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| Physics Question - ma = mg |
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| IanB:
--- Quote from: bostonman on June 23, 2021, 02:03:13 pm ---To divert a bit, I know (or believe to be true) that if I lift a box fast or slow, the same work is still done. If W = F * h, and F = ma, why would picking up the box faster not use more Work? Assuming no other forces except Earth gravity and the Force of the box, if I pick up the box 1m in 1s, my acceleration is faster than if I pick up the box 1m in 10s; thus making the Work larger. --- End quote --- Picking up the box faster does use more work. You are (1) doing work to overcome gravity, and (2) doing work to accelerate the box. Usually the work to accelerate the box cannot be recovered and goes to waste (like, for example, heat in the brakes of your car). The ideal minimum work to overcome gravity usually only occurs if you pick up the box infinitely slowly. In thermodynamics this is often called a "reversible" process. The box is never moving at any measurable speed, so you never do any excess work to accelerate it. Conceptually, you could get the work of acceleration back again (like regenerative braking), but this would never be 100% efficient and you always lose some energy in such a process. |
| Nominal Animal:
--- Quote from: bostonman on June 23, 2021, 02:03:13 pm ---If W = F * h, and F = ma, why would picking up the box faster not use more Work? --- End quote --- Because regardless of how long it takes, lifting a kilogram of weight in standard gravity of g=9.80m/s² upwards one meter requires one Joule of energy. (1 J = 1 kg m s⁻².) Remember, the a in W=mah is not the acceleration of movement, but the acceleration due to gravity against which you are doing the work. In physics, you cannot do the old scam of paving a driveway without agreeing about it with the owner, and then charging them for it. W does not describe *how* you did the work, only the *amount* of work. The forces you choose to apply to do work against gravity is your choice; they only affect whether a specific end result can be achieved, and how long that will take, not the work needed to achieve that specific end result. Consider, for example, that instead of lifting the 100 kg box we discussed in previous posts by hand, you use a mechanical hoist. What is, exactly such a hoist? Why, it is nothing but a mechanical device that acts as a force multiplier. There are many other such devices; hydraulic cylinders being among my favourites. Just by dint of their geometry, a force applied to a control surface, yields a much larger force on the output surface! And other than friction and mechanical wear, they spend no energy to do so! What magic is this? Well, no magic. A force in itself is not something we can exploit in any way. We can let the force do work, and convert or collect almost all of the energy released; or we can spend energy to cause a force to do useful work for us. A force in itself is not useful; it isn't even real, tangible, in the human sense. A force has the same utterly annoying feature potential energy has: to use them, a physical change of some sort must occur. It is not the force or the potential energy itself that we can exploit; only the change can be exploited. (This is much more fundamental than one might think, and is at the core of why the misguided dreamers dreaming of zero point energy or free energy will never see their dreams fulfilled: they dream of exploiting something that is, rather than something that happens.) --- Quote from: IanB on June 23, 2021, 03:40:42 pm ---Picking up the box faster does use more work. --- End quote --- Bullshit. That makes the asinine assumption that the energy spent to accelerate the box is not recovered. There is no reason for such an assumption; that energy is not "lost", nor does its amount affect the height lifted. Basically, you just made the claim that because you can do other work at the same time, more work is spent in the original task. Recovering just about 100% from acceleration is not hard, either. Converting it into useful energy in a specific form (say, electricity instead of say heat) can be hard; but there is nothing physically preventing such conversions from reaching essentially 100%. ("Essentially 100%" in this context means that in the human scale, we can approach infinitely close to the limit, even if certain (but not all) such energy conversions can never reach 100% mathematically.) If you, IanB, amend the claim to a human will spend more energy to lift a box faster, then I obviously agree. For a human, because of the antagonistic makeup of our musculature –– we have separate muscles for gross movements, and smaller, weaker muscles for fine movements –– the optimum "speed" (with respect to energy expenditure) is not zero, and depends on the physiology of the individual. We also have basically no facilities for recovering any of the work our musculature has done for later use. It is rather surprising, given that human is the one land animal species that given enough time, can run down every single other known land animal. There is no other land animal in existence that does distance running better than humans do. (Yes, a healthy trained human can run down a horse. There just aren't that many humans around that can still run the 200 miles or 300 kilometers necessary.) There have been several publicity stunts, "competitions" between a man and a horse, in the last century or so; but the human runners in these competitions are laughably bad compared to e.g. message runners in ancient Greece or Rome. (Consider the Mongol Derby, the longest horse (riding) race in the world. In ten days, you need to ride 1000 kilometers; you do get to switch horses very often, though, as we don't want to kill the horses. However, the record for a human running 1000 km is under six days for men, and under eight days for women. No horse can do that. Look up "ultramarathon"; you'll be surprised at what humans are actually capable of.) Humans cannot really recover any of the energy their musculature spends, other than a little bit of the waste heat, and with mechanical implements. Passive exoskeletons – collections of braces and springs – are already in use, that can double the range a fully laden infantryman can travel under their own power in any given day without compromising their fighting ability. They basically recover the work done by human musculature into springs et cetera, and use that energy to augment future movement. However, a bicycle is even more efficient (as it reduces the work needed in the first place), if there is a road one can use. |
| David Hess:
Go back to the beginning and figure out what is actually being measured. Scales measure *force* and not *mass*. Weight is force. Units of pounds are force. The Imperial unit for mass is the slug, although in the industry it is more useful to talk about pounds force and pounds mass. |
| TimFox:
If you apply more vertical force F to the mass M than the weight W of that mass, then when you stop applying that force, after moving through H vertical distance, the mass is still moving upwards, now being slowed by the acceleration of gravity g. The net force on the mass while you are applying it is (F - W), which accelerates it vertically so it may rise. If F = W, the mass does not accelerate, but may rise at a constant velocity (assuming you apply enough extra to overcome air resistance and other factors not included in this discussion). The kinetic energy of the mass when the force stops will be K = (F - W) x H, and the mass will continue to rise for a further vertical distance D = K / W, whereupon it stops moving up and begins to fall, accelerated by the acceleration of gravity g. |
| SiliconWizard:
Sorry if it has been said, I didn't read quite all. Your "weight", per se, doesn't just depend on gravity, but also on the fact there is a reaction force (equal but opposed to gravity when you are at equilibrium.) This is this reaction force (to illustrate: that just prevents you from "falling" down to the center of the Earth) that effectively gives you a "weight". Your weight is not an inherent characteristic that just depends on mass and gravity. It "expresses" itself through a reaction force. Without a reaction force that opposes gravity, you effectively have no "weight". The most (normally) well known case is freefall. When in freefall, any massive object has virtually no weight. |
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