively then F1=F2

Their magnitudes are equal, but their directions are different.

Calculating out F1 gives me F= (GM^2)/(d^2)

And by Pythagorean the distance to the horizontal mass is d[tex]\sqrt{2}[/tex]

so F3= (GM^2)/(2d^2)

So net force FN = 2F1+F3

When you perform the vector sum, there will be some cancellation occurring between F1 and F2 (so you cannot simply add the magnitudes together). Do you see what to do?

or (5GM^2)/(2d^2).

However this is not the proper answer...


Proper answer is 8.2 x 10^-3 N

Can someone help me with this please? Thank you!
 
  • #3
Thank you so much for your reply. I totally neglected that the net force would have superposition.

Thanks again
 
  • #4
godtripp said:
Thank you so much for your reply. I totally neglected that the net force would have superposition.

Thanks again

Sure, glad to help!
 

1. What is the formula for calculating net gravitational force?

The formula for calculating net gravitational force is F = G(m1m2)/r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.

2. How do I determine the direction of the net gravitational force?

The direction of the net gravitational force is always towards the center of mass of the system. This means that the force will be directed from one object towards the other, along the line connecting their centers of mass.

3. Can net gravitational force be negative?

Yes, net gravitational force can be negative. This means that the force is acting in the opposite direction of the positive direction chosen for the calculation. It does not change the magnitude of the force, only its direction.

4. How does distance affect net gravitational force?

As distance between two objects increases, the net gravitational force between them decreases. This is because the force is inversely proportional to the square of the distance between the objects. Therefore, the farther apart the objects are, the weaker the gravitational force between them.

5. What is the difference between net gravitational force and gravitational potential energy?

Net gravitational force is a vector quantity that represents the force between two objects due to their masses and the distance between them. Gravitational potential energy, on the other hand, is a scalar quantity that represents the energy associated with the position of an object in a gravitational field. While net gravitational force is a force that acts on objects, gravitational potential energy is the energy an object possesses due to its position in a gravitational field.

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