Hmmmm I guess I’ve been looking at this whole thing from the wrong perspective. You are right, the frictional force acting on the object would be dependent on its mass. They still accelerate at the same rate but their terminal velocities would be different. Sorry about that :smack:
To make up for it, how about a nifty terminal velocity calculator ?
True…but sometimes it’s hard to convince people that a steel ball, for instance, will weight less than one of lead or tungsten. (I had a prof that kept a tungsten ball–not very large–on the desk and often offered to visitors to pick it up, so he could see the look of surprise on their face when they could barely lift it. Tres amusing.)
Using something that people know is very light is a good illustration that people can visualize, but you are correct that with a lighter-than-air substance there is the additional effect of buoyancy (Archimedes’ Principle) which would add to the complexity of actually modeling the effect.
Stranger
Atmospheric buoyancy is a major factor, which is related to density. In air, drag alone does not determine the rate of fall. Try dropping a balloon filled with water and another one blown up with air that are the same shape, material, and C[sub]d[/sub], and let me know if they hit the ground at the same time.
[QUOTE=Dorjän]
You are right, the frictional force acting on the object would be dependent on its mass. They still accelerate at the same rate but their terminal velocities would be different. QUOTE]
I just had to do a :smack: of my own when I read that… correct me if I’m wrong, but frictional FORCE is not dependent on mass… just on shape and velocity.
frictional ACCELERATION (or decceleration) is dependent on mass.
To compare:
gravitational force is dependent on mass
gravitational acceleration is NOT dependent on mass. 
It’s true they will have different kinetic energies, but only the acceleration matters when calculating their speed. Acceleration due to gravity is independent of the object’s mass (as long as the object’s mass is negligible compared to the Earth’s mass). However, acceleration due to drag is dependent on mass. Given things like drag coefficient and velocity, you calculate a drag force, and the acceleration caused by that force is inversely related to mass. E.g. two spheres of different weight falling at the same velocity have the same drag force, but that force results in a larger (negative) acceleration on the lighter sphere. The relation is F=ma where F is the drag force, m is the object’s mass and a is the resultant acceleration.
Several issues here:
[ul]
[li]You can create a shockwave over (not in front of) objects at subsonic speeds. For example, as an aircraft approaches Mach 1, the fluid which is being accelerated over the wing goes supersonic before the vehicle itself is supersonic and you get a standing normal shock above the wing. You can’t get a shock in front of a vehicle (like a bow shock) in the transonic regime, only over the body in locally accelerated flows.[/li][li]Golf ball dimples are used to trip the boundary layer to turbulence. This decreases the wake size which has two effects: it reduces the drag and it stabilizes the flight because it reduces or eliminates oscillating vortices in the wake. At the speeds we’re talking about attaining in the OP, you’d be hard pressed to maintain laminar flow on any reasonably sized body so intentionally tripping turbulence is unnecessary and the trips would only add additional drag.[/li][li]The dimples tripping turbulence on a golf ball have nothing to do with shock waves. I don’t know what speed Tiger Wood gets off the club head, but I suspect you’d have to fire a golf ball out of a cannon to reach transonic velocities. If I’m wrong, please provide a cite because I’d find it very interesting.[/li][li]As noted above, raindrops are not teardrop shaped, but your other comments about the aerodynamic benefits of that body shape are accurate.[/li][/ul]
How about a lawn dart [sup]TM[/sup]?
“Look out belooooooowwwwww!!!”
How much air? If you added enough air that they had equal mass as well as volume and shape, they should hit the ground at the same time. Admittedly, a very special balloon would be required.
I think that might stretch (pun really not intended) the very meaning of the word “balloon”
Er, yes. I didn’t think I was unclear about that. Velocity due to acceleration is v=√(2ad), assuming no initial velocity. Drag effects create a force that reduces the acceleration by a=m/F[sub]D[/sub]. F[sub]D[/sub] varies with velocity (all else held equal), and hence is non-linear, giving you a resultant acceleration of v=√(2ad) - m/F[sub]D[/sub]
Kinetic energy is irrelevent to the discussion, or rather, is a result of how fast it is going and how much velocity is lost due to drag. I’m not sure where that came from, but it isn’t a consideration in this calculation.
