Four identical masses of 2.7 kg each are located at the corners of a square with 1.4 m sides. What is the net force on any one of the masses?

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

I don't understand why im not getting it right... i need help please!!

bruh i dont even know

To find the net force on any one of the masses, you need to calculate the gravitational force between that mass and the other three masses.

The formula you mentioned, F = (G * m1 * m2) / r^2, is correct. Let's break it down step by step:

1. Identify the variables:
- G is the gravitational constant, approximately 6.67430 × 10^(-11) N(m/kg)^2
- m1 and m2 are the masses (both equal to 2.7 kg in this case)
- r is the distance between the masses (the length of the sides of the square, which is 1.4 m)

2. Calculate the gravitational force between one mass and another:
F = (G * m1 * m2) / r^2
F = (6.67430 × 10^(-11) N(m/kg)^2 * 2.7 kg * 2.7 kg) / (1.4 m)^2

3. Calculate the net force on any one of the masses:
Since there are three other masses, you need to calculate the gravitational force between the mass under consideration and each of the other three masses. Then, you can find the net force by adding up these three forces. Due to the symmetry of the square, the forces will have equal magnitudes but will act in different directions. The net force will be the sum of these forces.

Therefore,
Net force = 3 * [(G * m * m) / r^2]

Substituting the values into the formula:
Net force = 3 * [(6.67430 × 10^(-11) N(m/kg)^2 * 2.7 kg * 2.7 kg) / (1.4 m)^2]

Calculating this expression will give you the net force on any one of the masses. Make sure you have used the correct values and units for each variable in your calculations.

To calculate the net force on any one of the masses, you need to consider the gravitational forces acting on it due to the other three masses. The formula you mentioned, F=((G)(m1)(m2))/r^2, is the formula for calculating the gravitational force between two point masses.

In this case, there are four masses, so you need to calculate the gravitational force between the mass in question and each of the other three masses. Once you have the forces, you can add them up vectorially to find the net force.

Let's go through the steps to calculate the net force:

Step 1: Calculate the gravitational force between the mass in question and each of the other three masses.

The formula for the gravitational force, F= ((G)(m1)(m2))/r^2, applies to each pair of masses. In this case, the masses (m1 and m2) are identical at 2.7 kg, and the distance between them (r) is the length of the diagonal of the square (1.4 m) because that is the distance between the centers of any two masses.

So, for each pair of masses, the formula becomes:
F = ((G)(2.7 kg)(2.7 kg))/(1.4 m)^2

Step 2: Calculate the net force by adding up the individual forces vectorially.

Since the four masses are located at the corners of a square, two forces are acting along the diagonal of the square, and the other two forces are acting along the sides of the square. The forces along the diagonal are equal in magnitude and opposite in direction, so they cancel out. The forces along the sides are acting at right angles to each other, so they also cancel out. Therefore, the net force on any one of the masses is zero.

If you are getting a different result, make sure you are using the correct values for the gravitational constant (G) and the masses (m1 and m2), and that you are using the diagonal distance correctly (1.4 m) in the formula.

Fopposite corner = G m^2/(1.4*sqrt2)^2

lined up with diagonal

get component along diagonal for the two adjacent sides, thus cos 45 = 1/sqrt2
Fadjacent corners = 2 G m^2 cos 45/1.4^2
= 2 G m^2 (1/sqrt 2) /1.4^2

sqrt 2 is about 1.4 so

F = G m^2 /4 + 2sqrt 2 G m^2/4
(2.
= G m^2 (1+2.8)/4
pretty close to G m^2 but do the arithmetic more accurately than I did in my head