Simple(?) physics question (need answer fast)

[Malacandra]

@california_jobcase

Oops. I believe teacher used

30 kg * 10 N/kg = 300 N
230 kg rounds to 200 kg

A = F/M, so 300 N / 200 kg = 1.5 m/s/s

Force is newtons, mass is kilograms, acceleration is meters per second squared (I don’t know how to do subscripts)

Code: CO[noparse][sub]2[/sub][/noparse]
Read: CO[sub]2[/sub]

Code: e=mc[noparse][sup]2[/sup][/noparse]
Read: e=mc[sup]2[/sup]

[RitterSport]

I want to thank everyone for the help, even tracking down where the teacher probably made the error. I need to go through Jragon’s corrected wrong solution (wow! that’s oxymoronic) again to really understand where the teacher went wrong, but I’ll let my daughter know that our solution was right.

This teacher also seems to confuse static friction and kinetic friction, which is really screwing me up. Frustrating.

[Frylock]

@Bemused

shrug. Reality is. And, actually, it’s “bureaucratic nonsense”.

Oh, I misspelled a word. You must be right about everything.

While there are exceptions I suppose, the typical scientist or engineer who would make the choice to enter the elementary or secondary classroom (and it is a choice that will cost money) does so out of personal interest and, usually, only under circumstances where money is not an issue.

I would suggest that the person with that kind of background who makes that kind of choice IS able to teach kids. Clearly, many scientists/engineers are NOT good teachers, but many are. And in this particular situation, mostly those who self-select will be good teachers. And if they’re not, everyone will know it soon enough.

You would suggest?

You’re a scientist. Show me the data. Where’s the research that says self-selection determines which experts are the best teachers?

Contrast this with the teacher who doesn’t understand science but has to teach it anyway. Why? Because someone has to do it. So (s)he takes a 6 week summer training course on science education and - bada boom! - is a science teacher. Who can’t do an elementary physics problem.

I agree with you partially here–I think the choice between someone who doesn’t know science but knows how to teach, and someone who does know science but doesn’t know how to teach, is a very unfortunately choice to have to make.

The basic point is that it has to be a lot easier to turn an experienced scientist/engineer/mathematician who has decided (s)he wants to teach into a good science teacher than it is to turn a teacher who doesn’t know science into a competent science teacher.

I agree with this too.

BTW I should clarify–I think teachers should be experts in their subjects. What I disagree with is the view that an expert simply saying they’d like to teach in any way qualifies them to teach.

I’m pretty sure they didn’t speak with some other expert. Wouldn’t have mattered if they did; we were right. We did indeed have the credibility with the school. And, yes. There had been other incidents involving this teacher.

Though the pattern of incidents may show she should eventually have been let go, in this particular incident, as you’ve told the story, it is clear that she was treated unjustly. Being the parent of the child in question makes irrelevant any “credibility” you had with the school.

[Jragon]

@RitterSport

I want to thank everyone for the help, even tracking down where the teacher probably made the error. I need to go through Jragon’s corrected wrong solution (wow! that’s oxymoronic) again to really understand where the teacher went wrong, but I’ll let my daughter know that our solution was right.

This teacher also seems to confuse static friction and kinetic friction, which is really screwing me up. Frustrating.

The incorrectness is that in an ideal pulley machine system, we know that ||T1||=||T2|| and ||a1||=||a2||, but T1 is not necessarily equal to T2, and a1 is not necessarily equal to a2. Remember that force and acceleration are vectors, they have magnitude and direction, we’re only guaranteed their magnitudes are equal in this case, not their directions.

The teacher likely said a1=a2=a, rather than a1=a; a2=-a which is how it should work assuming you have y pointing up and x pointing right (if y is pointing down then F[sub]b[/sub] = ma = m[sub]b[/sub]g - T – which gives the same result).

