# Free-body diagram of mechanical system

• PainterGuy
In summary, the person asking for help is questioning the direction of arrows in free-body diagrams for M1 and M2. They are also confused about the concept of positive direction and its importance in these diagrams. They have an additional question about the forces involved in an equation. The expert explains that the arrow directions indicate the sign convention for forces and clarifies the concept of net force. They also mention that sometimes a fictitious force is introduced to cancel the net force for certain analyses.
PainterGuy
Hi,

Question 1:
Do you think that the free-body diagram for M1 correct? It looks fine except that, I think, the arrow for $M_{1}\frac{d^{2}}{dt^{2}}x_{1}$ should point downward.

Question 2:
Similarly, I think that the free-body diagram for M2 is okay but the arrow for $M_{2}\frac{d^{2}}{dt^{2}}x_{2}$ should point downward instead. Could you please confirm it?

PainterGuy said:
I think, the arrow for $M_{1}\frac{d^{2}}{dt^{2}}x_{1}$ should point downward.
The arrow directions just indicate the convention for the positive direction. It doesn't matter how you draw them.

Thank you!

A.T. said:
The arrow directions just indicate the convention for the positive direction. It doesn't matter how you draw them.

"positive direction" for what?

Also you said that it doesn't matter but, in my opinion, it does matter how the arrows are drawn. Please see the diagram for M1 where I've drawn the F=ma arrow downward, and as a result the equation also changes.

I have another related question and came across it when I was trying to understand the involved equations.

-kx - b*v_x = m*a_x

To me the equation above means that at any time, the force accelerate an object in x direction is equal and opposite to the spring force and damping force; in other words, the net force is zero. But then why would the object move at all if some forces are pulling the object backward and the other force pushing it forward? It should remain stationary. Where am I going wrong? Thank you!

Last edited:
PainterGuy said:
"positive direction" for what?
The arrows indicate the sign convention to be used for the forces. If you get a positive value for the force, it means that the force points in the direction that the arrow indicates. If you get a negative value, the force points opposite to the arrow.
PainterGuy said:
I have another related question and came across it when I was trying to understand the involved equations.

-kx - b*v_x = m*a_x

To me the equation above means that at any time, the force accelerate an object in x direction is equal and opposite to the spring force and damping force; in other words, the net force is zero.
The net force is the right hand side. Sometimes you introduce a fictitious force to cancel the net force, because you are not interested in the acceleration, just the internal stresses (quasi static analysis).

PainterGuy and Lnewqban

## 1. What is a free-body diagram?

A free-body diagram is a simplified representation of a mechanical system that shows all the external forces acting on the system. It is used to analyze the motion and equilibrium of the system.

## 2. How do you draw a free-body diagram?

To draw a free-body diagram, you first need to identify the object or system you want to analyze. Then, draw a simple sketch of the object or system, including all the external forces acting on it. Finally, label each force with its magnitude and direction.

## 3. What are the types of forces included in a free-body diagram?

The types of forces included in a free-body diagram are contact forces (such as friction and normal force) and non-contact forces (such as gravity and tension).

## 4. How does a free-body diagram help in solving mechanical problems?

A free-body diagram helps in solving mechanical problems by providing a visual representation of all the forces acting on a system. This allows for a better understanding of the forces at play and helps in determining the net force and direction of motion of the system.

## 5. Can a free-body diagram be used for systems with multiple objects?

Yes, a free-body diagram can be used for systems with multiple objects. Each object should be represented separately, and all the forces acting on each object should be included in the diagram.

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