Yet again, it makes no odds whether the monkey climbs smoothly or jerkily. If the pulley is frictionless, and the rope is massless and inextensible, then at all times the force exerted by the monkey on the rope is identical to the force exerted by the rope on the bucket (necessarily - since there is no other resistance against which the monkey can exert force). Hence every move the monkey makes is exactly mirrored by the bucket, not a nanometre more or less.
In my best Lurch imitation… “uh uh uh uh ooh ooh ooh”.
Speed (or velocity) = the instantaneous measurement of how fast an object is moving in relation to something else (regardless of any forces acting on it). Chose your units, usually a combination of distance per unit of time, but none of them are units of force.
Acceleration = a measurement of the rate of change in the speed of an object (regardless of any forces acting on it). Units are the same as for velocity tied with an additional “per unit of time”, and still none of them are force units.
A much quoted equation: force = mass x acceleration (which is not force = mass x force). Any one of the three can be calculated from the other two. All of them are quite different things. In your view (force and acceleration are the same thing) then this most basic of physics equations is reduced to 1=mass.
Yes, gravity is one of the few basic forces in the universe. It is not an acceleration, but rather can cause it. Everyone does know this, at least everyone who paid attention in high school physics class.
And it does matter, because if a person doesn’t get the basics correct, and use the correct terminology, most people will lend little credence to any arguments made.
Upon consideration, I see that I am wrong. I am conflating the effort to extend muscles with the physics of the net force of the monkey’s motion. Chronos is essentially right, with the caveat that each pull of the monkey applies an increased force and a decreased force.
How? If the pulley has substantial friction, then yes, but if the pulley is essentially frictionless, then how?
We do it all the time in physics. Consider the free body diagram, where you apply each force independently, then calculate the resulting condition. It is the basis for statics in Engineering. Forces don’t only create motion, they also create *stress. *
Consider that tug-of-war case I mentioned. You have a rope. You have two guys, one on each end, pulling in opposing directions. Or two teams. Or two trucks. Or two monkeys. Doesn’t matter. You can look at the force one side is applying in one direction, the force the other side is applying in the other direction, the net direction of motion, and the tension in the rope, that is the stress in the rope.
This is a false reading of what Dr. Strangelove was saying. In the F=ma equation , mass is a proportionality constant*. For a given force it is a constant. He was not saying that constant = 1. He was saying that you cannot have a force without an acceleration. Notice the equation is written in terms of solving for Force. A Force requires mass and it requires an acceleration. If the mass isn’t changing, then the acceleration must in order to change the force.
Dr. Strangelove was stepping beyond high school physics into relativity and the nature of the actual cause of gravity. Is it a field property, like electromagnetism and charge? It can be treated that way, but general relativity says the true cause is a distortion of space-time. Then there is the elusive search for the proposed graviton, the subatomic particle equivalent to the electron and the photon. These are open questions in physics well beyond the high school level.
- Newton didn’t actually write F=m x a. Newton defined a Force as the time derivative of momentum, m x v. For most basic physics problems, mass can be considered constant and therefore time invariant, and thus we reduce to the ubiquitous F = m x a. However, there are situations where mass is not constant - rockets, for instance, which burn fuel and thus throw off mass in exchange for velocity. The form of the Force equation there has two terms: the time rate of change of velocity term (acceleration) and the time rate of change of mass term. The equation could also be affected if there is a discrete mass change, essentially creating two regimes of motion. Unless the monkey takes a dump or is propelling himself with flatulence, none of this is applicable to our problem.
Read what Irishman wrote. He is much more polite than me :). At any rate, my point was just that you can’t say that force causes acceleration or vice versa. They’re intertwined, and in the case of gravity you simply can’t tell the difference (at least until someone finds a violation of the equivalence principle).
In physics, one generally does not speak of a “net acceleration”, composed of the vector sum of a bunch of different accelerations: Just as there is only one velocity, so too is there only one time derivative of velocity, and that is the one and only acceleration.
