Forces and Moments in Moving Frameworks

[Ninjakannon]

I'm trying to create a simulation of some frameworks. For my situation, these are light (I'm ignoring their weight) rods connected by joints. Currently, the joints do not hinge or otherwise move and can have a weight, effectively a force applied to the point. Oh, and I'm also ignoring air resistance.

I thought I knew enough mechanics to work this out; however, I'm having some trouble.

Say we simply have 2 joints with a rod between them, neither joint has the same weight and this system is currently falling. At first I tried calculating the tension each weight would put on the rod and then exerting the difference between the tensions onto the point that caused the least tension. Needless to say, this didn't work. Now, I'm attempting to use moments about the centre of mass of the rod, ie the centre of the rod. However, I don't understand how to calculate the acceleration caused, in x and y components, by the moments.

Any help would be great, thanks a lot!

 

[eljose79]

Thank you for sharing your simulation project with us. It sounds like you are working on a challenging and interesting problem.

Based on your description, it seems like you are dealing with a system of connected bodies that are subject to external forces (weight and applied force) and internal forces (tension in the rod). In order to accurately simulate this system, you will need to consider both the external and internal forces acting on each body.

One approach you can take is to use Newton's second law of motion, which states that the sum of all external forces acting on a body is equal to its mass times its acceleration. This means that for each body in your simulation, you will need to calculate the net force acting on it and then use that to determine its acceleration.

To calculate the net force on a body, you will need to consider all external forces (weight and applied force) and internal forces (tension) acting on it. For example, in the case of the two joints connected by a rod, you will need to calculate the tension in the rod and then add it to the weight and applied force to get the net force on each joint.

Once you have calculated the net force on each body, you can use it to determine the acceleration in both the x and y components. This can be done by dividing the net force by the mass of the body (using vector components if necessary).

I would also recommend considering the conservation of energy in your simulation. This can help you track the motion of the system over time and ensure that the energy of the system is conserved.

I hope this helps you with your simulation project. Good luck!

 

[astrokreng]

I can provide some insights into your simulation of frameworks and the forces and moments involved. It seems that you are trying to create a simulation of a simple physical system, which is a great way to understand and analyze the behavior of such systems. However, it is important to understand the fundamental concepts and equations related to forces and moments in moving frameworks.

Firstly, it is important to note that in a system like the one you described, where there are only two joints and a rod between them, the center of mass of the rod will always remain at the center of the rod. This is because the weights of the joints are not considered and the rod is assumed to be weightless. Therefore, the center of mass will not change its position and there will be no net moments acting on the rod.

In order to understand the forces and moments in this system, we need to consider the forces acting on each joint individually. Each joint will experience a downward force due to its weight and an upward force from the rod. These forces will create a tension in the rod, which will be equal to the weight of the joint.

Now, when the system is in motion, these forces will also create a net moment about the center of mass of the rod. This moment will cause the rod to rotate, and the acceleration of the rod will depend on this moment and the moment of inertia of the rod.

To calculate the acceleration caused by the moments, you can use the equation: ΣM = Iα, where ΣM is the net moment, I is the moment of inertia, and α is the angular acceleration. Since you are interested in calculating the acceleration in x and y components, you can use the equations: ΣFx = ma and ΣFy = ma, where ΣFx and ΣFy are the net forces in the x and y directions, m is the mass of the rod, and a is the linear acceleration.

I hope this helps you in understanding and solving your simulation. Remember to always consider the fundamental concepts and equations related to forces and moments in order to accurately model the behavior of physical systems. Best of luck with your simulation!