off topic - ball collision with lever
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off topic - ball collision with lever
I realize this is not aviation related, but I know there are a lot of very smart people here, so I thought I would try asking here 
I'm an avid golfer, and have been reading up on the physics of
the swing, and ball clubface contact. I realize that the a golf
shot is a pretty complex event, but I'm trying to start with something a bit more simple <g>.
I'm trying to mathematically model a ball bouncing on a lever, with the pivot in the middle of the lever.
I'd like to calculate how high the ball would initially bounce,
depending on the ball hitting the lever at various distances from the pivot.
If it makes the calculations simpler, we can assume that that lever does *not* move around the pivot at the moment of impact. The focus being on how much energy is transferred between the ball and the lever, and not on any angles of the collision. I guess what I'm thinking is how the ball hitting other than the "centre of mass/gravity" of the lever
affects the resulting bounce.
I've been reading up, and have picked up "bits and pieces" of knowledge, just trying to piece them all together <g>.
Here's what I (think), that I know <g>:
1) The lever has a "moment of inertia", which wil influence
how quickly the lever will move when struck by the ball.
2) The lever has a "center of gravity/mass" which will affect the
amount of energy that is tranferred to the bouncing ball. The more "off centre" the ball hits, the less energy that will be transferred.
3) Greater speed or mass of the ball will affect the resulting speed that the lever moves, and the resulting bounce.
4) Greater mass of the lever will increase its moment of inertia, slow down it's speed, reduce the amount of energy lost by the ball.
4) When the lever moves, a "moment" will be introduced, the size of which depends on the lever's "moment of inertia".
5) There is a mathematical relationship between the lever's moment and its angular velocity.
6) From the moment or angular velocity of the lever, the amount of energy transferred between the ball / lever can be calculated.
7) Conservation of momentum will influence the energy transfer between the ball and the lever.
Thx for any info.
Mike
I'm an avid golfer, and have been reading up on the physics of
the swing, and ball clubface contact. I realize that the a golf
shot is a pretty complex event, but I'm trying to start with something a bit more simple <g>.
I'm trying to mathematically model a ball bouncing on a lever, with the pivot in the middle of the lever.
I'd like to calculate how high the ball would initially bounce,
depending on the ball hitting the lever at various distances from the pivot.
If it makes the calculations simpler, we can assume that that lever does *not* move around the pivot at the moment of impact. The focus being on how much energy is transferred between the ball and the lever, and not on any angles of the collision. I guess what I'm thinking is how the ball hitting other than the "centre of mass/gravity" of the lever
affects the resulting bounce.
I've been reading up, and have picked up "bits and pieces" of knowledge, just trying to piece them all together <g>.
Here's what I (think), that I know <g>:
1) The lever has a "moment of inertia", which wil influence
how quickly the lever will move when struck by the ball.
2) The lever has a "center of gravity/mass" which will affect the
amount of energy that is tranferred to the bouncing ball. The more "off centre" the ball hits, the less energy that will be transferred.
3) Greater speed or mass of the ball will affect the resulting speed that the lever moves, and the resulting bounce.
4) Greater mass of the lever will increase its moment of inertia, slow down it's speed, reduce the amount of energy lost by the ball.
4) When the lever moves, a "moment" will be introduced, the size of which depends on the lever's "moment of inertia".
5) There is a mathematical relationship between the lever's moment and its angular velocity.
6) From the moment or angular velocity of the lever, the amount of energy transferred between the ball / lever can be calculated.
7) Conservation of momentum will influence the energy transfer between the ball and the lever.
Thx for any info.
Mike
I haven't done any maths with it for years, which is why I wasn't any more detailed (I'm just not current enough on the stuff) but it's all to do with impacts of elastic objects and was how Newton explained devices like Newton's cradle. I'm pretty certain how to solve the problem will be covered by any physics textbook that uses the law.
G
G
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O'Reilly, the first publisher you check for an IT book, publish:-
Physics for Game Developers
By_David M._Bourg
November 2001
0-596-00006-5, Order Number: 0065
344 pages, $39.95 US, $59.95 CA, £28.50 UK
"Colliding billiard balls. Missile trajectories. Cornering dynamics in speeding cars. By applying the laws of physics, you can realistically model nearly everything in games that bounces around, flies, rolls, slides, or isn't sitting still, to create compelling, believable content for computer games, simulations, and animation. Physics for Game Developers serves as the starting point for enriching games with physics-based realism"
I haven't read the tome, but the sample chapter looks like a very readble coverage of the subject. Maybe it will help.
HTH
Physics for Game Developers
By_David M._Bourg
November 2001
0-596-00006-5, Order Number: 0065
344 pages, $39.95 US, $59.95 CA, £28.50 UK
"Colliding billiard balls. Missile trajectories. Cornering dynamics in speeding cars. By applying the laws of physics, you can realistically model nearly everything in games that bounces around, flies, rolls, slides, or isn't sitting still, to create compelling, believable content for computer games, simulations, and animation. Physics for Game Developers serves as the starting point for enriching games with physics-based realism"
I haven't read the tome, but the sample chapter looks like a very readble coverage of the subject. Maybe it will help.
HTH
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Thanks Romeo.
G,
I have a book called "Stress Without Tears", which is "A primer on aircraft-stress analysis requiring no advanced mathematics".
He has some nice detailed examples of the moments / bending forces on a wing spar.
He shows how to calculate the forces along an arbitrary seqment of the spar. That is somewhat related to what I'm trying to calculate.
I might have to consult an aerodynamics book for info on how the air "bounces" off the wing though
Mike
G,
I have a book called "Stress Without Tears", which is "A primer on aircraft-stress analysis requiring no advanced mathematics".
He has some nice detailed examples of the moments / bending forces on a wing spar.
He shows how to calculate the forces along an arbitrary seqment of the spar. That is somewhat related to what I'm trying to calculate.
I might have to consult an aerodynamics book for info on how the air "bounces" off the wing though
Mike
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Look up "Centre of percussion" in any good physics text"
also...
It might be useful to regard the club as being an impedance matching device between you and the ball.
After an excellent landing you can use the airplane again!
also...
It might be useful to regard the club as being an impedance matching device between you and the ball.
After an excellent landing you can use the airplane again!
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>Look up "Centre of percussion" in any good physics text"
Ok thanks, any other "phrases" ?
>It might be useful to regard the club as being an impedance matching device between you and the ball.
Huh ???? Too "deep" for me <g>.
Mike
Ok thanks, any other "phrases" ?
>It might be useful to regard the club as being an impedance matching device between you and the ball.
Huh ???? Too "deep" for me <g>.
Mike
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