Ooft. I goofed in using the term “shockwave”. Rather, you get a area of higher pressure in the stagnation region in front of the object. The air flowing out of this region can actually be moving outboard and rearward faster than the object is moving relative to the ground FOR, even at transitional subsonic speeds. You lose energy in pressuringing the air in front, but gain in terms of higher flows over the body (“wetted surface”) in regimes where the boundary flow is turbulent.
[QUOTE=micco]
[ul][li]Golf ball dimples are used to trip the boundary layer to turbulence. This decreases the wake size which has two effects: it reduces the drag and it stabilizes the flight because it reduces or eliminates oscillating vortices in the wake. At the speeds we’re talking about attaining in the OP, you’d be hard pressed to maintain laminar flow on any reasonably sized body so intentionally tripping turbulence is unnecessary and the trips would only add additional drag.[/ul][/li][/quote]
I’d have to conditionally disagree with this statement. Depending on the configuration and speed of the object, creating turbulence can offer a reduction in drag, particularly if it interferes with vortexing in the seperation region. In addition, moderating the turbulence can help prevent destablizing vortex-induced vibration. We’re not talking about dimples or Homer Simpson-inspired “speed holes”, but it in free-fall objects features are sometimes added to increase turbulence for this purpose. I’m looking for a good cite to throw at you, but haven’t found anything online yet.
I should have said “idealized raindrops”; in reality, as has been noted, surface tension prevents sharp breaks or points and other dynamic effects (like angular momentum) pull the drops into different shapes depending on size. A solid object would best terminate in a sharp point that would (theoretically) prevent any vortex from forming and in reality would act as a nucleation point for turbulent seperation.
Stranger
Equal mass and volume would be equal density. Along with equal shape (and assuming no difference in surface roughness) they’d have the same drag AND buoyancy (in effect, they’d be identical.)
Buoyancy is a factor in considering substances that are lighter than or within the same magnitude of order density of air. For anything solid (not counting ultralight solids like polymer aerogels) buoyancy in air at atmospheric pressure isn’t really an issue.
Stranger
Can we make something so big that it accelerates the Earth towards IT at faster than 9.8 m/s/s while still pretending earth is the frame of reference?
Sure. Two masses are attracted by a force proportional to their masses and inversely proportional to the square of their distances, usually designated as m and M. (Guess which one is the Earth?) We normally dispense with m when calculating acceleration due to gravity because M is so much bigger*, but if you want more force (acceleration), all you need to do is use a mass that is comperable in mass to the Earth; say, a small ball of neutronium, two meters in diameter.
But it’s kind of hard on the Earthlings. Maybe you should try your experiement on Venus first, instead.
Stranger
*You can pretend the Earth is your frame of reference, if you like, although technically it will be under acceleration, which gives kind of tricky results in relativity. But your problem won’t last too long, methinks. Crunch.
As a bit of a side note, doesn’t an accelerating frame of reference give somewhat dubious results even in plain old newtonian physics?? Imaginary forces and the like. For instance, if your frame of reference is a rotating space station, the effect of inertia will manifest as an apparent force (centrifugal force) which isn’t really there. Not that difficult to deal with if you know it’s an illusionary effect and why it seems to be there, but it’s tripped up a lot of people who weren’t clear on it IIRC.
You made a comment (unquoted in my reply) about dropping jugs on your foot. That’s where it seemed you were confusing the KE of a falling object with it’s velocity or acceleration.
You’re correct about the effect of turbulence. My point is that in this situation, it is extremely unlikely that you’d need to intentionally trip the boundary layer using things like dimples. On any reasonable size object at the speeds we’re talking about here, you’re going to get natural transition to turbulence unless you take extreme measures to stabilize a laminar flow.
On the other hand, if you really want to reduce drag, you can design your vehicle to reduce wake effects (like you mention regarding the aft profile of a boat) and then try to maintain laminar flow. Laminar flows have much lower viscous drag because of the velocity profile in the boundary layer, but it’s very hard to maintain laminar flow. There has been work done on things like laminar flow wings for an F-16, but in many cases they have to resort to tricks like using suction to stabilize the boundary layer before it can transition to turbulence. The OP probably wouldn’t allow active stabilization of the BL in the design he seeks, but it might be possible to design an object which maintained laminar BLs naturally. Quite the opposite of intentionally tripping turbulence.
