# What is the Resultant Gravitational Force on a 4.00 kg Object?

• chocolatelover
In summary, the conversation discusses how to calculate the resultant gravitational force on a 4.00 kg object placed at the corner of a right triangle, with three other masses placed at the other corners. The equations and solutions for the individual forces are provided, and it is reminded that forces are vectors that can be added together to find the resultant force. The conversation also clarifies the coordinates of the masses and the correct notation for the forces.
chocolatelover
Hi everyone,

Homework Statement
Three uniform spheres of mass m1=2.00kg, 4.00kg, and m2=5.50 kg are placed at the corners of a right triangle. Calculate the resultant gravitational force on the 4.00 kg object, assuming the spheres are isolated from the rest of the Universe.

Fg=m1m2/r^2

## The Attempt at a Solution

F32=-6.67X10^-11Nm^2/kg(5.5kg)(4kg)/4^2= -9.2 X 10^-11i

F13= -6.67X10^-11Nm^2/kg^2(4)(2)/3^2= 5.9X10^-11j

Thank you very much

Please describe--even better, provide a diagram of--the triangle and its dimensions and the relative locations of the masses.

Recall that forces are vectors. You find the resultant by adding up the individual force vectors (add them like vectors, not plain numbers).

Thank you

The triangle is placed in the second quadrent, where m3 is at (0,0) m2 is at (-4,0)m and m1 is at (0,3)

Does this look correct?
F32=-6.67X10^-11Nm^2/kg(5.5kg)(4kg)/4^2= -9.2 X 10^-11i

F13= -6.67X10^-11Nm^2/kg^2(4)(2)/3^2= 5.9X10^-11j

Thank you

I didn't check your arithmetic, but your setup looks good. Now find the magnitude of the resultant force.

Thank you

I just need it in terms of i and j. So, wouldn't that be correct the way it is? F32 is negative and F13 is positive, right?

Thank you

The signs of your final answers are correct. But I don't know what you mean by F32 (versus F23). Is that the force on 3 from 2? Realize that you want the force on mass 3, and that F32 = -F23. (Just be consistent.)

Thank you very much

Regards

## 1. What is "resultant gravitational force"?

Resultant gravitational force refers to the total force exerted on an object by multiple sources of gravity. It is the vector sum of all the individual gravitational forces acting on the object.

## 2. How is resultant gravitational force calculated?

To calculate the resultant gravitational force, you need to know the masses of the objects involved, their distances from each other, and the universal gravitational constant. The equation for calculating resultant gravitational force is F = G * (m1 * m2)/ r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.

## 3. Why is resultant gravitational force important?

Resultant gravitational force is important because it is responsible for the movement of objects in space, including the orbits of planets around the sun and the moon around the Earth. It also plays a crucial role in determining the weight of objects on Earth.

## 4. How does distance affect resultant gravitational force?

The force of gravity between two objects is inversely proportional to the square of the distance between them. This means that the greater the distance between two objects, the weaker the gravitational force between them. So, as distance increases, the resultant gravitational force decreases.

## 5. Can resultant gravitational force be negative?

No, resultant gravitational force cannot be negative. Since it is a vector quantity, it has both magnitude and direction. The direction of the force is always towards the center of mass of the objects involved, so it is always positive or zero. A negative resultant gravitational force would imply that the objects are repelling each other, which is not possible according to Newton's law of universal gravitation.

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