Equilibrium of systems in acccelerating frame

In summary, the conversation discusses the use of torque equations and the choice of point for consideration. Two different torque equations are presented and it is noted that they do not give the same solution. The conversation also mentions other equilibrium equations and the potential for mistakes when using a calculator.
  • #1
serverxeon
101
0
69g5g8.png


I've drawn the following FBD (using D'alembert prinicple)
[The N in my drawing is the F_A stated in the question]

579kn.jpg

----------------

Assuming my FBD has nothing wrong, am I right to say that I am free to choose my torque equation about ANY POINT?

somehow my solutions vary depending on my point of consideration.

Torque eq about CM:
N + 2Fy cos(30) -2Fx sin(30) = 0

-or-
or eq about pivot:
N - 2mg cos(30) - 2ma sin(30) = ma

It just doesn't give the same solution.
--------------------------------------------
My other translational equilibrium eqs are:

ma - Nsin(30) + Fx = 0
Fy + Ncos(30) - mg = 0
 
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  • #2
solved.

my mistakes when pressing the calculator )=
 

FAQ: Equilibrium of systems in acccelerating frame

What is the Equilibrium of Systems in Accelerating Frame?

The equilibrium of systems in an accelerating frame refers to the state of balance or stability that occurs when the net force acting on a system is zero in a frame of reference that is experiencing acceleration. This means that the system is not accelerating relative to the frame of reference, even though the frame of reference itself is accelerating.

How do you determine the Equilibrium of Systems in Accelerating Frame?

To determine the equilibrium of systems in an accelerating frame, you must first identify all the forces acting on the system and their direction. Then, you must calculate the net force by adding all the forces together. If the net force is equal to zero, the system is in equilibrium. If the net force is not equal to zero, the system will experience acceleration in the direction of the net force.

What is the difference between Equilibrium in Accelerating Frame and Inertial Frame?

The main difference between equilibrium in an accelerating frame and an inertial frame is that in an inertial frame, the system is not accelerating and the forces acting on it are balanced, resulting in zero net force. In an accelerating frame, the system may still be in equilibrium, but the frame of reference itself is experiencing acceleration, meaning that there is a non-zero net force acting on the system.

What are some real-life applications of Equilibrium of Systems in Accelerating Frame?

Equilibrium of systems in an accelerating frame is a fundamental concept in physics and has many real-life applications. Some examples include designing structures that can withstand forces during earthquakes, understanding the stability of objects on a moving vehicle, and predicting the behavior of objects in a rotating frame, such as a merry-go-round or a centrifuge.

How does Newton's Second Law apply to Equilibrium of Systems in Accelerating Frame?

Newton's Second Law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration, applies to equilibrium of systems in an accelerating frame. In this case, the net force is equal to zero, so the acceleration is also equal to zero. This means that the mass of the system is not accelerating relative to the frame of reference, even though the frame itself is accelerating.

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