MTs, WM2D, and WM Basic Language Script Code

[agor95]

Hi Wubbly

Good piece of analysis and illustration.

I look forwards to the next two examples related to this movement.

P.S. This analysis help others.

All the Best

[Wubbly]

Thanks agor95.

Even Mr. Calculator knew the answer to this one.

[Fletcher]

Thanks also Wubbly, for taking the time and effort to produce your post.

It brings the message home, especially for those not using sims.

And if it loses 20 J then it takes 20 J of Work to reset the lever-weight (not counting frictions).

cheers

[agor95]

Hi Wubbly

I did some checking and it appears you can have 'Mr. Calculator' running on your PC.

Cheers

[agor95]

Hi Wubbly

I popped into your Album above and found a treasure trove of salient analysis.

There is an aspect of that analysis I did not see. Could you help on this item?

A mass dropping with various initial speeds, based on your resent post.

You have proved so well the 20J of work done.

However how much work in done when the mass arcs down with initial y-axis accelerations faster than 9.81 m/s2?

This should effect for Force applied part of the equation?

So a sample of runs starting from 0 speed to 10 m/s would be inlightinging.

Regards

[Wubbly]

I don't see how that would change anything except the final number. Look at the distance and velocity equations. They all have a term for initial position or initial velocity. If the initial value is non-zero it makes the final number larger (or smaller) because you started with something other than zero.

The Energy would be: E final = E initial + delta E

Or potential energy: PE final = PE initial + delta PE

[agor95]

Let's say I have a conceptual itch that needs a really good scratch.

Using your 45 degree by sqrt[2] as a frame work.

The force of gravity is 9.81 on a static mass.

The itch is when the mass in not static.

So start with a stationary mass and end up with 20J of Kinetic Energy movement.

Then increase the initial mass's momentum and see the Kinetic Energy at the end of the arc.

If the mass is accelerating down, due to the arc path, it's motion should reduce the effect of gravity.

Well I have scratch that itch.

[Wubbly]

Here's another spreadsheet that integrates torque x angle. It is similar to the previous spreadsheet except the height is not fixed at 2 meters.

The user enters a mass, radius, and sweep angle, and the spreadsheet calculates the height, the PE, and it calculates the integral of torque x angle over the total sweep angle.

It uses a fixed number of integration steps (100), and you can compare the work integral to the PE calculation. The two numbers should be close to each other. If the spreadsheet used more integration steps the numbers would be closer as you discovered from the previous spreadsheet posted.

There is a third graph of the potential energy lost. If you compare this graph to the work integral of torque x angle, you can see they are the same.

Conclusions:

The work done is the potential energy gained or lost.

torque x angle = PE gained or lost

[Wubbly]

Searching through the albums, you discover Broli did the math on this 11 years ago in this post HERE.

You get more torque at a larger radius, but you operate through a smaller angle, and broli's math shows the work or energy of the torque x angle integral is exactly the same for a given height drop. A larger radius doesn't help you.

Path_Finder was a little confused in that old thread because he was looking at the areas that the angles swept through. But those sweep areas have nothing to do with the torque or the work.

Below is a cleaned up version of what I believe broli was trying to show. 11 years later it finally makes sense.

So what does this tell us? That moving a mass to a larger radius and then back again is completely futile in our search? Probably. Still can't imagine how Bessler supposedly solved it.

[Wubbly]

There are always other things to do with your life.

[Fletcher]

LOL .. thanks Wubbly !!

[agor95]

LOL - Thanks we need at. We should always strip the problem down. Would a person then be called a stripper?

You know your calculations are compelling and also the excel works in Linux / LibreOffice Calc.

Which means they are compelling every where.

I think I am looking at this compelling proof from a dynamic point of view.

We can integrate steps with each step as a static calculation.

Or we can look at each step as a snapshot if a dynamic acceleration point of view.

All the Best

[Georg Künstler]

Wubbly wrote:

So what does this tell us? That moving a mass to a larger radius and then back again is completely futile in our search? Probably. Still can't imagine how Bessler supposedly solved it.

The problem is the fix axle view.
Every loose axle will cause a problem when the masses are rotating.
They rotate off center.
So what Bessler did he managed the off center rotation on one side of the wheel.
I have made several suggestions how to do that, the easiest way is a moveable window frame in the wheel.
A window frame will change the structure from a square to a parallelogram.
When doing that, the wheel is out of balance, and generate torque.
The masses move with different speeds.
A window frame alone normally will collapse, but not so in the wheel.
It has some freedom of movement.

[Wubbly]

MT026 Version 2

Here's an updated version of MT026.

In the previous version, the user had very little control over the geometry so a dialog box was added to give the user more control.

Since you can't add a rotational spring and attach it to two rod constraints, the two rods connected to the sliding mass were replaced with two rectangles. This allowed a rotational spring to be added at the hinge joint of the rectangles to capture the energy of the outward slide and return it back into the system.

A run-time control was added for the K constant of the rotational spring.

Observations:

It runs similar to an MT001

[Wubbly]

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