It is amusing how many of my peers still hold to the notion that heavier things fall faster. Not a higher terminal velocity, but the intuition that they accelerate faster. Hilariously tough for folks to shake.
Add air resistance into the mix, and denser materials do fall faster. Coins vs. napkins. Plums vs. crumpled balls of paper
I'd actually take the lesson the other way. It's hilariously tough for model-makers to acknowledge real-world noise that prevents their theoretically precise models from delivering reliable results.
> There are no experimental results mentioned anywhere in this book, except in one place where there is a ball, rolling down an inclined plane, in which it says how far the ball got after one second, two seconds, three seconds, and so on.
> The numbers have ‘errors’ in them – that is, if you look at them, you think you’re looking at experimental results, because the numbers are a little above, or a little below, the theoretical values. The book even talks about having to correct the experimental errors – very fine.
> The trouble is, when you calculate the value of the acceleration constant from these values, you get the right answer. But a ball rolling down an inclined plane, if it is actually done, has an inertia to get it to turn, and will, if you do the experiment, produce five-sevenths of the right answer, because of the extra energy needed to go into the rotation of the ball.
> Therefore this single example of experimental ‘results’ is obtained from a fake experiment. Nobody had rolled such a ball, or they would never have gotten those results!
> “If I ask you a question during the lecture, afterwards everybody will be telling me, ‘What are you wasting our time for in the class? We’re trying to learn something. And you’re stopping him by asking a question’.”
In my experience there are almost just 2 types of motivated students: those who want to understand the content of the course and those who want a good grade and ultimately graduate.
There's often a conflict of interest between them. For example the first group wants to learn more, ask more questions, go deeper. The second group sees this as a threat because the additional content may now be on the exam as well. And they often misunderstand this behavior of the first group as just being teacher pleasers/pets.
Or from own experience: when you tell the prof that he accidentally started to cover the same topic that we already covered in the last lecture (because you're there to learn more), you will annoy a lot of people who hoped to get one fewer lectures to study in the course. Less content, less effort, same grade.
You hear the first group having passionate discussions on physics or programming over a beer, while the other group discusses all the latest info of which prof is how demanding, what the grading criteria are, what the deadlines are, which departments you should or should not take courses from, where they have mandatory presence, who does multiple choice tests and who does free-text exams.
I don't have much to conclude, just an observation.
The reality I've learned is your intuition isn't necessarily wrong, it might just need more information. Arisotlian..."physics" isn't wrong neccessarily, it's just a model of motion under certain conditions (everyday conditions on Earth under an atmosphere or/and on friction-full surfaces) Newton's 1st can be thought of a generalization of Arisotle's (or anyone's) intuition...which to make things worse, physics' 101 students are not taught about.
One of the things I think was the best ideas I learned in physics is that physics is all about approximations. Theorists tend to forget this annoyingly, but it helps keep naive scientists from using words like "fundamental" without qualifications, or saying garbage statements like "Newton's law X is wrong."
This is exactly why making more FCI-style questions is so hard. They shouldn't be sensitive to things like air resistance -- a question whose answer is completely changed by realistic air resistance isn't a very good one.
I covered that with terminal velocity. And it isn't just falling, but going down a hill. Folks commonly think heavier bikes will go faster down a hill. That isn't how that works.
Faster bikes will go downhill faster. Both the acceleration of the bikes and their terminal velocity are determined by aerodynamics (on very steep hills) and rolling friction (on less steep ones), and those do not change much with bike weight.
Heavier things really do fall faster in the sense that they also pull the earth towards them which increases the relative acceleration and thereby decreases the time until they hit each other.
F = G * m1 * m2 / r²
This tells you that the acceleration of mass 1 is independent of the mass 1 and only depends on mass 2 and the acceleration of mass 2 is independent of mass 2 and only depends on mass 1. But the relative velocities will increase when either m1 or m2 is increased.
E.g. a black hole with the mass of the earth will hit the ground of a (perfectly rigid) earth in almost half the time as a feather would.
Heavier things do gain kinetic energy faster when falling, it's easy enough to confuse "being hard to stop" with "moving fast." Intuitively, the heavier object has "more" of something but in casual conversation "kinetic energy" isn't a common or familiar term. If you haven't studied enough physics to reach for that concept, I'm not surprised a lot of people just settle on "faster" when attempting to describe it.
Yeah, and we have words for that. Momentum, is a good one.
I should clarify the last time I had this conversation, I'm talking about 40+ year olds building bikes. They were thinking a heavier bike would accelerate faster down a hill. That just is not how that works.