In physics-related engineering fields, it is common to speak of a “net acceleration”, composed of the vector sum of a bunch of different accelerations. Each individual component acceleration is the result of some individual force, divided by the mass. Mathematically, this approach is equivalent, but it strikes a physicist as a bizarre interpretation.
Intertwined does not mean one is the other (gravity is not “an acceleration”).
Irishman is bringing relativity into things. I didn’t think that anything relating to the monkey and bucket deal was reaching relativistic type magnitudes. I’m not sure what his reply has to do with supporting your claim that gravity is an acceleration. If you go to a party where everybody is talking Newtonian physics and start claiming that gravity is an acceleration, than you are going to go home alone.
You can’t have acceleration without a force. You can have force being applied without causing acceleration, especially with equal, opposing forces.
The equivalence principal only says that if you are in a box and feel yourself being pressed in one direction, you can’t tell if it is due to gravity or acceleration. It in no way indicates that gravity is an acceleration.
Gravity is a force. Acceleration is a term for the measurement of the rate of change of a velocity. Acceleration cannot cause a force.
To twist a quote… 'However gravity is a type of force, I regret to say, which has not been, is simply not, nor will ever be a acceleration".
A=BxC does not mean, or even imply that A and C are the same thing and you can’t tell the difference between them. If they were, then there is no need to make them separate parts of the equation.
Actual relativistic effects are unimportant here. The point is that in General Relativity, gravity is a fictitious force exactly analogous with centrifugal force. The force of gravity is really the result of the acceleration of an inertial particle as measured in a curved coordinate system (hence why all fictitious forces are proportional to mass, just as with F=ma). The acceleration is real (for some of the observers), but in no frame is there an actual force (aside from those required to keep the particle on its curved path). With both gravity and centrifugal force, the acceleration appears “out of nowhere” (though we can pretend that a force caused it if we want).
But gravity might be a field more like electromagnetism, where particles are attracted to each other based on “charge” (in this case, mass-energy). In this case, particles are accelerated because there is a force on them. No one knows yet which interpretation is more like reality.
Well, I could just go straight to the source:
*A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton’s equation of motion in a gravitational field, written out in full, it is:
(Inertial mass) * (Acceleration) = (Intensity of the gravitational field) * (Gravitational mass).
It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body.
— Albert Einstein*
If you want to play semantic games and say that gravity causes the acceleration without being the acceleration, or some such, go right ahead. Nevertheless, as Einstein said, it is the acceleration that’s independent, not the force. Hence–in GR–it’s more fundamental.
We know that GR is wrong, of course, but so far it’s the best thing we’ve got as a theory of gravity.
Again, see centrifugal force–despite the name, it’s not an actual force. Depending on your view, it’s not a real acceleration either, but if you take that view then neither is gravity.
Curious. I can certainly see value in both approaches. I suppose then, that a physicist would deny that an “acceleration field” would even exist. I see an acceleration field as a more natural way to talk about centrifugal effects (not to mention gravity), but if particles are stationary in the rotating frame, then it requires us to speak of net acceleration. Without that, you need centrifugal force, so that a stationary particle has no net forces on it.
An acceleration field isn’t a problem to a physicist, as long as you’re referring to the total acceleration field, and not breaking it up into a superposition of component acceleration fields.
Hmm. I’d think that’s the most natural operation of all, given that just about every other field in physics can be broken up into a superposition of subfields.
I can certainly agree there is only one resulting motion, and thus there is only one resulting acceleration. However, from an analysis standpoint, it is important to understand all the contributing features that lead to that resulting motion. Thus vector mathmatics applied to all the features.
Those features are typically called “forces”. If Newton’s First Law is to be accepted, each of those forces must have a corresponding acceleration. Without an acceleration, they are not forces, and if they are not forces, they do not affect the motion of the object.
To the engineer (I guess), acceleration is what is trying to happen to the object, as well as the result of the sum of those independent components.
A push here and a push there and a pull here and a pull there all contribute to the final resulting motion, if any, as well as the stresses within the object. Understanding those stresses is often as important as understanding the resulting motion. How else to know if your truss is beefy enough to withstand the load, if your bridge can carry the traffic, etc?
