Gravitational force acting between objects

I will keep that in mind for the next problem. In summary, we are calculating the magnitude of gravitational force on object 1 due to the other 3 objects located at the corners of a rectangle with sides of 2 meters and 1 meter. This is done by finding the gravitational force between 1 and each of the other objects, splitting those forces into x and y components, and then adding them together to get the total force. For the given values, the magnitude of gravitational force on object 1 is 7.8*10^-9 Newtons. This same method can also be applied to solve for the magnitude of gravitational force on object 1 in a similar scenario with 3 1kg objects located at the corners
  • #1
Abu

Homework Statement


4 10kg objects are located at the corners of a rectangle sides 2 meters and 1 meter. Calculate the magnitude of gravitational force on 1 due to the other 3.

(Same sort of idea)
3 1kg objects are located at the corners of an equilateral triangle of side length 1 meter

Homework Equations


F= Gm*M/r^2

The Attempt at a Solution


So, let's say that I am finding the gravitational force on 1 for the rectangle (labeling the rectangle clockwise starting from the top right). My first idea was to find the gravitational force between 1 and 4 which would be directly to the left.
Then I wanted to find the gravitational force between 1 and 2 which would be directly below the rectangle. Then I wanted to find the gravitational force between 1 and 3, which would be directly diagonal from 1.

So here are my calculations for those, in order:
Force on 1 due to 4: 6.67*10^-11 10*10/2^2 = 1.67*10^-9
Force on 1 due to 2: 6.67*10^-11 10*10/1^2 = 6.67*10^-9
Force on 1 due to 3: 6.67*10^-11 10*10/√5^2 = 1.334*10^-9

But I don't know what to do from here because my answer is wrong. Am I supposed to be adding these 3 forces together, or is there a vertical and horizontal component I am missing or something?

I am assuming that if I understand how to do the rectangle one, I'll be able to do the triangle one. I may need help with that one too though
If my question isn't clear, I'll be happy to clarify it for you. Thank you.
 
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  • #2
Abu said:
Am I supposed to be adding these 3 forces together,
Yes, but as vectors. Do you know how to add vectors?
 
  • #3
haruspex said:
Yes, but as vectors. Do you know how to add vectors?
Do you mean you want me to split the forces into x and y components? like 1 to 4 would be in the x direction and 1 to 2 would be in the y direction?
 
  • #4
Abu said:
Do you mean you want me to split the forces into x and y components? like 1 to 4 would be in the x direction and 1 to 2 would be in the y direction?
Yes, and what about 1 to 3?
 
  • #5
haruspex said:
Yes, and what about 1 to 3?
Okay so I found the angle with tanΘ=1/2, then Θ = 26.5 degrees
I found the component of 1 to 3 in the X direction to be:
cos26.5= x/1.334*10^-9 and it equals 1.193*10^-9

For the component of 1 to 3 in the Y direction I did:
sin26.5 = y/1.334*10^-9 and it equals 5.95*10^-10

and then adding the x and y components together now would make

X
1.67*10^-9 + 1.193*10^-9 = 2.862*10^-9
Y

6.67*10^-9 + 5.95*10^-10 = 7.3*10^-9

And then imagining this as a triangle with X and Y components, I just use
F = √(2.862*10^-9)^2 +(7.3*10^-9)^2
F = 7.8*10^-9 Newtons

Is this correct? Sorry for the late responses.
If so I think I'm going to try the triangle one next.
 
  • #6
Abu said:
6.67*10^-9 + 5.95*10^-10 = 7.3*10^-9
I would keep one more digit of precision here. Other than that, this all looks right now.
 
  • #7
haruspex said:
I would keep one more digit of precision here. Other than that, this all looks right now.
Thank you for your help, I appreciate it.
 

FAQ: Gravitational force acting between objects

1. What is gravitational force?

Gravitational force is the attractive force that exists between any two objects in the universe. It is responsible for keeping planets in orbit around the sun and for the formation of galaxies.

2. How is gravitational force calculated?

The gravitational force between two objects is calculated using Newton's Law of Universal Gravitation: F = (G * m1 * m2) / d^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

3. Does the distance between two objects affect the strength of gravitational force?

Yes, according to Newton's Law of Universal Gravitation, the strength of gravitational force is inversely proportional to the square of the distance between the two objects. This means that the farther apart the objects are, the weaker the gravitational force between them.

4. How does mass affect gravitational force?

The greater the mass of an object, the stronger its gravitational force. This is because mass is directly proportional to gravitational force in Newton's Law of Universal Gravitation.

5. Can gravitational force be shielded or canceled?

No, gravitational force cannot be shielded or canceled. It is a fundamental force of nature that exists between all objects with mass. However, its effects can be counteracted by other forces, such as electromagnetic or nuclear forces.

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