[standingwave]

@RitterSport

To me, it looks like she subtracted the mass of the boulder from the mass of the car for some reason. To calculate the acceleration, isn’t it the force due to gravity acting on the boulder and the total mass of the system (boulder + car)?

   car---------O
  ------|      |
        |      |
        |      |
            boulder  

It looks something like the above (the O is the pulley). The car is sitting on a cliff.

Why the total mass? It seems to me (and statics/dynamics was about thirty years ago for this sparky) that once you’ve determined the force acting upon the car is 294N, then you have a 230kg car with a 294N force acting on it:

car---------> 294N

a = f/m = 294N/230kg = 1.28 m/s^2

What am I missing?

[Jragon]

That’s if they’re not tethered together (i.e. you have a mass in free-fall). If you draw a free-body diagram, the only relevant forces acting on the system are tension and gravity on the block, but the force of gravity on the block is acting not just on the block, but the system ITSELF, and the mass of the system is being affected.

Remember, mass is the measure of an object’s resistance to change in speed, and force is the measure of an attempt to change its velocity. The attempt to change the velocity is done by the hanging block, but the attempt to RESIST the motion is done by the entire system.

This is why I like the long method (which I did above, albeit intentionally incorrectly) better, not only is it better once you get to rotational dynamics with non-ideal pulleys, but it is a bit more transparent about why you use the mass of the system.

[standingwave]

@Jragon

That’s if they’re not tethered together (i.e. you have a mass in free-fall). If you draw a free-body diagram, the only relevant forces acting on the system are tension and gravity on the block, but the force of gravity on the block is acting not just on the block, but the system ITSELF, and the mass of the system is being affected.

Thanks, I realized my error shortly after posting, as is often the case. I believe the source of my problem was trying to apply a static analysis to a dynamic system.

[billfish678]

This is one of those problems where checking the limits of the equation you derive makes for a good double check.

If the mass of the boulder is zero, the car ain’t gonna move and the acceleration should be zero. If the mass of car is zero, the car should accelerate at one G, like the boulder would normally do in free fall.

You plug those two scenarious into “your” equation and you see if get what you think you should get at the limits. If things blow up, go negative, or otherwise seem off, then the equation might have an error in it.

[Chronos]

Quoth Bemused:

In any case, the teacher told her in front of the entire class that she had done it wrong and her design had a short circuit in it. Why this came about, I have no idea.

So, my daughter - who was very upset at being humiliated this way - came home and asked her parents about it. Now, as it happens, her mother is a physicist who teaches at a university. Her father (me) is a physicist who has worked in industry pretty much forever and has done a considerable amount of electronics design along the way.

And what she had done…was perfectly correct. No errors, no short circuits, or anything else.

I’ll bet you I can tell you what the assignment was, and possibly also what circuit your daughter turned in, and I can also tell you how the teacher’s thought process was working that led her to think your daughter’s circuit had a short.

The problem was to figure out how to wire together two three-way switches so that you could turn a light on or off with either one (you often see this at opposite ends of a hallway, or at the top and bottom of a flight of steps). There’s one standard way to do this, that has a variety of subtle advantages to it, and which is how it’s usually wired in a house. There’s also an almost-right way, that will give the right behavior for the light bulb, but is a short circuit when the light is turned off. And then, there are also about four other ways of doing it that you’ll never find in a book, and which are subtly inferior to the standard way, but which still work correctly and without ever shorting out. And one of those alternate ways of doing it looks almost exactly like the way that does have the short.

So what I’m guessing happened is, your daughter managed to come up with the way that looks like the one with the short. The teacher had never seen that way before, but recognized that it wasn’t the standard way. And she’d probably seen the short one before, and had to explain to students that it wasn’t acceptable because of the short. Presented with a circuit that she knew wasn’t the standard one, and which looked a lot like the one with the short, she jumped to the obvious (but wrong) conclusion.

Am I close to the mark?