Consider this: if one can only talk about the one resulting acceleration from the one resulting motion, then how can one describe the direction of the motion? Coordinate axes require the ability to divide an acceleration into components.
ruh-roh, you originally took Dr. Strangelove to task for this statement:
Read that first sentence again, and tell me how it differs from “F=ma”. He said Force and acceleration are related by mass. You can’t have a force without an acceleration and you can’t have an acceleration without a force.
His second sentence is pointing out the nebulousness of the word “Gravity”. Gravity is a term we apply to the effect we see, the mutual attraction of objects, i.e. objects fall when unsupported. What I think he was trying to point out is the question of whether that effect is caused by some material cause, such as an electromagnetic field effect mediated by photons or electrons and protons, or if it is an imaginary construct like coriolis or centrifugal force. Thus my explanation that General Relativity says it is the latter, but there are proponents who think there may yet be the former. Either way, the result is the same - objects fall when unsupported.
However, he might just have been saying “we call the effect gravity: that word applies to the force the object experiences as well as the corresponding acceleration. Both are described by the word gravity.” When we wish to specify the force versus the acceleration, we will use more specific terms, like the weight, or describe the acceleration as the g-field.
Even the abbreviation for the acceleration of gravity is g for “gravity”.
As an analogy, it is like you are using Bohr model definitions of an atom to tell a quantum dynamicist that he doesn’t know what he’s talking about. He’s saying electrons are a “probability cloud” around the nucleus, and you’re arguing they’re point masses orbiting like planets around the Sun. And then you’re lecturing him on accurate use of terminology.
No!
No, no, no, no, NO!
I’ve been screaming this at my monitor while reading these various responses.
My wife thinks I’m losing at my First-Person Shooter game (again).
So, I’m gonna take a stab at this thing and throw in my 50-cents’ worth. I suspect many of you will laugh at this and, in fact, some of that is intentional. I also suspect that the stuff you’ll laugh at won’t be my humor but my crappy understanding of physics and mechanical principles.
I’ll start with the caveat that I actually passed High School Physics with only a D- [After the first semester, I transferred to Business Law, which requires less math.] but then in College I got an A in Physics 103 (for Poets).:dubious:
So I’ll carry over some of the initial odd questions:
What color is the rope?
No, seriously, what is the diameter of the disc of the pulley? (It’s actually slightly relevant for my last section)
And I’ll carry over some of the basic assumptions that others have retained:
- Gravity is constant throughout the experimental chamber
- The system starts out with proportional distribution of weight – bucket [filled with non-evaporating inedible object(s)] and rope --versus-- monkey and rope are evenly balanced on the pulley and not yet moving.
- The ball-bearings or bushings or lubrication on the axle of the pulley completely nullifies friction
- The rope has been chosen to properly fit the pulley (or vice versa) so there’s no sideways play or pinching of the rope by the groove or the block. We’re assuming the pulley isn’t going to restrict movement of the rope so that we don’t have to calculate how much extra force is required to get the pulley to distribute force evenly. Note, however, that we can’t assume complete nullification of friction between the rope and the pulley’s groove. A lack of friction there means the pulley won’t be able to distribute applied force; the rope will slide in the groove when pulled or the disc will spin without imparting movement to the rope; why bother specifying it in the system if it’s useless? It exists to impart, rather than restrict, movement of the rope.]
And some questions that I felt are actually relevant but nobody else seems to care about.
A) What is the pulley-disc made out of? Steel? Plastic? Aluminum? Wood?
B) How long is the rope?
C) How far below the system is the nearest surface (e.g. floor, interior bottom of the box, ground, stable supported planetary structure, etc.)?
The problem is that we’ve got two separate main interpretations which affect the subsequent discussions:
R1) The rope is weightless or has been looped below the hanging monkey to come back up and attach to the bottom of the bucket to make its weight automatically balance itself out.
R2) The rope has weight and starts out proportionally distributed in order to achieve the balance in #2 above.
Now this physics charlatan will criticize the professionals of theoretical and applied physics for invoking and even calculating Newton’s three laws but refusing or failing to completely apply them. My understanding – and yes, I’ll admit again that I bombed out in high school and wimped out in college – is that Newton’s three laws are a package deal. In other words if we’re applying the first law (in particular) to parts of our contrived system, then we have to apply it to all of the system.
