Evidently teaching physics is hard
falstad.com
falstad.com
This seems to me that years of physics/science teaching has ruined the ability of these students to actually think.
A child that has seen a movie or documentary about astronauts floating around in a spacecraft, may very well guess that the pen would float. "Space" seems to be the common denominator, not "on a large rock". From most perspectives, the earth looks nothing like the moon.
This seems to me that years of physics/science teaching has ruined the ability of these students to actually think.
The more you know, the more options you have to consider before coming to a conclusion. Considering all the, mutually influential, effects that could play a role, you may simply get overloaded. The problem isn't the capacity to think, it's the ability to easily and swiftly dismiss all irrelevant factors. I believe I could have made this mistake in my first year as a physics student.
This was a big problem when I played rapid-fire, Jeopardy-style trivia games in school. One learned to dread questions that were in a field you actually knew. The knowledge slows you down!
Trivia questions are generally written by knowledgeable non-experts. But a question which is clearly phrased from the perspective of a knowledgeable non-expert can be imprecise enough to cause an expert to pause, and pauses are deadly in rapid-fire trivia.
It's hard to construct a perfect example, but suppose you got a question that boils down to "who first demonstrated radio"? A lot of people will blurt out "Marconi" -- he did, after all, apparently score the first patent for a radio set, and he was a good self-promoter. But the physicist or historian, who might know about Tesla and Oliver Lodge, will object, or at least hesitate for a fatal moment.
It's an inverse square law based on the distance between the objects (and also the mass, but the distance is the key factor in this scenario). The earth is 200,000+ miles away, which is why the moon's gravity will win out over the earth's.
It's really sad that college physics students failed so badly at the question.
Even if, at 200,000 miles, the Earth's gravity was stronger than that of the Moon's, the pen would still fall to the Moon.
Think about it.
I liked the explanation given by my high school physics teacher: in the end, it boils down to frame of reference -- since both the moon and the pen are in orbit (aka perpetual free-fall), the earth's gravity basically becomes "background" to the situation and has no effect on the relationship between the pen and the moon.
It's not the concept of gravity, the mathematical formulas, or anything else that's really hard to grasp. Looking at things from the right frame of reference is hard, and not just in physics either. I struggle with this in my daily work, even for simple things like getting widgets to align correctly relative to each other.
That bothered me. So I checked Wikipedia:
Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).[4] [25] The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the Sun is on average 389 times farther from the Earth, its field gradient is weaker
So the distance does matter, it seems. Can anyone figure out under which conditions a pen doesn't fall to a moon?
The rotational speed matters as well. If a planet were to turn fast enough that the centrifugal force is stronger than the gravitional force, it would shed matter, and a pen would be first to go. (Do such bodies exist? Anyone knows? Presumably, it would have to be solid to stand a chance)
[This is all quite off-topic, of course. Yay for random thoughts on physics]
When there is a force holding the moon in place that doesn't act on the pen as well, or the pen is really far from the moon.
Orbit is a special case, so assume earth, moon and pen start at rest. They will all start accelerating towards their combined centre of mass. The pen essentially doesn't contribute at all to the location of the centre of mass; If moon and earth had quasi-zero radius, the pen would hit the object first on whose side of the centre of mass (CM) it started on. (the objects' acceleration will be such that their individual CMs would hit the CM at exactly the same time, so the objects nearest the CM will accelerate slowest)
earth - pen - CM - moon -> pen hits earth first.
earth - CM - pen - moon -> pen hits moon first.
The original question is clearly the latter case. In fact the pen and the moon are so close compared to any third objects, and the pen's mass so irrelevant, that you can treat them as being in the moon's frame of reference. So unless there's a force acting on either the moon or the pen which isn't acting on the other (this can never be true for gravity), the pen will always drop to the moon.
Because this is true in general, it is also true in orbit.
Aside: Note that there cannot be any tides on the moon because the moon itself rotates around its own axis at the same rate as it rotates around earth. Also, the water involved in tides doesn't start floating off - it is still very much attracted to the earth, and the deformation of such a gigantic body of water is extremely slight - metres of deformation of a shell with a radius of ~6300km. You won't notice the pen's reaction to that sort of force.
If you were traveling at the same speed as the moon and at the same distance from the earth you would not be in earth's orbit because you weigh approximately 0, while the moon has enough mass to actually exert some pull on the earth. So the moon's gravity is what's keeping you orbiting around earth, you're not orbiting around the earth only the moon is and it's taking you for a ride.
