# Universal Gravitation Law Problem

• kluya
In summary, the coordinates of m3 are (0, 0.6925m) and the net gravitational force acting on m4 is (5.21 x 10^-11 N) i + (2.1525 x 10^-10 N) j.
kluya
I apologize for my English, it's not my native language.

## 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.

Last edited by a moderator:

Hello,

Your solution to the first question is correct. The coordinates of m3 are (0, 0.6925m).

For the second question, your approach is correct but there are some mistakes in your calculations. The net gravitational force acting on m4 can be calculated by adding the individual forces in the X and Y directions. So, the net force in the X direction would be F1cos(60) + F2cos(60) = 2F1cos(60). Similarly, the net force in the Y direction would be F1sin(60) + F2sin(60) + F3 = F1sin(60) + F2sin(60) - F3 (since F3 acts in the opposite direction).

Using these equations, the net force in the X direction is 2(5.21 x 10^-11 N)cos(60) = 5.21 x 10^-11 N. And the net force in the Y direction is (5.21 x 10^-11 N)sin(60) + (9.024 x 10^-11 N)sin(60) - (3.477 x 10^-11 N) = 2.1525 x 10^-10 N.

Therefore, the net gravitational force acting on m4 is (5.21 x 10^-11 N) i + (2.1525 x 10^-10 N) j.

I hope this helps. Keep up the good work!

## 1. What is the Universal Gravitation Law?

The Universal Gravitation Law is a physical law that describes the force of attraction between any two objects with mass. It states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## 2. How can I calculate the force of gravity between two objects?

The force of gravity can be calculated using the Universal Gravitation Law formula: 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. What is the value of the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant in physics that is equal to 6.674 x 10^-11 N*m^2/kg^2. It is used in the Universal Gravitation Law to calculate the force of gravity between two objects.

## 4. Does the Universal Gravitation Law apply to all objects in the universe?

Yes, the Universal Gravitation Law applies to all objects with mass in the universe. This includes both celestial bodies, such as planets and stars, and everyday objects on Earth.

## 5. What is the relationship between the Universal Gravitation Law and Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation is a specific case of the Universal Gravitation Law. It states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, with the gravitational constant included in the equation as a proportionality constant.

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