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Originally Posted By: Master1
So, we were asked if, in a frictionless vacuum, applying force perpendicular to the direction of a moving object would a) increase its speed, B) decrease its speed, c) make it turn, or d) do nothing.

I figured that both a and c were right. Clearly the object will start to move in a new direction, making c correct. However, my physics teacher said that as it begins to move in the new direction, it will lose speed in the original direction. I fail to see how this happens. Can anyone clarify?


(a) is definitely correct: The component of the object's velocity in the original direction will not change. The object originally had zero velocity in the perpendicular direction, and over time that component of it's velocity will increase. As a result, its overall speed can only increase. To express it quantitatively, let the original velocity be v_x, in the x direction. The velocity in the y direction is initially zero. So, before the force begins to be applied the speed is just |v_x|. As the force is applied over time, v_y, the velocity in the y direction is a function of time, and the overall speed is sqrt(v_x^2 + (v_y(t))^2).

As to whether the object 'turns', this depends on what one means by 'turning', and on whether the force was applied over some non-zero period of time, or was just an instantaneous impulse. If the force is not applied in line with the object's center of mass (assuming that the object isn't point-like), then the object will begin to rotate (and will continue to do so even after the force is no longer being applied. If that isn't what was meant (and I'm guessing that it wasn't), then if the force is applied over some period of tie, the object will move along some non-straight line curve during that time. Of course, once the force is no longer being applied the object will once again resume traveling in a straight line.

Originally Posted By: waterplant
If the perpendicular force has a greater velocity than the object then it would increase in speed (see billiards).

I'm not sure quite what you're getting at here, but I think you may be confusing the application of some idealized force with a collision between objects.
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Originally Posted By: Master1
I figured that both a and c were right. Clearly the object will start to move in a new direction, making c correct. However, my physics teacher said that as it begins to move in the new direction, it will lose speed in the original direction. I fail to see how this happens. Can anyone clarify?


wow, your physics teacher apparently needs to read up on how newton's first law works

for the record, what will actually happen is that the object's speed will increase, and the direction of its velocity will change
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Right, that's what I thought would happen. He wrote the questions in ten minutes as we were reading the into to force, so he probably wrote his question wrong. Or answered it wrong. It's funny because we went over Newton's Laws right before he answered this question.

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Originally Posted By: Master1
However, my physics teacher said that as it begins to move in the new direction, it will lose speed in the original direction. I fail to see how this happens. Can anyone clarify?

This is bad on all levels. Aside from the fact that velocity components add quite nicely, you can't lose speed in a direction. Speed is a scalar, not a vector, and you don't have speed in a direction, you have velocity in that direction.

—Alorael, who thinks it's a fairly major problem for the teacher to get just about every part of a problem and its answer wrong. Oh, and "make it turn" doesn't really make any sense. It might turn end over end, it won't make a right-angle turn like a car at an intersection, but it will have a new trajectory. Which of those are or are not turns?
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Originally Posted By: Master1
Right, that's what I thought would happen. He wrote the questions in ten minutes as we were reading the into to force, so he probably wrote his question wrong. Or answered it wrong. It's funny because we went over Newton's Laws right before he answered this question.


Wait until you get into graduate school. I've had exams where the students find that the professors made mistakes on the questions. Written prelims are especially bad when we recognize the question from a text book and can tell exactly what was copied wrong.
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I'm not so fussy about speed vs velocity when you are specifying a single direction in the first place.

 

But I think here the problem is just ambiguity in what is meant by 'applying force perpendicular to the direction of a moving object'. Once the object accelerates in the perpendicular direction, then the direction of its motion is changing. If the force was not applied for just an instant, as Niemand suggested, but instead continues to be applied, then this is the critical question: is the force to be maintained perpendicular to the original direction of motion? or is it supposed to shift so that it remains perpendicular to the instantaneous direction of motion at any later time?

 

In the first case, velocity and acceleration are indeed vectors whose components evolve independently, and so the speed in the initial direction never changes, and the object gains speed in the perpendicular direction.

