Sarah Fox wrote: > > Sarah: Freight train/car = keystick. First concrete barrier = front rail. > You = wippen/hammer. The second wall = the strings. The "ouchy" effects of > colliding with a second barrier are an indication of your kinetic energy. > Both you (the wippen/hammer) and the freight train/car (keystick) are set > into motion at the same time. My point is that no matter the scenario, the > same amount of energy will be transferred to the strings. In the case of > the freight train, there's much more wasted energy in the form of > unneccessary kinetic energy in the vehicle beneath the seat of your pants. Yes I see what you were getting at now... the freight train is the leaded key, and the car is the sprung, and I get smashed inbetween the knuck and the capstan either way if you choose to pump up the volume enough :) > -------------- > > 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. Ya see... thats the rub.... I still have this little itch telling me alls not quite well in Smallville with this.... Why not a collision ??? its not like the parts are all one solid piece of material with 100 percent compliance.... but I have to grant you've sprinkled a healthy portion of powder on my bump.... Still.. there's enough of an itch left to get me to run that experiement just to see. And boy are you going to hear it if the leaded key ends up the more powerfull :)... but to continue...... > 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. So what happened to mass times velocity ??? Isnt that going to explain quite a bit of the difference in damage ? > > > 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." Hmmmm... wheres my asprin.... Personally... I have to kind of believe you can crank up the marbles velocity to several (hundred) times the bowling balls before its going to have the same effect.... I mean... of course the keystick wont move as fast or as forcefull... or however way you look at it if you play it softly. Either way it looks to me like we are mixing up what we are talking about here... So tell me... why cant I correctly view the amount of force exerted on the keystick by either the bowling ball or the marble in terms of their inertia ? > > > 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. 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. > Grin... gotta admit you are taking me for a bit of a ride here.... > > 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. > > 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. > We are floating around out in space with this right ??? :) > > 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. I think I begin to see where you are going with this... > 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. Ok... I see all of this... I'm not quite sure how this relates directly to the earlier discussion.... which had to do with showing that the lead became a load rather then an aid when it was accellerated past 9.8 m/sec ^2... but perhaps a few readings of this will make that clear. > > Ric: Lets take one of your overstated examples... if velocity is the only > determinant here.. then ok...say you have this feather moving along at a > velocity of 50 metes per second... and it runs into your freight train... > just how fast do you think the freight train is going to move in response. > Ric: What this really illustrates is that its best to stick to examples that > closely resemble our piano action to begin with. > > Sarah: No, no! This is a good example. It illustrates the difference > between a system of collisions and a system of mechanically connected > elements! A feather moving at 50 m/s wouldn't move a freight train very > much, granted. However, glue the feather to the caboose and THEN accelerate > it to 50 m/s. NOW you've got the train moving! ;-) Ah.... I mean.. wait on here... accellerating the feather to 50 m/s whilst its glued on to the caboose is the same thing as saying the feather isnt really there... in fact I wouldnt be suprised that if you tried to accellerate that feather...and the feather alone... it would be in existance for very long. Besides... our piano action isnt all that coupled... the parts bang into each other.... at least to some small degree. > Ric: Grin... Im not convinced. In fact... so far I'm more inclined to think > the other way around. It will be a delight to test your claims against the > experiment I mentioned earlier. Because if I am wrong... then the spring > counter balance will do more work, and if things turn out the other way > around... well... you've got some explaining to do :) > > Sarah: Dunno... I think this is all a process of a thousand tweaks. We've > probably gotten to tweak # 503, with 497 to go! I'm certain inertia is an > important part of the equation, but how much inertia and where? Well, > that's a matter of tweaking too. ;-) No doubt... :)... In anycase tweak 503 is going to have to be read a few times back and forth, and up and down before I am comfortable that I know for sure that I've understood you correctly. > Peace, > Sarah > I'll get back to you on this when I do :) Cheers RicB -- 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
This PTG archive page provided courtesy of Moy Piano Service, LLC