Yep. Note that although the term “relativity” has become associated with Einstein’s theories of General and Special relativity, Newton and his contemporaries (and even their predecessors) were aware of the affects of classical relativity (the effect motion of bodies with respect to each other.) Einstein merely (merely!) eliminated the notion that there is a fixed (objective) frame of reference for all observers.
Centrifugal force is definitely a real force, from the perspective of the person within the rotating frame of reference. It will show a gradient with radius from the center of rotation (hence, all rotating systems have a fixed frame of reference about the axis of rotation), but it is no more illusionary than forces due to linear acceleration.
Coriolis force, on the other hand, is literally right off the wall, or rather through it. If you start throwing curve balls unintentionally, you might start to consider whether you are trapped on a rotating space station, but again, the effect dwindles to insignificance with a larger and proportionally slower rotating body.
Stranger
Classical relativity – cool. That’s the second thing I’ve learned today, at least
Fictitious forces… wasn’t meaning to pick on centrifugal force, it’s just one of the more famous ones. The sensation of getting pushed back in your seat if you’re sitting in a train that’s picking up speed, for instance, is equally a fictitious force in my book.
Well, all forces all just eddies* in the space-time continuum.
“And this is his sofa, is it?”
Stranger
Okay, they’re distortions, not “eddies” but then there’s no pun. Lighten up, will ya?
The force pushing you into the back of your train seat is exactly as real or fictitious as the force pushing your butt into the bottom of the train seat. If you want to call gravity fictitious along with centrifugal and coriolis and the like, I’m fine with that, and if you want to call all of them real, that’s OK, too, but you can’t consistently say that centrifugal force is fictitious while gravity is real.
Not meaning to be extremely argumentative, but… well, just watch me!!
Seriously… I’m not extremely up on my dynamic physics, but I thought the idea of real forces versus fictitious forces was pretty well established. If you want to insist that they all come down to distortions in the space time continuum or something, that’s… well, I’d like a bit more explanation as to exactly how a space station rotating causes distortions in the continuum, but basically that’s fine with me.
Personally, though, I don’t see where the inconsistency is in labelling any effects due to an accelerating frame of reference ‘fictitious forces’, and any that are due to the four basic powers of the universe (gravity, EM, weak and strong) as ‘real forces’. I’m willing to accept that it might be an arbitrary distinction, but I definitely don’t see that it’s inconsistent.
To add to that, in dynamics (or kinetics) we sometimes apply something called a “D’Alembert” force to an object under acceleration, which is a force equivelent to its inertial resistance to change of velocity. (F=Ma for linear motion and T=Meω[sup]2[/sup] for angular motion.) It is a force, so far as someone pulling a heavy railcar along a frictionless track can feel, but there is no apparent external cause; just Newton and his annoying laws which geeks like to bash Hollywood for not respecting. 
Also, in some cases, such as the application of Castilgliano’s Theorem (used to find deflection of a member via the associated change in strain energy) we’ll set up a problem that uses a “dummy force” in the equation and then set it equal to zero when solving the problem for a particular solution. See Mark’s Standard Handbook for Mechanical Engineers, pg 5-42 for an example of this, or any standard text or handbook on mechanics of materials. (Sorry, it’s the first reference I have at hand, and I’m too lazy to go hunt down a Roark’s for a specific page reference.) I know this isn’t what you mean by an apparent force, but it is the only example of a truely ficticious (i.e. an artifact of the mathematics) force that I can think of offhand.
But “felt forces” are just as real as any other kind of force, and as Einstein demonstrated with GR, acceleration due to thrust is instantaneously indistinguishable from acceleration due to gravity, though you’ll obviously be able to discern one from another if you can accurately measure the shape of the field. For all we know, gravity is just the result of space expanding around us, though the mathematical treatment of that particular hypothesis leads to some very awkward results that make M-Theory look sane. “Dr. Lucy, you have some 'splaining to do!”
Stranger