I) An object at rest tends to stay at rest – unless acted upon by another force.
II) There is a formula that allows us to predict results… F = ma
III) For Every Action there is an equal and opposite reaction
Raw Mechanics
So we have this monkey starting at rest (I). Bonzo and his rope are on one side of the pulley, the bucket and its rope are on the other side, and it doesn’t matter whether Bonzo and/or the bucket are dangling at the ends of their ropes or part-way up (with or without rope dangling below them) because the entire system is in equilibrium with gravity + rope + monkey = gravity + rope + bucket.
Bonzo pulls downward on the rope because that’s how he usually climbs. If he’s a relatively brilliant chimp and is excruciatingly slow at pulling himself upward, he could conceivably refrain from disturbing the balance of the system. His body will rise exactly as much as he pulls down on the rope (III). It will take him a hell of a long time, but he’ll get to the pulley and the bucket won’t move. Once he grabs the block or disc and lets go of the rope, the bucket will drop.
Well, so that’s not going to happen since chimps can’t be expected to have that kind of insight, foresight, or patience. Besides, there’s a banana bolted to the top of the block (we had to mount the system somewhere) and Bonzo is hungry.
So we have this monkey starting at rest (I)…see above…
Bonzo pulls downward on the rope because that’s how he usually climbs. He doesn’t do this slowly or delicately, he just reaches up and gets a grip, then yanks that hand down in order to swiftly haul his body upward. This effort introduces a force which upsets the balance of the system. The pulley will distribute the force equally on each side of the axle (III) so that the monkey will initially rise and the bucket will move just as far upward at the same time.
NOW BONZO HAS INTRODUCED MOTION right there at the block-axle-disc of the pulley. The pulley had to move in order to do what it does: balance forces.
The corollary to Newton’s First Law (Inertia) is that An object in motion tends to stay in motion – unless acted upon by another force. Gravity is a constant in our experimental chamber, so its effect remains nullified for calculating the equilibrium of the system. And the frictionless bearings we installed so we wouldn’t have to calculate the effects of friction (or heat loss) have now become a liability. They are not acting as a force against the continued revolving of the pulley.
If our rope is weightless (R1), Bonzo’s single action will make the pulley take bights from the bucket side and transfer them to the monkey side at a constant rate until the bucket reaches the top and, since it can’t fit through the space between the groove and the top of the block, the motion will be forced to stop. If our rope has weight (R2) Bonzo’s single action will make the pulley take bights from the bucket side and transfer them to the monkey side at an accelerating rate until the bucket reaches the top. The motion will still have to stop. 
Invoking sentience:
It’s quite possible that Bonzo will make only that one attempt to climb upward, at which time the pulley will distribute his force and feed rope to his side, and he’ll get scared and simply clutch the rope in fear while he descends on his growing length of rope. It’s also possible that the chimp will not be freaked-out by the rope ‘making’ him move down when he was trying to go up and he’ll continue his climbing action at the same rate. Assuming he does this, he will be adding more force to the turning of the pulley disc, increasing its rotational speed each time and thereby increasing the rate at which rope is fed to his side each time.:smack:
It’s more likely, though, that with the first attempt to climb upward, Bonzo will be surprised by the rope lengthening on his side and his resulting descent. He will think he’s falling as a result of trying to climb and react by increasing his climbing effort in order to escape whatever he fears is down there, probably by pulling downward harder and faster on the rope. This, of course, will make the rate at which rope is fed to his side each time increase even faster (I suspect at a sporadic rate rather than at a calculable constant).:mad:
Assuming that the experimental chamber is somehow illuminated (at least so we Dopers can watch and laugh), Bonzo is going to see the bucket-and-rope rising as he’s descending. Since UP is the way he really wanted to go and assuming we don’t have a pulley disc that’s more than a few feet in diameter (I told you I’d get back to this question), Bonzo will leap from his rope to the other rope – I’ve seen monkeys and chimps do this kind of thing at the Zoo; it’s kinda fun to watch – thereby adding his weight to the weight of the bucket. Rope <> Rope + Monkey + Bucket and not only will the pulley stop spinning to feed the rope away from the bucket, but it will reverse its spin so that bucket + monkey will plummet faster than monkey or bucket were moving earlier. If Bonzo is lucky, the length of rope he started on will have a knot – one that’s bigger than the space between the groove and the top of the block – at the end. :eek:
–G!