 

But in the second case, it's not so simple. As the force shifts around to remain perpendicular to the changing motion, it acquires a component in the direction opposite to the original motion. So this does make the object lose speed in that direction, just as the teacher said.

 

If the magnitude of the force changes as well as its direction, then the resulting motion can be quite complicated. But if the force's magnitude is constant, and only its direction changes (in order to remain perpendicular to the motion at all times), then the motion that results is exactly a circular orbit at a constant speed.

 

Presumably this is what the teacher was getting at, since circular motion under a central force is an important basic physics concept that is probably on the curriculum. As we can see, it's not that easy to explain clearly.

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You know, I was under the impression that even if the force lasts only for an instant, the speed won't change. Consider the definition of work and the work-kinetic energy theorem: no work is done, because the force is perpendicular to the displacement of the object, and no work done means that no change in kinetic energy is possible. A quick Google search on "force perpendicular to velocity" shows a whole bunch of people saying essentially what the teacher under discussion said.

 

I'm not sure how to explain this purely with forces and accelerations, though. Maybe the issue is that applying a force perpendicular to the velocity for an instant is fundamentally ambiguous, and we need to ask whether the force's absolute direction or relative direction is intended to fixed even if it's just for an instant. People normally mean the latter when they talk about this, but nothing in the wording prevents it from being the former. I find that unsatisfying, though.

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Well, a force that really lasts only for 'an instant' doesn't really do anything at all. But the idea is to consider a so-called 'impulse', a very strong force applied for a very short time, such that the integrated change in momentum is finite. In this case, the force is so strong that it gives the object finite velocity in the force's direction, even during the short interval in which the force acts. So the force does manage to do some work, if it keeps fixed direction. It's one of those order-of-limits things.

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Originally Posted By: Student of Trinity
Presumably this is what the teacher was getting at, since circular motion under a central force is an important basic physics concept that is probably on the curriculum. As we can see, it's not that easy to explain clearly.

As he explained it to me, it was clear that he was trying to get at circular motion. I understand that the speed in circular motion would stay the same, but his way of phrasing it was incorrect, leading me to assume that the force was being applied only in the direction perpendicular to the initial direction. Given that my teacher is known for being wretched at explanations, I think I'm going to have a fun year...
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Originally Posted By: Student of Trinity
Well, a force that really lasts only for 'an instant' doesn't really do anything at all. But the idea is to consider a so-called 'impulse', a very strong force applied for a very short time, such that the integrated change in momentum is finite. In this case, the force is so strong that it gives the object finite velocity in the force's direction, even during the short interval in which the force acts. So the force does manage to do some work, if it keeps fixed direction. It's one of those order-of-limits things.

So yeah, it basically boils down to the fact that a momentary force perpendicular to the motion is actually an ill-defined concept in itself, conventionally defined as the teacher described but not necessarily so. Okay. I buy that.
Originally Posted By: Lilith
F = ma. a = delta-v / delta-t. So yeah, you need a non-zero delta-t in order for acceleration and therefore force to be meaningful.

Well, in algebra, yes. But in calculus, you take the limit as delta-t goes to zero (a = dv/dt), so an infinitesimal amount of time isn't really a problem for calculus-based physics.
Originally Posted By: Master1
Given that my teacher is known for being wretched at explanations, I think I'm going to have a fun year...

Physics is also terribly hard to explain anyway. Everything logically connects, but it's hard to take people from "I don't get it at all" to "I see the big picture and also how it applies in this particular case," which is how virtually all of physics proceeds.
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Originally Posted By: Kelandon
Well, in algebra, yes. But in calculus, you take the limit as delta-t goes to zero (a = dv/dt), so an infinitesimal amount of time isn't really a problem for calculus-based physics.


Yeah, I was assuming that he wasn't yet at the point where calculus really started to get involved in teaching physics, since for me it wasn't until near the end of first-year university.
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It's true that I'm in regular old "Gifted and Talented" Physics, I'm also in Calc 2-3 (real Calc 3, not what most secondary schools call Calc 3).

 

EDIT: My point being that I understand calculus principles and hate that physics is being explained without them. After all, what was calculus made for?

