When I took physics in high school, Gravity was introduced to me with an equation. After 5 minutes discussion, everyone in the room would have known how to answer the question about "Dropping a rock on the moon."
I find it hard to believe that a high school physics student, just fresh from studying gravity module, wouldn't realize that a rock dropped on the moon would fall down. Doesn't pass the smell test.
Being introduced to gravity with an equation is not nearly enough to figure out how things will behave. It takes calculus to describe the motion of falling things even without air resistance. Even if someone straight-up tells the students that gravity accelerates things at the same rate regardless of mass, they're probably not going to believe it without some experiments.
Edit: a quiz to maybe prove my point :) On the moon, if you throw a rock, what shape would its arc describe?
Edit2: not a straight line when you drop it, silly!
It's not even guaranteed to be a straight line if you drop it, due to variations in the density of different parts of the moon, radiation pressure, particles in the way (yes, the vacuum isn't absolute), any magnetic effects, gravitational gradient caused by other celestial bodies, etc.
The arc will approximate a conic section of some kind, depending on how hard you throw it. Within the usual level of ability of a space-suited human throw, it will approximate to an ellipse so close to parabolic as to be impossible to tell the difference before it hits the moon. Throw it harder and it'll approximate to an ellipse. You are only going to be able to approximate a circle if you stand on the highest point on the Moon and throw at exactly the circular orbital speed horizontally, although gravitational perturbations will usually break the orbit. It'll approximate a parabola if you throw at exactly the escape velocity, and a hyperbola if you throw even harder than that.
> tells the students that gravity accelerates things at the same rate regardless of mass
Please get your wording right, there is a big difference between force and acceleration. It is trivial to prove, that things are not accelerated by gravity at equal rate.
PS: I am not usually wording-nazi but since you started with calculus...
You have it backwards, qwerta. If the feather and the hammer fall to the ground in the same time they must have accelerated at the same rate. Of course the hammer has more force applied by gravity and the feather has less; that is why the hammer is heavier!
Yes, but in atmosphere it would be accelerated at a different rate. Stationary objects are not accelerated at all, because gravitational force is compensated.
As I was saying, there is difference between force and acceleration.
I read sp332's original comment as having an implicit "in the absence of other external forces" (gravity accelerates things at the same rate regardless of mass) as that's often implied when generally discussing forces and acceleration.
After all, it becomes hard to talk about the relationship between force and acceleration, if you can't even say that the acceleration of an object is proportional to a force acting upon it - because there might be other forces you've not taken into consideration! Yes, I won't accelerate an object if I try to push it into a barrier, because the barrier will exert an opposing force that resists my effort. Yes, an object might fall up if I "drop" it, because it's in an updraft that combined with it's drag coefficient causes more force up than gravity exerts.
But springing those sorts of situations on people as "gotchas" isn't useful in a general discussion about the essence of a concept. Unless otherwise specified, assume ideal point masses in a vacuum (or whatever). If you want to add opposing forces of some kind to complicate^W make the situation more realistic later on as a more advanced topic, that's fine, so long as that's specified up-front.
If complicating factors are not specified up-front, it's assumed that they're absent, because there are an infinte possible set of complicating factors which could be present but have not been mentioned yet.
After all, in an atmosphere it could be accelerated at the same rate, as there's a (previously unmentioned) anemometer and computer-controlled rocket attached to the object which are set up to produce a thrust which exactly compensates for the wind resistence! So ner! :-)
(And, in fact, sp332 specifically stated "even without air resistance" to explicitly constrain the conditions under which their example was valid)
This is not about edge conditions, but about two different concepts. Saying "gravity accelerates" does not make sense by definition, at least we should say "gravitational force accelerates".
The confusion is between the transitive and intransitive forms of the word "acceleration". If I say "the pen accelerates", this implies net acceleration of the object. If I say "gravity accelerates the pen", this implies gravity's contribution towards net acceleration. Air resistance diminishes net acceleration, but not the acceleration as contributed by gravity.
sp332 was fine. It's common for astrophysicists to talk about gravitational fields in terms of "acceleration fields" rather than "force fields". This is because the acceleration contributed by gravity only depends on a single argument (distance from the celestial body's center) as opposed to a force-field's two arguments (distance, the pen's mass). And next time you hear "g = 9.81 m/s^2 for all objects on earth's surface", the physicist is referring to gravitational acceleration, regardless of whether or not the object is moving.
That wasn't my point really. Oh well! I though most people would pick a parabola, which is a decent approximation for short throws but not the real shape.
It's an ellipse, but it is so elongated that it is extremely close to a parabola. If the entire mass of the moon was concentrated in a single point at its centre, and the projectile could pass through the moon, then the projectile would follow a parabola-like path and go down below the moon's surface, until it started curving around the other side of the centre and back up to its starting point. It's only when you look at the uninterrupted path that the difference between the parabola approximation and the ellipse becomes apparent.
The parabola results from assuming that the force due to gravity on the object is constant (which is a decent approximation over short vertical and horizontal distances). In fact it will change magnitude and direction as the projectile moves.
The curvature of the surface of the moon doesn't matter, but the fact that the rock is orbiting the center of the moon just like a satellite would is the insight that Newton needed a smack on the head to get :)
Would I be wrong if I said that the deviation between the parabola and the elliptical orbit trajectories is probably much smaller than the tidal effect of the earth and the sun, solar wind and other external forces on such short trajectories? And as such the elliptical model is "as wrong" as the parabolic one?
After all, a model is only as good as the precision of the results it produces...
It's not numerical approximations I'm worried about. It's the fact that if you don't understand what's going on underneath, you're not going to have good "intuition" when someone asks a question like: what happens when you don't ignore air resistance.
I distinctly remember my physics I teacher in highschool giving the class the classic "You fire a bullet and drop a bullet at the same time" question, at the conclusion of a lecture on gravity. Barely a tenth of the class got it correct, even though they were capable of deducing the correct answer from what they had just learned.
I find it hard to believe that a high school physics student, just fresh from studying gravity module, wouldn't realize that a rock dropped on the moon would fall down. Doesn't pass the smell test.