Here’s the thing, though. Her problem wasn’t in failing to recognize at first that the circuit was correct-- That’s actually a very easy mistake to make, even for one with expertise in physics. Her problem was in her attitude when both your daughter and you tried to explain that it was right after all. And that sort of attitude could show up just as easily in an expert physicist, but is in fact the sort of thing they’re looking to avoid with the teaching certification. The teacher’s problem was not that she wasn’t a good enough physicist, but that she wasn’t a good enough teacher.

[CookingWithGas]

I can’t contribute directly to the OP but wanted to mention two things relevant to the side discussion.

I always though I would like teaching (I taught software design and programming in a corporate training program for a couple of years) but I make about 3 times what I would make as a teacher. And the part I like best is the classroom work but I guess that’s really only a small part of the job. Discipline, grading, dealing with parents, lesson planning, etc., is the hard part.

I was in my daughter’s teacher’s office when she was in the fifth grade pointing out to the teacher that the International Date Line was not the same as the 0th longitude line, as she had put on a flash card. She finally changed the flash card, but admitting only that “most” sources agreed with me. I asked her to provide even one that agreed with her and never heard back.

[Bemused]

@Chronos

I’ll bet you I can tell you what the assignment was, and possibly also what circuit your daughter turned in, and I can also tell you how the teacher’s thought process was working that led her to think your daughter’s circuit had a short.

The problem was to figure out how to wire together two three-way switches so that you could turn a light on or off with either one (you often see this at opposite ends of a hallway, or at the top and bottom of a flight of steps). There’s one standard way to do this, that has a variety of subtle advantages to it, and which is how it’s usually wired in a house. There’s also an almost-right way, that will give the right behavior for the light bulb, but is a short circuit when the light is turned off. And then, there are also about four other ways of doing it that you’ll never find in a book, and which are subtly inferior to the standard way, but which still work correctly and without ever shorting out. And one of those alternate ways of doing it looks almost exactly like the way that does have the short.

So what I’m guessing happened is, your daughter managed to come up with the way that looks like the one with the short. The teacher had never seen that way before, but recognized that it wasn’t the standard way. And she’d probably seen the short one before, and had to explain to students that it wasn’t acceptable because of the short. Presented with a circuit that she knew wasn’t the standard one, and which looked a lot like the one with the short, she jumped to the obvious (but wrong) conclusion.

Am I close to the mark?

Here’s the thing, though. Her problem wasn’t in failing to recognize at first that the circuit was correct-- That’s actually a very easy mistake to make, even for one with expertise in physics. Her problem was in her attitude when both your daughter and you tried to explain that it was right after all. And that sort of attitude could show up just as easily in an expert physicist, but is in fact the sort of thing they’re looking to avoid with the teaching certification. The teacher’s problem was not that she wasn’t a good enough physicist, but that she wasn’t a good enough teacher.

It has been more than a decade ago, and I really don’t remember the circuit. There were no subtleties, though. It had a branch, and there was a switch and a light and a resistor. My daughter pointed to the node where the branch occurred and said her teacher said there was a short circuit here. She couldn’t explain it, and I didn’t understand it; there was nothing wrong with the circuit, but I can’t reconstruct it now.

Now the reality is that the teacher did have a bit of a problem with me and my wife. We had tried to get the school interested in the science olympiad program - we had tried to get this teacher interested. We did not succeed. So, finally, I had a conversation with the principal and then with the school board, and with their blessing I started a team by simply announcing it as an extracurricular activity that I was volunteering to run. I then drafted my daughter, a couple of her friends, a couple of other parents, and we were off and running.

Well, the kids got into it in a really big way, and after awhile I had most of the 5th through 8th grade kids involved in it, and many of their parents, and it pushed out a number of other extracurricular activities because everyone wanted to work on this.

In fact, it was a much bigger success than I had ever expected, and the kids were all very enthusiastic.

Well, this teacher felt threatened by all this, and frankly she wasn’t a very good teacher anyway. I tried a couple of times to pull her into it, but she didn’t want to and I stopped trying.

