How is force distributed orthogonally along a material plane?

In summary, pL1 is trying to solve a problem involving the angular momentum of a rotatable spring-board-attachment, but doesn't know how to do it. If anyone could help him out, that would be much appreciated! Thanks!
  • #1
pL1
7
0
Hello,

I want to simulate a plane thin rectangular board attached to one spring below at each end. (So there are 2 springs in total.) The springs span the entire edges. The spring-board-attachment is a rotatable axis.

I can't find out how the force acts on the springs. I don't know whether there will be any force on the spring below at the farer end. If I press directly above one end onto a spring only this spring gets compressed while the other does not because the board only rotates around its axis? If I press onto the center of the board, both springs receive equal force. What is with any other point of pressure though? What's the downwards force onto the springs??

Thanks!

pl1
 
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  • #2
Welcome to PF!

Hello pL1! Welcome to PF! :smile:
pL1 said:
What is with any other point of pressure though? What's the downwards force onto the springs??

To find the force on each spring, take moments about the other spring. :wink:
 
  • #3
This sounds good!

Thank you!

And thank you for the welcome!

pL1
 
  • #4
Hello,

I was actually unable to write down the motion equations for the angular momentum. However I have derusted myself a bit and wrote down the Euler-Lagrange DE system.
Now I don't seem able to solve it. It may even be unsolvable as the setup incorporates a gravitational pendulum of sorts for which the DE can't be solved analytically.

This is why I am thinking of solving it numerically. Now I obviously have to do 2 (infinitesimal) rotations around 2 different rotation points in 2D space in one iteration. But the question is: what's the result of 2 such rotations: vector addition of each start-/end-rotation connection vector? I can't make up my mind.

http://www.alice-dsl.net/l.hansen/spring_board_Euler_Lagrange_DE.PNG

Thus thanks for any help!

pL1
 
Last edited by a moderator:

1. What is meant by force distribution along a material plane?

Force distribution along a material plane refers to how a force is spread out or distributed over the surface of a material in a perpendicular direction. This is important to understand in order to determine the strength and stability of a material under different types of external forces.

2. How is force distributed orthogonally along a material plane?

Force is distributed orthogonally along a material plane by evenly spreading the force over the surface of the material in a perpendicular direction. This can be achieved through the use of mechanical fasteners, such as screws or bolts, which distribute the force evenly over the surface of the material.

3. What factors affect force distribution along a material plane?

There are several factors that can affect force distribution along a material plane. These include the type and thickness of the material, the type and placement of mechanical fasteners, and the direction and magnitude of the external force being applied.

4. How does force distribution affect the strength of a material?

The way force is distributed along a material plane can greatly impact the strength of the material. When force is evenly distributed, it can help to evenly distribute the load and prevent any weak points or stress concentrations. This can make the material stronger and more resistant to deformation or failure.

5. Can force distribution be controlled or manipulated?

Yes, force distribution can be controlled and manipulated through various methods. The use of different types and sizes of mechanical fasteners, as well as altering the direction and magnitude of the external force, can all affect how force is distributed along a material plane.

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