It actually is though! The force due to air resistance is the primary thing slowing down the bike and rider, and the force, which doesn't change with mass, slows down a heavier bike less, and so a heavy bike will be rolling faster than a lighter one at the bottom of a hill, all other things being equal.
Right, you can hit a higher velocity. You will not get extra acceleration. That is my entire point.
That is to say, the force from the air does not actively slow you down. It prevents you from speeding up, after a point. (Aerodynamics are, of course, more complicated. But this general model is pretty solid.)
Such that if I want to accelerate faster down the hill, I have to pedal to cause that to happen. Or add a motor.
The heavier bike will reach the terminal velocity of the lighter bike sooner than the lighter bike will. If that's not extra acceleration then I don't think you're looking at the problem from a practical perspective.
Yes, acceleration due to gravity is the same, but air resistance has less effect, at all speeds, on the heavier bike. The rate at which the heavier bike gains speed is higher. It accelerates faster.
This is just disagreement over magnitude. And what it means to hit higher acceleration.
Take my statements to be, it won't hit a meaningful higher acceleration. Not that it won't necessarily accelerate for longer.
In general, you will accelerate down the hill at 9.8 m/s^2 modified by the incline. No matter how heavy the bike is. (Within the realm of realistic weights.).
Yes, the points you are raising are true. But within the realm of the biker and realistic bikes, not really relevant.
The velocity of the bike+rider is proportional to their mass. Realistically this can range over two orders of magnitude, which can be particularly relevant in a racing context.
It sounds like there could be a 100x difference between a light guy on a light bike and a heavy guy on a heavy bike. Sounds hard to believe, so I'm intrigued too :).
There is a larger gravitational force on heavier things because they're heavier. Trouble is, they also have more inertia, which exactly counteracts the larger force (because of the principle of equivalence) and so they fall at the same acceleration as lighter objects.
You can say that two larger things attract each other more than smaller things. Especially as they get closer to each other. Catch, of course, is all things on the earth are in the noise range compared to, you know, the earth. If you are talking about gravity and acceleration on the earth, you are talking about 9.8 m/s^2. Pretty much period.
And yes, there are terminal velocities that impact maximum speed. Acceleration, though, is not velocity.
It's correct. Terminal velocity is irrelevant here; it's true outside the atmosphere too. I really am talking about force and acceleration.
It's clear that there's more force on a heavier object. How much force do you have to apply to counteract a bucket full of rocks from falling to the ground, vs. an empty bucket? Your arm is certainly applying more force to the former.
So then the question becomes Why doesn't the full bucket fall faster? Because it has more inertia, and thus it's more difficult to accelerate. But there's also more force, which overcomes this difficulty. The amount of greater force is exactly identical to the greater inertia, so the acceleration remains the same. The "exactly identical" here is no coincidence.
Ah, I see what I screwed up. I was sloppy and saying force, but really only talking about acceleration.
So yeah, that makes sense.
Similarly, I only mentioned terminal velocity because I said faster. Which could apply there. But my point was focused on acceleration of falling objects. I get that there are a lot of ways to muddy that discussion. As exemplified by my postings. :).
If your model can't be used to predict things in reality, then what good is it? If I throw a feather down from a rooftop and then I let a brick fall down, the brick will hit the earth first. The heavier thing falls "faster".
You can use a bunch of words to explain what's really going on there, but it won't change that the brick hits the earth first, hence it falls faster. Unless you can predict the future correctly and communicate this simply to your peers, what's the point of being correct in the terminology?
I distinguished between velocity and acceleration.
My point was strictly that many people will falsely think gravity somehow meaningfully pulls lighter objects at a lower rate. This despite days off lessons that gravity on Earth is basically a constant.
That is to say, if your model of speed of things falling is hinged solely on gravity, it will not be predictive in the extremes.
Of course, most folks aren't playing in the extremes, so the simple model will be fairly predictive of everything they do actually toss around the room. Can easily explain why the stack of books fell at the same speed as the basketball when the dresser was knocked over. :)
Doesn't explain why the paper plane glides, though. I was always frustrated in physics class. There just wasn't enough precision to describe reality and everytime a test said "ignore friction" I would mentally shout out "but there is friggin' friction". Math made a lot more sense and it was only with advanced math knowledge that I would finally be able to make sense of some of the entry physics stuff.
If only they had told me everything (including friction), then maybe phyics would have made a lot more sense to me. But then again, school math never even mentioned imaginary numbers. School is very incomplete.
Because science aims to discover what is really going on under the hood. And that matters. By breaking the problem into vacuum and non vacuum you get a better understanding.
