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

I think I have to separate the four masses but I'm not sure how to do that??? Thanks

Huh? Radius on a square? The sides are 10cm center to center. You have to convert to meters. the 1.41s? The distance across the square diagonal...

thank you for that answer you are amazing!

hey bob its frank here, your younger brother.. well done answering this question you always understood physics better than i did back in high school that's for sure!!

Uhm, to get the length of the diagonal, you should compute it using pythagorean theorem sqrt(.1^2+.1^2)=0.141

To solve this problem, you can use the concept of Newton's Law of Universal Gravitation. According to Newton's Law, the gravitational force between two objects is given by the equation:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.

In this case, we have four masses, but we can calculate the net gravitational force on one of them by considering the forces due to the other three masses. We will apply Newton's Law of Universal Gravitation separately for each pair of masses.

Let's call the mass at the bottom left corner "Mass A," and the other three masses "Mass B," "Mass C," and "Mass D." We want to find the net gravitational force on Mass A due to Masses B, C, and D.

To separate the forces, we will consider each pair of masses individually and then add up the resulting forces as vectors.

1. Calculate the force on Mass A due to Mass B:
The distance between Mass A and Mass B is the length of the side of the square, which is 10.0 cm or 0.1 m. Putting this information into the equation, we get:

F_AB = (G * m_A * m_B) / r_AB^2

2. Calculate the force on Mass A due to Mass C and Mass D:
The distance between Mass A and Mass C or Mass D is the length of the diagonal of the square, which can be found using Pythagoras' theorem:

Diagonal = √(Side Length^2 + Side Length^2) = √(0.1^2 + 0.1^2) = √0.02 ≈ 0.141 m

Putting this information into the equation, we get:

F_AC = (G * m_A * m_C) / r_AC^2
F_AD = (G * m_A * m_D) / r_AD^2

3. Find the net force:
Now, to find the net gravitational force on Mass A, we need to sum the forces acting on it due to Masses B, C, and D. Since the forces are vectors, we have to consider both the magnitudes (size) and the directions.

Let's say the force on Mass A due to Mass B is F_AB, the force on Mass A due to Mass C is F_AC, and the force on Mass A due to Mass D is F_AD.

Since Mass B is at the bottom right corner of the square, the force F_AB will be acting horizontally towards the left.

Masses C and D are at the top left and top right corners of the square, respectively. The forces F_AC and F_AD will be acting diagonally towards Mass A.

To find the net force, we need to add the vectors together:

F_net = F_AB + F_AC + F_AD

Calculate the individual magnitudes using the formulas obtained, and take into account the direction each force acts. The final answer will provide you with the magnitude and direction of the net gravitational force on Mass A, due to the other three masses.

For the radius it is supposed to be r^2. Would I use 10.0cm^2 or 5cm^2? and would I convert that value to meters? Also where did the 1.41s come from? Thank you

No, don't separate them. Use arguement of symettry.

Pick a corner. The force on it is from across the scquare (the diagnol ), so the force is along the diagonal. Call this force 1.
The other forces (adjacent corners) are along the line connecting them, but resolve that into two components: along the diagonal, and perpendicular to the diagonal. But if you examine the perpendicular force, each of the adjacent corners are in opposite directions, and cancel. So all that is left is the force component of each along the direction of the diagonal. Call this force2

Force net: Force1 + 2*force2 (both adjecent corners)
= GMM/(1.41s)^2 + 2GMMcos45/s^2 where s is side length.