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New ode problem

ValeryOchkov
24-Ruby IV

New ode problem

New ode problem (for Alan, Viktor and all):

A steel ball (with d=100 mm and Ro=7800 kg/m^3) was thrown upward. He has reached a certain maximum height (h.max=250 m) and fell to the ground after a certain time (t.end=17s).
What is the initial speed of the ball and what is a value of the coefficient of drag k (F.drag=k S Ro.air v^2). Ro.air=1.225 kg/m^3 or is a function of the height.

See for the start here http://communities.ptc.com/message/187832

1 ACCEPTED SOLUTION

Accepted Solutions

Thanks, Alan!

I would like to use the Maximize function but:

ball-2.png

PS

Better to have:

better.png

View solution in original post

14 REPLIES 14

Please, Valery. Sorry, without units (MC 14).

Ball.GIF

Viktor

Viktor

Thanks and Sorry,

not v(t)^2 but v(t)*|v(t)| or v(t)^2*sign(v(t))

And attach please the file!

What is it with you and throwing balls in the air Valery!!!

Oh well, attached is my version - in Prime 2, with units.

Alan

Alan, show a picture please. I do not have MC Prime now!

Viktor

Viktor

Actually, my 'solution' is wrong! I made an incorrect assumption. For some reason I'm unable to edit my earlier post! But I can edit this one!!!

I'll try to generate a correct solution later today, and will post a picture of it as well Viktor.

Alan

Up and down phases are symmetrical only by k=0!

1) How to do it automatically (see the picture, Mathcad 15 and Mathcad Prime files)?

2) Has the problem solution by this initial data?

ball.png

Here's my automatic answer. Of course the up and down movements are not symmetrical, as I had assumed in my first post, because of the drag! I've not bothered with the Archimedes upthrust as it's a small effect.

Alan

Here are the images, for Viktor:

ValeryBall1.PNG

ValeryBall2.PNG

v0 seems very high!

Thanks, Alan!

I would like to use the Maximize function but:

ball-2.png

PS

Better to have:

better.png

Yes, tend = 15s gives smaller v0 and k. The system is very sensitive to tend, and, as it stands fails for tend of 14s or less. Can you determine (automatically) the minimum value of tend for which the program will find a solution?

Alan

We can carry out real experiment - shoot guns or catapults cannon ball straight up and measure the time of flight and maximum lift of the cannon ball!

Ro=f(h)

Valery Ochkov wrote:

We can carry out real experiment - shoot guns or catapults cannon ball straight up and measure the time of flight and maximum lift of the cannon ball!

Ro=f(h)

Expensive method!

In terms of the model, the minimum possible time that doesn't lead to a failure to converge, is when k is zero. This gives a tend of 2.sqrt(2.hmax/g).

Alan

AlanStevens wrote:

Valery Ochkov wrote:

We can carry out real experiment - shoot guns or catapults cannon ball straight up and measure the time of flight and maximum lift of the cannon ball!

Ro=f(h)

Expensive method!

Alan

But I have in Moscow Kremlin one device for this experiment:

http://communities.ptc.com/servlet/JiveServlet/downloadImage/102-1424-2-7169/450-325/Chris-Valery-Kremlin.png

A symbolic solution of the problem (Maple):

a) k=0

ball-boundary-symbol.png

b) k>0

ball-boundary-symbol-k.png

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