Okay, we’ve put this chimp through a lot.
So now it’s Bedtime for Bonzo.
Ronnie, take over.
OK smartass. 
I understand your explanation (Really. I think!), but how do you account for the illustrated lab test linked to earlier, where the robot climbed the rope (like the monkey), and the bucket rose as well, at half-speed? How does that reconcile with your scenario?
Interesting point about the angular momentum of the pulley. Since you bring it up though, the pulley would resist spinning as the monkey initially accelerates, so under the conditions of a massive pulley with frictionless bearings, it should cause the monkey to ascend more quickly than the bucket once he starts climbing. I’m not certain but I believe this will balance out the effect you bring up so that once the monkey stops climbing, both he and the bucket will be stationary.
Quite poorly, I must admit.
My first instinct is to point again to my caveat that I got only a D- in high school physics, but that was a cop-out from the start and it didn’t stop me from blathering on and apparently didn’t stop you and Snailboy from reading my contribution. My second instinct is to say, “Well, I never saw that video” since I couldn’t get it to play, here at work. However that was too much of a cop-out even for me, so I followed that link from a computer at home.
My contribution above was a typically (for me) long-winded post to basically gripe, “You posit a drag-less pulley in the set-up but fail to account for said pulley (and its lack of friction) when arguing Newtonian physics! Such hypocrisy!”
In my mind, we had a monkey, a counterweight, and a rope on a suitable pulley.* The rope I imagined was more like the 3" thick cotton/hemp thing that hangs from the school gym ceiling and dares everyone not to laugh while the class wimp repeatedly fails to pull himself up to the mid-point. A suitable pulley would be similarly massive, of course, and the frictionless axle/bearing/pivot-point would cause the problems I described. In contrast, the video showed relatively thin thread and two very light pulleys made for high efficiency and low weight. I also tend to think the separation of the pulleys creates a system which effectively negates the weight of the thread and the pulleys are designed to minimize their own inertia.
I suppose one could say I’m reaching (and stretching real hard to do so) for excuses and I’m willing to admit that while invoking my original caveats. On the other hand, I don’t think the system in the movie is built to the specifications of the original question, particularly where the “rope” is concerned. It may be that I, like several others, have been fixating on the effect of the weight of the rope transferring from one side of the pivot-point to the other and arguing that the shifted weight is not negligible. Again, I think the key is in how much the rope weighs versus how much the monkey and/or bucket weigh.
I think Snailboy may be right, though. If the pulley has enough inertia to keep spinning after it’s pulled, it will also have enough inertia to resist that initial pull when it occurs. That means I improperly invoked the corollary to Newton’s First (such hypocrisy!) in my analysis.
And we saw the climbing machine in motion and in action, but we weren’t allowed to observe the system for any time afterward. It still seems to me that there’s a shift of mass (the line being drawn in by the machine) from one side of the balance to the other. Since the line in the video is very light (like tooth floss) the system might not display the effect of that shift until after the climbing motion has stabilized.
–G?
Has this never been tried at a zoo?
*I edited out my point that the set-up could just as easily talked about a frictionless fulcrum-point in the air, held in place by heuristics. It was yet another distraction and failed to support my point.
There is another thread that is related, here. The OP, Princhester, says it is not a restatement of the monkey-on-a-rope problem, but I think it is. What do y’all think?
The other thread’s problem is related, but it is not the same.
Can’t we all just get along? What is the difference?
Forces other than gravity being involved.
In this problem, it’s clear that something or another, at least, is moving, since the length of rope between the monkey and the bucket is changing. In the other problem, the length of string between the masses is not changing, and the whole question is whether anything will move at all.