Mudbird

"How The Mind Works" by Stephen Pinker is a good read too.

Mr. Skeptic, you are a lifesaver. So all I had to do was set -kx = f(k) itself, without multiplying or adding anything else. Where I went wrong was in confusing the Spring Force with the Spring Potential Energy, and the Friction Force with the "work" done by friction. The problem was enormously more simple than I thought. It took me a minute and a half once I got the right variables in place. Thank you ever so much for explaining step-by-step, in complete sentences that my word-oriented brain can follow. Your assumption that I don't know calculus is half right: I've taken it over and over but have yet to master it. I wish there were more explication in the physics class of EXACTLY how the concepts of calculus apply to the formulas we are memorizing. I try to take apart all the units and quantities to see what makes them tick, so to speak, but I can't always put them back together right. Thanks again for your help. When you have a chance, would you mind posting the convenient, calculus-based way of solving this type of problem? If it's not too much trouble. Cheers, E.R. "Mudbird"

"buma has a more fluid sound, with no sharp spikes in the tone or ...spokenness.... whereas kiki is more likely to be pronounced with a sharp intone at the i, so you have kind of an up-down" What a fascinating topic. I would bet money that the graph of the actual sound waves for "buma" and "kiki" would resemble the corresponding objects to a convincing extent. I mean a more sinous curve versus one with visible sharp spikes.

I'm sorry, I just feel so stupid about this. I've covered pages with calculations and wasted hours that I needed for even harder homework. Can someone please patiently explain to me where, in the spring's path, I should expect to find the highest velocity. Near or at the starting point (-5cm)? Near zero (equilibrium)? Past zero? Surely the spring must be slowing down by then? Presumably the ball moves at the same speed as the spring as long as they are in contact (there will be some deformation of the ball, which is described as soft rubber, but we're not asked to calculate that). Is the speed of the ball increasing or decreasing while it is in contact with the spring? At some point the spring reverses direction while the ball keeps going forward. To me it seems logical that, before this happens, there would be a gradual lessening of the forces exerted by the ball and spring against each other. There must be a point, BEFORE the spring bounces back, when the spring's effect on the ball becomes negligible, and I would guess that that is the point when the ball's speed is highest, as friction will slow it down thereafter. The maximum speed according to my book is about 26% higher than the speed at exit, and occurs before the ball passes x=0. What I can't figure out is HOW to find out where along the gun barrel this maximum speed occurs. Or, conversely, how to find the speed itself so I can work out the distance. Do I need the derivative of acceleration? Can someone please tell me what's happening here? Thank you so much.

Okay, thank you... I actually had arrived as far as setting 1/2kx^2 = f(k)x, but when the distance traveled worked out to 4.2 cm (or x= -.008) instead of 4.6 (or x=-.004) I thought I must be doing something wrong and started over. I've worked it through this time. Taking the initial spring potential energy 1/2k(.05m)^2 as the total energy of the system, I then subtracted f(k)(.008m) from that to get 1/2mv^2 = .008656. This yields a velocity of 1.807 m/s after the spring has moved 4.20 cm. Once again, the book says the max velocity should be 1.79 m/s, at a distance of 4.60 cm from the firing point, or -.4 cm from equilibrium. Was I supposed to divide that .008 by two somewhere along the line? Thanks for taking the time to help me.

The answers to these problems are in my book, but I need a little help understanding just how they fit together. The spring is compressed 5 cm from equilibrium, and the projectile travels 15 cm from the compressed point to the opening of the gun barrel. They want the velocity at exit (which I got right), and the MAXIMUM velocity, which apparently occurs just BEFORE, not AT, spring equilibrium or x=0. Variables: kinetic friction = .032 N (constant for length of gun barrel, 15 cm) mass of projectile = 5.30 g = .0053 kg spring constant = 8.00 N/m starting point x = -5.0 cm = -.05 m ending point xf = 10.0 cm = .10 m = (xi + .150 m) I need to find the x-value where velocity is maximized, and the max velocity itself. I would have thought that was just where the ball separates from the spring which has been pushing it - at that point the only force in effect would be friction within the gun barrel, slowing it down from there on. (We're not looking at what happens after the ball exits the barrel.) For exit velocity I got v^2 = [2(.032N)(.150m)]/.0053kg = 1.9622 (m/s)^2 Taking the square root of that I got v = 1.40 m/s, which agrees with the book. Now for max velocity I assumed that the spring would be pushing the ball right up to x=0, at which point the ball would begin slowing down due to friction. That is, the ball would have traveled 5.00 cm to reach max v, which I then calculated as 1.78 m/s. However, the book says max v = 1.79 m/s and occurs after 4.60 cm of travel, or at x = -.40 cm. All I can figure is that the spring's force is diminishing as it gets closer to 0, so the spring itself is slowing down while the ball is speeding up, and that the ball actually leaves the spring behind just before reaching x = 0. I reasoned that acceleration of the ball from the spring then ceases (drops to zero) and since acceleration is the derivative of velocity I should be able to find a max value of v by setting a=0. It's at this point that my brain freezes up and I stare at the wall. A) Am I on the right track, or is something else going on here? B) How do I set up the equation for finding the maximum velocity? Thanks.

The last people who introduced themselves were posting in 2004? Really? Well, hi, folks, I'm Eman and I go to college with a bunch of people half my age, and at present I'm struggling through my second bout with Calc II as well as Physics. Nice forum you've got here. Cheers, "Mudbird"

How would you use this in a kinematic equation? For example if height (x) is given by a constant times seconds-cubed, and an object is dropped from height x at time t, how do you figure out its falling time? If acceleration is not constant, then what is it? Thanks.