Hi Sarah... Not really disagreeing with you below... just writting my own thoughts down.. (I find that helpfull) and perhaps clarifiying where we are talking past each other, and where my perspectives are not yours. That makes it hopefully easier to identify where there are misconceptions and allow them to be ....reconcieved as it were.. :) Comments below. Sarah Fox wrote: > > Sarah: The moral of this little thought experiment is that it is the > velocity of the key, not the inertia, that affects how fast the wippen moves. > > Ric: Ok... drop a 20 pound lead on the key... now tell me ... is it the > leads velocity... or is it the leads inertia that will get things moving. > > Sarah: LOL! Now you're talking my language! ;-) This is a different sort > of situation, though. You're talking about a collision -- which doesn't > actually happen. Fair enough, but let's talk apples and oranges: Let's > compare a 10 kg bowling ball and a 10 g marble. Drop both from the height > of a meter. Kinetic energy in both will be the product of gravitational > force times distance (1). However, the kinetic energy of the bowling ball > will be much greater, since the gravitational force on the bowling ball will > be directly proportional to its mass. Considered another way, the bowling > ball and marble will fall at the same rate and will therefore have the same > velocity squared. Since kinetic energy is equal to 1/2 mass times velocity > squared, the bowling ball's kinetic energy will be a thousand times that of > the marble. Fair enough. There will be a lot of key repair to do in one of > those examples. > > 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. 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. 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. 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. > > 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 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. > However, let's equalize > these two situations and take them back to an energy in/ energy out sort of > analysis. Let's take our entire setup on a ride on the space shuttle, at > some enormous expense to the American taxpayer. > > 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. 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 ? 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 ?... > > > 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 :) > > Peace, > Sarah -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html http://www.hf.uib.no/grieg/personer/cv_RB.html
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