By my back of the envelope calculation at 384,000km the earth's pull would be .0025m/s^2 while at the the moon's surface it's pull is 1.625m/s^2. So the earth's gravitational influence would be about 1/1000th of the moon's, so the moon would be the overwhelming force causing the pen to drop.
I just asked my friend the question (since I wanted to send him the link) and he started asking all sorts of follow up questions because he couldn't believe I'd be asking him such an easy question.
The moon in question could be Phobos, Titan, Europa etc
So drop your pen in a dusty part of Saturn's rings for example and it might be the biggest "moon" around and start attracting smaller bodies to itself.
I've seen people drop pens on to moons like that, and can confirm that they fall to the "surface" pretty quickly. (Sorry, I'll be back off to Reddit now to say 20 Hail Marys.. :-))
Unless it's an imaginary moon. I'll give you that.
When I was in college, every once in a great while, I'd be stopped on the street and asked some question, usually by a psychology student. I'm not necessarily happy today with the smart-aleck I was then, but my answers were always completely off the wall. Q: Who's the Vice President? A: Paul Newman. Q: What's to the north of the U.S.? A: Africa. (I'm making up the questions. They were about general knowledge, but I no longer remember what they were).
I mean, there wasn't anything at stake. Why the hell wouldn't I give completely off the wall answers? So, somewhere, there are a bunch of people laughing at stupid American college students at least partially because of my answers.
Ok, so if someone asked me a question like that in the street today, I would probably answer exactly the same way (haven't matured all that much apparently). Wouldn't you?
That said, the page said pretty explicitly that the question was asked on actual quizzes, which presumably means the students expected to be graded.
On the positive side: they presented 40 of the 48 wrong answers they got. 34 of the 40 came from first-semester physics or astronomy. So at least it appears the majority of second semester and higher level students got it right.
Only in my dreams ... only in my dreams.
You don't even need to take the class to know the answer is C.
So the only people who have ever seen this video you refer to are people well over forty, people who have been shown a videotape in (e.g.) a physics class, and people who have caught it on YouTube, a medium which is only a handful of years old and where it is hard to find moonwalk videos among all the piano-playing cats.
It's probably hard for young people today to appreciate what life was like before home video recording. You had to hope for the TV networks to rerun something in order to see it a second time! There were also only half a dozen channels on TV. And we had to walk to school uphill both ways in the snow...
Hey, the pen really could float away, no? The centrifugal force on a rotatating body is mv^2/2. If this is exactly equal to the gravitational force, the pen would "stay where it is". And if it rotates faster than that, the pen would "float away".
"If a pen is dropped on a moon, will it: A) Float away B) Float where it is C) Fall to the surface of the moon
"So a bunch of us TA's got together and gave our physics classes quizzes asking this question. Out of 168 people taking the quiz, 48 missed the question. The responses are below. Some people didn't write comments. The spelling and grammar were not changed, however, clarifying comments are enclosed in []'s."
All I can say after reading the comments is "Wow!" (I had to laugh to keep from crying.) The student responses from Physics 324 - Modern Physics for Engineers have to be seen to be believed.
Also, I don't really understand how it would be intuitive for the Earth to attract the pen and not the Moon.
The classic gravity analogy is billiard balls sitting on a stretched sheet of plastic. The force of gravity is like the slope of the dents on the plastic - very steep around individual bodies and dropping off quickly after that. So drop something close to any given body and it's going to have a much greater influence than a larger body further away.
Here's another fun one: A student is standing on a rock orbiting a stellar body at a distance of eight light-minutes. The stellar body is much, much more massive than the rock. The student drops a pen. What happens to the pen?
It hangs from the chain that attaches it to the desk to keep it from being stolen even though the bank is "too big to fail".
The problem can be easily answered by using a thought experiment. Unfortunately many of such techniques are usually not taught in classes unless you are a in a Physics class for Physics majors.
(on HN a few months ago).
I believe the earth's gravity is stronger than the moon's even on the surface of the moon. In order to get the correct answer a student must think about orbital velocities and the way velocity helps objects stay in orbit and not fall to the ground, even if there is a gravity force exerted on them. And then the student would have to imagine the pen not as something stationary on the moon, but as something that is travelling around the earth (with the moon) at high velocity, and then the student would have to realise that the pen has sufficient orbital velocity not to fall to the earth, but in relation to the moon it has very little orbital velocity, so it will fall to the moon and not to the earth.
So my point is this is not that simple and it requires some imagination and complicated reasoning to get the right answer.
Of course most people should get it by remembering the moon landing videos and remembering how the astronauts were bound by the moon's gravity in those videos, but maybe kids these days have not even seen the moon landing videos.