Three Particles - Gravitational Force

In summary, the question asks for the magnitude of the net gravitational force acting on particle A, given the masses of particles B and C and their distances from particle A. The correct method is to calculate the force from B on A and the force from C on A separately, then add them together to find the total net force. Simply adding the masses and distances and plugging them into the same formula will not yield the correct result.
  • #1
Student3.41
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Homework Statement



The masses of these particles are mA = 379 kg, mB = 500 kg, and mC = 140 kg. d1 = 0.558 m and d2 = 0.279 m. Calculate the magnitude of the net gravitational force acting on particle A

(Attached Diagram of Particles.)

Homework Equations



F=Gm1m2/r^2

G=6.673x10^-11Nm^2/kg^2

The Attempt at a Solution



The question asks what is the magnitude of the g force acting on particle A. So, I added the masses of particles b and c.

Particle B and C = 640kg

F = (6.673x10^-11)(379kg)(640kg)/(0.558m+0.279m) = (0.0000162)/(0.701)= 0.0000231N (WRONG)

Then I thought particle C has no effect on the force of particle A so I just used the mass of particle A and B.

F=(6.673x10^-11)(379)(500)/(0.558)^2 = (0.0000126)/(0.346) = 0.0000364N

Then I added the Force from A-B and Force B-C...

Fa-b=0.0000364N

Fb-c=(6.673x10^-11)(500)(140)/(0.279)^2 = 0.0000600N

Therefore, 0.0000364N+0.0000600N=Fnet=0.0000964N

Can anyone help?
 

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  • #2
Find the force on A due to B on on its own then A due to C on its own.Both forces on A act in the same direction so to find the total force just add them.
 
  • #3
Hi Student3.41! :smile:
Student3.41 said:
The question asks what is the magnitude of the g force acting on particle A. So, I added the masses of particles b and c.

Particle B and C = 640kg

F = (6.673x10^-11)(379kg)(640kg)/(0.558m+0.279m) = (0.0000162)/(0.701)= 0.0000231N (WRONG)

You can't do that!

You must add the force from B to the force from C (ie, use the formula twice, separately) …

you can't just add the masses, and add the distances, and then chuck them all into the same formula! :rolleyes:

Try again. :smile:
 
  • #4
Thank you!, got to analyze the problem more :bugeye:
 
  • #5


I would approach this problem by first recognizing that the gravitational force between two particles is a vector quantity, meaning it has both magnitude and direction. In this case, the direction of the force will be towards particle A.

To calculate the magnitude of the net force on particle A, we can use the equation F=Gm1m2/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two particles, and r is the distance between them.

Using this equation, we can calculate the force between particle A and B as FAB = (6.673x10^-11)(379kg)(500kg)/(0.558m)^2 = 0.0000364N. Similarly, the force between particle A and C is FAC = (6.673x10^-11)(379kg)(140kg)/(0.279m)^2 = 0.0000964N.

Since these forces are acting in the same direction, we can simply add them together to get the net force on particle A: Fnet = FAB + FAC = 0.0000364N + 0.0000964N = 0.0001328N.

Therefore, the magnitude of the net gravitational force acting on particle A is 0.0001328N.
 

What are three particles and how are they related?

Three particles refer to the three fundamental particles in the universe: protons, neutrons, and electrons. These particles are related through their interactions with each other and the forces that act upon them.

What is the gravitational force and how does it work?

The gravitational force is the force of attraction between any two objects with mass. This force is described by Newton's Law of Universal Gravitation, which states that the force is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between them.

Can the gravitational force be felt at a distance?

Yes, the gravitational force is a long-range force and can be felt even at large distances. However, the strength of the force decreases as the distance between objects increases.

How does the mass of an object affect the gravitational force?

The mass of an object directly affects the strength of the gravitational force. The greater the mass of an object, the greater the force of attraction it will have on other objects.

Why is the gravitational force considered a universal force?

The gravitational force is considered a universal force because it acts between all objects with mass in the universe. It is not limited to specific types of particles or objects, and it affects all objects equally regardless of their size or composition.

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