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Originally Posted By: Dikiyoba
As Dikiyoba went to a high school that only offered one calculus class, what does "real Calc 3" entail?


Calc 1 is probably a single variable differentiation/integration/limits. It's an easy class for high schoolers. Calc two and up is probably more like a multivariable class, with partial differentials, differential equations, contour/surface integrals, and more advanced stuff like that. I'd image that the order varies depending on the college/highschool.
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We have Calc AB and BC. I just put numbers instead of letters.

A is limits through derivatives.

B is definite and indefinite integration and associate topics.

C is all the other weird stuff. We've done series. We're finishing integration from last year. We'll also be doing multivariable and some other things I can't think of at the moment.

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Originally Posted By: Nikki.
Unless Calculus is called something else in England, and I sincerely doubt that, I don't believe I've ever taken a single class in it.


American mathematics teaching is structured differently. In Australia (well, Victoria at least), there's Further Maths, Mathematical Methods and Specialist Maths, which all have a bit of everything but with a different focus and pitched at different skill levels (for example, Further is the easiest and deals mostly with applied mathematics, particularly in business and finance, while Specialist is the hardest and involves fairly sophisticated calculus and trigonometry). In America, maths is normally broken up into individual subject areas instead: Algebra, Calculus, Trigonometry, etc. I'm guessing your system is more like ours?
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Still different. In the UK, from age 16 onwards, mathematics is optional. Historically you picked just 3 subjects (they increased it to 4 recently). I think under 40% study maths at that age so 60% never encounter calculus. (Out of those whose who stay at school post-compulsion.)

 

Generally at 16 students tend to pick all subjects on either 'arts' or 'sciences'. E.g. maths, physics and chemistry or e.g. history, political science and english. That's just a stereotype of course, there is a certain amount of mixing (personally I did maths, history and french, but then I am a bit of a freak). However most study maths because it is required by other subjects (physics/engineering).

 

Either way I don't think I would describe any of the maths I did at school as fairly sophisticated. In 2004 they also made it easier because too many students were dropping it.

 

Edit: Updated after finding the 2010 stats from BBC website. It's even worse than I thought. Out of 1,197,490 AS level entries, there were 112,847 for mathematics (9.4%). Assuming 4 subjects per student the participation rate would be 37.6% at age 17.

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Originally Posted By: Micawber
Generally at 16 students tend to pick all subjects on either 'arts' or 'sciences'. E.g. maths, physics and chemistry or e.g. history, political science and english. That's just a stereotype of course, there is a certain amount of mixing (personally I did maths, history and french, but then I am a bit of a freak). However most study maths because it is required by other subjects (physics/engineering).


Interesting. Over here English is mandatory for everyone up to year 12, and some kind of maths is mandatory up to year 11. The very best students will generally study both Specialist Maths and at least one foreign language (often Latin, especially if they want to get into law), because those are the subjects that give the best contribution to tertiary entrance scores. They'll pick their remaining subjects based on specific requirements for the course they want to get into (for example, Chemistry is at least very strongly recommended for prospective med students).
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Originally Posted By: Prick of a needle
Do they teach you how to reach the light-wave equation from the Maxwell equation?


By "fairly sophisticated" I meant "fairly sophisticated compared to Methods, in which the most complicated calculus you will learn is finding the area under part of a graph of a polynomial function using integration." I didn't encounter either of those equations at all in high school despite doing pretty much every maths and science subject on the state curriculum. Honestly, I thought your hopes would come a little more pre-crushed, you know?
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Originally Posted By: Lilith
Honestly, I thought your hopes would come a little more pre-crushed, you know?


I was hoping that the grade schooling abroad was better than the domestic one smile
So when you say calculus you don't mean infitesimal calculus I gather (or is it gander, but gander is a male goose)?
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Originally Posted By: Prick of a needle

So when you say calculus you don't mean infitesimal calculus I gather (or is it gander, but gander is a male goose)?


Wikipedia says "infinitesimal calculus" consists of differentiation and integration. We did those. I am assuming that Wikipedia's definition is incomplete.
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Proofs, lots and lots of proofs.

