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kluya

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I apologize for my English, it's not my native language.

There's three masses of 1 kg each set in an equilateral triangle of side length 0.8 meters. Mass m1 is located in coordinates (-0.4m, 0) and m2 is located in coordinates (0.4m, 0). What are the coordinates of m3?

A fourth mass (m4) is placed in the opposite direction to m3. Determine the net gravitational force that acts over m4 due to the other three masses.

F = G(M1)(M2)/D^2

I think I've solved this but I'm extremely unsure about it so if someone could solve the problem to check answers that would be fantastic.

Here's what I did:

First I bissected the original triangle and applied Pythagorean Theorem to obtain the height which I got as 0.6925 meters.

Then I made a free body diagram of m4 that looked like this:

[PLAIN]http://img175.imageshack.us/img175/5175/fbdd.jpg

I applied Newton's gravitation equation to get F1, F2, and F3. F1 and F2 were 1.042x10^-10 Newtons, and F3 was 3.477 x 10^-11 Newtons. Then I applied cosine and sine of 60 on F1 and F2 to calculate the forces in X and Y axis; this resulted in 5.21 x 10^-11 N in the X axis and 9.024 x 10^-11 N in the Y axis, per force. Then I added the forces on each axis; I got 0 on the X axis and 2.1525x10^-10N on the Y axis.

Like I said, I'm really bad and prone to making mistakes in this subject so I'm very insecure about my answers, especially the second one, so if someone could solve it to check my answers I would be really thankful.

## Homework Statement

There's three masses of 1 kg each set in an equilateral triangle of side length 0.8 meters. Mass m1 is located in coordinates (-0.4m, 0) and m2 is located in coordinates (0.4m, 0). What are the coordinates of m3?

A fourth mass (m4) is placed in the opposite direction to m3. Determine the net gravitational force that acts over m4 due to the other three masses.

## Homework Equations

F = G(M1)(M2)/D^2

## The Attempt at a Solution

I think I've solved this but I'm extremely unsure about it so if someone could solve the problem to check answers that would be fantastic.

Here's what I did:

First I bissected the original triangle and applied Pythagorean Theorem to obtain the height which I got as 0.6925 meters.

**So my answer to the first question was (0,0.6925m).**Then I made a free body diagram of m4 that looked like this:

[PLAIN]http://img175.imageshack.us/img175/5175/fbdd.jpg

I applied Newton's gravitation equation to get F1, F2, and F3. F1 and F2 were 1.042x10^-10 Newtons, and F3 was 3.477 x 10^-11 Newtons. Then I applied cosine and sine of 60 on F1 and F2 to calculate the forces in X and Y axis; this resulted in 5.21 x 10^-11 N in the X axis and 9.024 x 10^-11 N in the Y axis, per force. Then I added the forces on each axis; I got 0 on the X axis and 2.1525x10^-10N on the Y axis.

**So my answer to the second question was 2.1525x10^-10N.**

Like I said, I'm really bad and prone to making mistakes in this subject so I'm very insecure about my answers, especially the second one, so if someone could solve it to check my answers I would be really thankful.

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