Hi Ric, Workin' my way back... > > Now let's consider what happens with the key: First assume the key has a > > good bit of inertia. The bowling ball will squash it, and the piano will go > > "BANG." The marble will strike it, and the piano will go "bing." Yes, > > there's a difference. However, look at the velocity of the keystick during > > this process. The keystick will move at roughly the precollision velocity > > of the bowling ball but at only a fraction of the precollision velocity of > > the marble. This is a velocity difference, and that accounts for the "BANG" > > vs. the "bing." > > It would seem to me that it would be just as easy to explain the keysticks end > velocity in terms of inertia. Obviously, and said in everyday words... the > resitance of the key to being accelerated is nothing compared to the bowling > balls resistance to having its velocity changed.... where as the marbles inertia > is not enough to overcome that of the key...and that being the case... of course > the piano will go bang in the first case and ping (at best) in the second place. right! > As I understand the rest of what you are pointing at... if we look at applying x > amount of newtons to the keystick.... the resulting velocities of the parts is > not given unless you know both the mass and its velocity that is responsible for > those x amount of newtons. I'm not sure which arguments you're referring to. If it helpsl, F=ma (force = mass times acceleration), however you want to twist it around. T=Ia (torque = moment of rotational inertia times rotational acceleration, if you prefer). For the purposes of the problem at hand, try to imagine a massless spring applying a force to the keystick. The less the inertia of the action, the faster the keystick will accelerate in response to that force. > And space example notwithstanding, we are on earth > and every peice of mass will necessarilly have to react to that 9.8m/sec/sec > acceleration. Said another way... in order to get your marble and your bowling > ball to hit the key with the same force in Newtons will require cranking up the > marbles speed to some pretty fantastic levels... grin...... I'd like to see the > dent in the key top. LOL! > Still... I dont see how you can say that it is a velocity difference in the key > that accounts for the bang or ping in the piano. Its what bangs into the key > that accounts for the difference in the keys velocity to begin with... the key > can only achieve a given velocity dependant on that driving force. And in doing > so... that driving force must overcome the inertia of the key, and that of the > parts sitting on the capstan. You might be misunderstanding me here. Whether you drop a marble or a bowling ball, the velocity of the ball will be the same. However, the velocity of the keystick will be very different. I'm saying it is the velocity of the *keystick* that ultimately determines hammer velocity and note loudness, all other things being equal. > > Now, if you want to equate the bowling ball / marble to the keystick and > > look downstream from this point, fair enough. Remember, however, that the > > keystick and the wippen do not "collide," as with this example. BUT IF THEY > > DID... (assuming the finger accelerates the key, then leaves the finger, > > whereupon the key's capstan contacts the wippen heel)... OK, using the > > above example, the "bowling ball" keystick has a lot of kinetic energy and > > "whams" the wippen heel. The "marble" keystick has much less kinetic energy > > and "pings" the wippen heel. Velocity is the same, true... until you look > > at wippen velocity... but that's another story. > > Seems to me its the same story... just drawn up a little different... what ? Same as above: ball velocity is the same. Wippen velocity after the collision is different. I guess what I was saying was that: IF the keystick were to collide with the wippen after coming completely up to velocity, and IF after colliding, the keystick would apply no further force to the wippen, then a heavier keystick moving at the same velocity as a lighter keystick would impart more energy to the wippen, and the wippen would thus move more rapidly. Of course as Don Gilbert pointed out, this is an angular system, but... > Same velocities, difference in mass moving an equal mass... The whippens > resistance to change its velocity is overwhelmed by that of the massive > keystick, and not by the featherweight one. Thats one things inertia loosing out > (or not) to anothers. OK, yes.. > > Now, in our microgravity lab, we accelerate the bowling ball over a distance > > of, say, 1 cm, with a force of 1 Newton. We similarly accelerate the marble > > over a distance of 1 cm with a force of 1 Newton. Both now have the same > > kinetic energy. The bowling ball moves very slowly towards the wippen, > > which is a super light 10 g, for simplicity sake. The marble moves very > > quickly towards an identical 10 g wippen. When these balls hit their > > respective wippens, the wippens bounce off of them. We're interested in > > finding out the wippen velocity. > > Yeahsss... but... you've changed the rules. Suddenly the <<marble keystick>> > and the whippen are of the same mass to begin with. I only did that so that we could have a nice, elastic collision (yes, there are inefficiencies in the felt, I know...) and transfer 100% of the kinetic energy from the "marble keystick" to the wippen. I took liberties here, just to make the illustration a bit more clear. > Secondly you've removed the > constant acceleration of gravity which in one sense allows you to do everything > in slow motion. Back on earth if you hit the whippen with an equal amount of > mass as the whippens then the whippens velocity is the marbles velocity adjusted > by the whippens orientation with respect to gravity... yes.. I mean you could > feasably get the whippen and ball to react just as that rack of 5 hanging steel > balls below if you hung things right ... or what ? Yes, the entire thing could be done on a "frictionless" air hockey table, but it wouldn't be as much fun. ;-) On Earth, gravity will become irrelevant if you do everything VERY, VERY fast, such that the forces are extremely high -- much higher than that of gravity. > Looks to me that we are still at how much hits at what speed. Tho I think I see > where all this is going.... > > The bowling ball will continue right through the whippen... and this is the > wasted energy you are talking about.... yes ?... analogous to banging into the > key bed with the keymass ?... YUP!!! :-) > > When the marble strikes the wippen, the kinetic energy is transfered totally > > to the wippen (assuming elasticity). The marble is then halted, and the > > wippen moves forward at the same velocity of the marble. (It's like those > > executive playtoys -- the racks of five hanging steel balls that click back > > and forth.) > > > > When the bowling ball hits its wippen, not much will happen to the > > velocity of the ball. The wippen will bounce off it and move forward at > > approximately twice that velocity. > > > > This is all well and good, and it might appear that the bowling ball is more > > effective at moving its wippen. However, consider that the bowling ball > > wasn't moving very fast in the first place. Kinetic energy being equal, the > > marble would move Sqrt(1000), or approx 32, times as fast as the bowling > > ball. In the end, the ratio of wippen velocities would be 1:16, with the > > marble's wippen moving much faster. > > > > But energy is conserved. Where does the energy go? Well, our astronaut > > friend doesn't need to catch the marble, as it halts where it strikes the > > wippen. He/she does, however, have to catch the bowling ball before it > > strikes the delicate navigation console. To bring the ball to a halt, > > he/she would have to apply the equivalent of 1 Newton of force (or a bit > > less, actually, considering that around 6% of the ball's kinetic energy was > > lost to the wippen) over 1 cm of distance. > > Hmmm... sounds like you are talking about momentum... and perhaps I am mixing > inertia with momentum where I shouldnt. Admitedly I have to learn to use all > these terms quite a bit more precisely then my present understanding allows for. > Still, perhaps this dialouge may be representative of how some others attempt to > sort all this out, and if so... any constructive resolve can be instructive and > help us all along. So... comment away and lets get this ironed out :) Yes, I think you've been using "inertia" like either "momentum" or "kinetic energy." Momentum is mass times velocity. Kinetic energy is 1/2 mass times the square of velocity. Inertia has nothing to do with velocity. Think of inertia like mass. Anyway, I'm indeed talking about kinetic energy. That's the universal medium of exchange in this whole mess, at least as I manage to conceptualize it. Peace, Sarah
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