So, I do believe that this is what was behind the whole thing. I also know that there had been other incidents, and when we went before the school board about this - and my approach was NOT “this is a bad teacher”, my approach was “this teacher is wrong about this, and is not willing to communicate with us about it” - I went before them as someone they knew, who had made all the children very enthusiastic about science.

We never suggested the teacher should be fired, and although we made the authority argument WRT the specific issue, we also said that we’d be more than happy to work with her on these things to help her out. I should point out that my wife teaches teachers how to teach science, working for a local university, and she has subsequently become somewhat prominent in the state of Ohio in that particular field. We are now separated, and I am in Arizona doing satcom work.

So, what I know happened is that the board looked at us, who had the kids all excited, and looked at the teacher who was, through her own choice, not participating in this. They did not doubt at all that we were correct in what we said about the particular issue, and the teacher was obviously displaying what could only be called a bad attitude.

As it happens, the replacement science teacher promptly started to feel threatened; he felt like we were way into what should be his turf. He and I had a conversation, and after that he joined the team as a coach. As time passed, he took on more and more of it and after my daughter graduated, I stepped down as head coach (our team at that time was ranked about 6th in the state) and continued as an event coach while he took over as head coach.

He was a much better science teacher but a few years later got fired because he couldn’t control his temper. Oh well.

[Bemused]

@Jragon

I think this gets into what I’ve heard referred to as the “Silicon Valley Problem.” Where engineers and scientists in Silicon Valley don’t participate in activism when it leads to what they believe is the right conclusion to a law affecting their field (i.e. opposing SOPA) because they’re so used to a meritocratic system in their every day lives that they simply assume the objectively best answer will eventually win out naturally.

Your proposal, Bemused, assumes that the self-selecting teachers that do poorly will be weeded out very quickly, when this simply isn’t the case. I’ve seen several horrible teachers, and I’ve known several qualified (meaning both accredited legally and academically) teachers in the same field looking for work that never manage to replace the terrible ones. It’s not as simple as “better replaces the worse.”

My proposal certainly does assume that. No question about it. And I absolutely agree that, given the current setup, it wouldn’t work that way.

I greatly fear I am hijacking this thread, and I don’t want to do that and didn’t intend this. But nonetheless, as you say, there are many very bad fully accredited teachers in the system. I personally know some simply outstanding teachers, and I also know some that certainly should be fired. But they’re not.

So, letting the self-selected professional scientists into the classroom without bothering with a teaching certification arguably would improve things. The scientist who is a poor teacher won’t be any worse than the incompetent science teacher and will probably be better than the incompetent science teacher who is also a bad teacher.

And the system needs to be changed so that the bad teachers can be eliminated anyway.

Now, I think education is in a bit of a sorry state, there aren’t enough people in the field who know the material to even authorize the correct textbooks or curriculum, as Feynman famously noted, but I don’t think “loosening the requirements” is going to fix too many problems, and could easily make it worse before it makes it better, and teaching kids really isn’t something you want to rock the boat with too hard. Experiment too much and you end up with 4 years of kids woefully under-educated while you tried to find the best solution.

We are already teaching science at a third world level; the great debates in this society that have scientific/technological components are frequently carried forth by incompetents as a result. How could it possibly be worse than it already is?

Great science classes ARE available for some high school students in the AP programs. But we need good science classes for all other students. And we don’t have those at all.

[Bemused]

@billfish678

This is one of those problems where checking the limits of the equation you derive makes for a good double check.

If the mass of the boulder is zero, the car ain’t gonna move and the acceleration should be zero. If the mass of car is zero, the car should accelerate at one G, like the boulder would normally do in free fall.

You plug those two scenarious into “your” equation and you see if get what you think you should get at the limits. If things blow up, go negative, or otherwise seem off, then the equation might have an error in it.

Checking the limits is a good thing to do with any problem. If the behavior makes sense at the limits, then that greatly increases your confidence that your answer is sensible.

I did the exact same thing you describe here, when I was looking at this problem.