# Solve Free Body Diagrams: Tension, Gravitational, Equations

• MagLok
In summary, the conversation is about a problem involving free body diagrams and finding the equation for a system of masses. The solution involves finding the tension force and plugging it into the equations for each mass. The final equation is a = m/(m1+m2) * g, which can be plotted on the x axis.
MagLok

## Homework Statement

http://img258.imageshack.us/img258/7172/testiiifo2.jpg Here is an image of the problem (taken from a practice test.)

F=ma

## The Attempt at a Solution

I drew the free body diagrams for each, but I have no idea what the equation would be. I came up with equations for each mass, and solved for a in one, plugged into the other and got this.

Tension Force (string, m2) - Grav Force (earth, m2)=M2*((-tension force string, M1)/m1)

Last edited by a moderator:
If this is not descriptive enough, please let me know and I'll run to my friend's house and scan my work.

Well, if you draw the free body diagram for figure 2, you simply have for each part, the one sitting on the table is:

Tension = m1 * a

The one hanging is:

mg - Tension = m2 * a

Plug in for the tension:

mg - m1 a = m2 * a
mg = (m1+m2) a
a = m/(m1+m2) * g

So you would need to plot m/(m1+m2) on the x axis. Hope this helps.

Yes, thank you much Runelord :-D

## What is a free body diagram?

A free body diagram is a simplified visual representation of an object or system, showing all the forces acting on it without any external influences. It helps to analyze and solve problems related to motion and equilibrium.

## What is tension in a free body diagram?

Tension is a force that occurs when an object is pulled or stretched by another object. In a free body diagram, tension is represented by arrows pointing away from the object, showing the direction and magnitude of the force.

## How do you solve for gravitational forces in a free body diagram?

To solve for gravitational forces, you need to identify the mass of the object and the acceleration due to gravity (9.8 m/s² on Earth). Then, use the equation Fg = mg, where Fg is the gravitational force, m is the mass, and g is the acceleration due to gravity. Plug in the values and solve for the force.

## What are the equations used in free body diagrams?

The most common equations used in free body diagrams are Newton's Second Law (F=ma), Newton's Law of Universal Gravitation (Fg = G(m1m2)/r²), and the equation for calculating tension (T = μmg). Other equations may be used depending on the specific problem being solved.

## How can free body diagrams be used to solve problems?

Free body diagrams allow you to break down a complex system or object into individual forces, making it easier to analyze and solve problems related to motion and equilibrium. By correctly identifying and representing all the forces acting on an object, you can use equations and principles of physics to solve for unknown variables and understand the behavior of the system.

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