How is force distributed orthogonally along a material plane?

AI Thread Summary
The discussion revolves around simulating a plane thin rectangular board attached to two springs at each end, focusing on how forces act on the springs when pressure is applied at various points. It is noted that pressing directly above one spring compresses only that spring, while pressing at the center distributes force equally to both springs. The user seeks clarity on calculating the downward force on the springs when pressure is applied at different points. They initially struggled with motion equations for angular momentum but have moved on to using the Euler-Lagrange differential equations, which they find challenging to solve analytically. The user is considering a numerical solution and is inquiring about the result of performing two infinitesimal rotations around different points in 2D space.
pL1
Messages
7
Reaction score
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
 
Physics news on Phys.org
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:
 
This sounds good!

Thank you!

And thank you for the welcome!

pL1
 
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:
Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Thread 'Gauss' law seems to imply instantaneous electric field propagation'

Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
View full post »

Thread 'Do electron density waves accompany EM waves in coaxial cables?'

Maxwell’s equations imply the following wave equation for the electric field $$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2} = \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$ I wonder if eqn.##(1)## can be split into the following transverse part $$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2} = \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$ and longitudinal part...
View full post »
Thread 'Recovering Hamilton's Equations from Poisson brackets'

Thread 'Recovering Hamilton's Equations from Poisson brackets'

The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing. The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##. But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
View full post »

Similar threads

I How Does Changing Mass and Spring Force Affect Watch Oscillators?
Replies
11
Views
2K
I Finding the Axis of Rotation with Given CoG and Force Point
Replies
32
Views
2K
I How Does Force Distribute Across Protrusions in a Symmetric Object?
Replies
11
Views
1K
A Equipartition theorem and Coupled harmonic oscillator system
Replies
3
Views
2K
Calculating the spring force constant K
Replies
14
Views
2K
Convert moment force at lever support
Replies
1
Views
2K
How Does Spring Force Affect Net Force in Physics?
Replies
3
Views
1K
An error made in a kinematics question about a spring launcher?
Replies
16
Views
1K
I How Does Torque Affect Balance on a Self-Balancing Electric Unicycle?
Replies
10
Views
3K
Question about springs and rotational/translational energy
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top