Motor Daddy Posted July 10, 2008 Share Posted July 10, 2008 As Mr Skeptic has already implied, the thing we call weight, as measured with a bathroom scale or equivalent, is really the normal force. We should try and keep clear what is asked, and what is being measured. So you are accelerating at 32.174 ft/sec^2 when you are standing on the scale? The FORCE is the amount of force required to STOP the acceleration. There is no acceleration at that point while standing on the scale. The acceleration is continuously increasing as you are "free falling" towards the Earth, because you are continuously getting closer to the Earth as you fall, so the acceleration increases. When the acceleration is zero, so is the force, according to Newton's F=ma. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 Unfortunately gravity doesn't work quite the same way. Gravity is exerting a force on you equal to mg, where g is the free-fall acceleration due to gravity. Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 Unfortunately gravity doesn't work quite the same way. Gravity is exerting a force on you equal to mg, where g is the free-fall acceleration due to gravity. If you are free falling, there is no specific "g", as it is continuously changing. If I am standing on my scale, what is my acceleration? Link to comment Share on other sites More sharing options...
iNow Posted July 10, 2008 Share Posted July 10, 2008 If I am standing on my scale, what is my acceleration? Relative to what? Why are we bothering doing this again with you? Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 If you are free falling, there is no specific "g", as it is continuously changing. Sure there is. The equation only cares about one specific point in time. If I am standing on my scale, what is my acceleration? 0 m/s2. That doesn't matter, because you're misapplying F = ma. The equation's used to tell what force could have caused a given acceleration, or what acceleration is created by a specific force (or a few other permutations on that). You need to remember that with gravity as you're standing on a scale, you're experiencing not one but two forces. They're equal and opposite, so yes, there is zero net force being applied. The forces cancel out. But that does not mean that there is no force being exerted on you at all. Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 Sure there is. The equation only cares about one specific point in time. What is a point in time? Like, say, 12:00:00-12:00:00? Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 Sure. In any case, the change in g is so miniscule over small distances that we can safely ignore it. Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 Sure. There is no such thing as "a point in time." You can NOT stop time, Cap'n. In any case, the change in g is so miniscule over small distances that we can safely ignore it. No, we can't ignore it. That is like ignoring a .00000000000000000000001 second duration. That is unacceptable, Cap'n. Time does not stop. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 How can you have a single discrete point on a totally continuous graph? Answer: we can, and we do it all the time. Mathematics, and especially calculus, helps us take care of these problems. The counterexample to your claims is that physics actually works and provides accurate answers. Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 How can you have a single discrete point on a totally continuous graph? Answer: we can, and we do it all the time. Mathematics, and especially calculus, helps us take care of these problems. The counterexample to your claims is that physics actually works and provides accurate answers. Yeah, I know you do it all the time, that is the problem. There is no "point in time." Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 I don't mind approximating a bit. The errors introduced, supposing you are correct, are too small to be measured. Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 I don't mind approximating a bit. The errors introduced, supposing you are correct, are too small to be measured. While the error may be too small to be measured by our very limited measuring devices, the concept is completely wrong. There is no "point in time." Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 Why is there no such thing? Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 Why is there no such thing? Because time is a duration, continuously "flowing." You can't stop time. Link to comment Share on other sites More sharing options...
Cap'n Refsmmat Posted July 10, 2008 Share Posted July 10, 2008 Why do you have to stop it? Link to comment Share on other sites More sharing options...
Motor Daddy Posted July 10, 2008 Author Share Posted July 10, 2008 Why do you have to stop it? Because that is what you would have to do to have a duration of 12:00:00-12:00:00. ALL motion in the universe would have to STOP. Link to comment Share on other sites More sharing options...
John Cuthber Posted July 10, 2008 Share Posted July 10, 2008 Why? If I drive a cap past some point there's a (single) time when the front of that car passes that point. The car doesn't need to stop. What's the difference? Link to comment Share on other sites More sharing options...
ajb Posted July 10, 2008 Share Posted July 10, 2008 Not that there is much point in saying this as MotorDaddy is now gone, but for all the rest of you, calculus is what is needed to understand "infinitesimally small durations of time". His issues are philosophical not mathematical. Link to comment Share on other sites More sharing options...
john5746 Posted July 10, 2008 Share Posted July 10, 2008 His issues are philosophical not mathematical. That's being very PC. I would love to see him tell a cop that his radar gun could not have taken a measurement, because time doesn't stop. He would get an attitude adjustment real quick. Link to comment Share on other sites More sharing options...
Sisyphus Posted July 10, 2008 Share Posted July 10, 2008 Again, not that it matters, but instantaneous velocity ("at a point in time") is still defined as the ratio of distance traversed to time expired, just that the time is approaching zero. So no, it's not "zero." It's "infinitesimal," which means nonzero but smaller than any finite quantity. Put another way, it is the value towards which the ratio gets closer and closer as you reduce the "time" value more and more. Practically speaking, we generally don't bother thinking in those terms, but that's where it comes from, and it's closely tied with the origins of calculus. Link to comment Share on other sites More sharing options...
ajb Posted July 11, 2008 Share Posted July 11, 2008 Again, not that it matters, but instantaneous velocity ("at a point in time") is still defined as the ratio of distance traversed to time expired, just that the time is approaching zero. So no, it's not "zero." It's "infinitesimal," which means nonzero but smaller than any finite quantity. Put another way, it is the value towards which the ratio gets closer and closer as you reduce the "time" value more and more. Practically speaking, we generally don't bother thinking in those terms, but that's where it comes from, and it's closely tied with the origins of calculus. In practice, for linear motion it is absolutely fine to think of velocity as the distance travelled dived by the time taken. For more general motions calculus is needed. That's being very PC. I would love to see him tell a cop that his radar gun could not have taken a measurement, because time doesn't stop. He would get an attitude adjustment real quick. Not knowing calculus was his Achilles heal. Link to comment Share on other sites More sharing options...
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