You haven't done real calculus (and suffered accordingly) until you proved something like Cantor's lema (which is one of the easier proofs once you understand the gist of it)

or the midpoint( or midvalue, I'm not sure how you call it in English) theorem

or the Weierstrass extreme value theorem.

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I hate to mention this to the Brits here, but I'm afraid that pretty much the rest of the world is quite suspicious of all British educational credentials, from A levels to PhD inclusive. The concern is that UK education is too narrow and too rushed, and so if you hire someone with X credential from the UK, there's a worrisome chance that they will not actually have the preparation you're expecting.

 

Obviously there are plenty of brilliantly educated British people. But the system as such is viewed somewhat askance.

 

I never seem to have needed Cantor's lemma. I did a bunch of Weierstrassian epsilon-delta proofs in first year university calculus, but I think we all thought they were fun. And the intellectual juggling involved in thinking about convergence and orders of limits actually is useful, from time to time, in physics. We frequently ignore it, but at least we know the risks, and we can figure out how to patch things up if it should turn out to be necessary.

 

I did once use that stuff to deduce an important existence lemma. We found a mouse in the office, and named it epsilon because it was small. Then we realized there had to be a delta, and looked for a second mouse. It existed.

 

The mice turned out to be coming from behind a mysterious ancient locked door that all four of us in the office had wondered about and then forgotten. Somebody showed up to open it, in the name of pest control, and we discovered a closet full of drafting supplies. Pencils, pencil sharpeners, drawing boards, rulers, stencils, French curves, exacto knives. A plug-in electric eraser, like a drill with a rubber bit. And an alarming number of bottles of Tylenol. A whole world that had vanished with the advent of laser printers.

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As a product of the British education system, I tend to agree. Holding GCSEs, A-levels and a degree is no guarantee that someone is competent at anything other than passing exams (and maybe only X% good at that, since the pass mark is often not so high). I guess dependent on the subject the PhD might potentially take you a bit further, however I have heard discouraging things about PhDs in experimental sciences (i.e. PhD students can be basically lab flunkeys).

 

As an manager who has had to interview candidates (and then work with them after, in some cases) I can also empirically say that the qualifications on someone's CV is not often a reliable indicator of their knowledge or skills.

 

When it's said "what matters is who you know, not what you know" part of the truth is that if you once work with someone who is really highly skilled, then you will recommend them and/or want to work with them again. There is a severe shortage in the world of skilled people who have any clue what they are actually doing.

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I had quite possibly the worst teacher I have ever seen — and while I've mostly been incredibly fortunate with good teachers, I've had a few really abysmal ones, so this was remarkable — for an Analysis class that I dropped after a few weeks of beating my head against a wall. Proving calculus with epsilon-delta stuff sounds pretty cool, but literally teaching yourself how to do it with a book that is useless and a teacher who is actively harmful (because he's confusing) is bad.

 

The college-track California educational system is maybe the polar opposite of the British system, in that everyone has to continue taking more or less everything (math, science, English, history, foreign language) except maybe in the final year of high school. There is a fairly substantial difference between AP or Honors courses and regular courses in most schools, though, perhaps as a result.

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Originally Posted By: CRISIS on INFINITE SLARTIES
Is that any less true of the American system, at least up to the level of a BA/BS? You can get a bachelor's degree with remarkably low grades and minimal effort, particularly if you're at a private university.

In some departments you don't even need to take the upper division classes (for junior and senior students), at least that happened until the University of Arizona tightened degree standards. Still you can graduate without learning anything useful.
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Not quite true. There aren't a lot of jobs that you aren't qualified to do without an English major, except perhaps the most illustrious work as an academic in the field of English, but there are definitely things it can help with, and there are jobs that prefer the degree.

 

And then there are the many, many jobs that don't really tie in with any particular degree. All they really want to know is that you're capable of graduating and reasonably intelligent.

 

—Alorael, who looks askance at certain non-discipline degrees. If you manage to graduate without a focus, maybe your lack of focus could be a problem.

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