Simple(?) physics question (need answer fast)

Factual Questions
1

Hi! This isn’t technically a homework question – I’m helping my daughter study for a science test. We had done this question and got the result on the answer sheet, but during review, the teacher said that the answer on the sheet was wrong, and I can’t figure out how. My daughter didn’t get the alternate explanation.

Anyway, here’s the problem. I hope description is clear enough.

There is a car being pulled by a boulder hanging off of a cliff (imagine a boulder attached to the car, with a pulley between them, hanging off the cliff). The car’s mass is 230 kg, the boulder’s mass is 30kg, no friction, it’s on Earth, the tension of the string is uniform, basically an ideal physics question. What is the acceleration?

Thanks in advance!

2

F=ma

What’s the force that’s pulling the car?
What’s the resulting acceleration?

3

No, I know that. I didn’t want to bias the results with our answer, but here’s what we did:

Total mass = 260 (230 for the car, 30 for the boulder)
Total force = 30N * 9.81 m/s2 ~ 294

acceleration = F/M = 294/260 = 1.13

Teacher says that’s wrong and the answer is approx. 300/200 = 1.5

4

Sounds like sig figs (significant figures) to me. Since there’s no .0 after the 30 and 260, we round off to the tens place. Hence the 300 / 200 = 1.5 because the 9.81 rounds off to 10.

5

If you want to round off that severely, though, 260 should round off to 300, not to 200, giving you an acceleration of 1.

6

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.

7

You did it right. The force is given by the mass of the boulder times the acceleration of gravity. The net acceleration of the system is the force acting on the system divided by the mass of the system.

Watch your units, though. You wrote:
Total force = 30N * 9.81 m/s2 ~ 294

which is apparently a typo. What you meant was:

Total force = 30Kg * 9.81 m/s2 ~ 294N

8

Right, sorry about the screw up on the units. I thought we did it right, and it matches the answer in the answer-guide, but the teacher said that that was wrong.

This teacher is kind of a screw up (here’s hoping she doesn’t post here), so it could be that she was just wrong the second time. Frustrating, though, and confusing enough for kids just trying to learn this.

If anyone else has an explanation on how the answer could be 1.5, I’d love to hear it.

9

Finding qualified science teachers for school is a chronic problem. Qualified people can make far more money in industry, and the educational system insists that a qualified scientist get an education certificate in order to teach in primary or secondary schools. Many (most) people who might be inclined to teach in a school out of personal interest (including, I might add, me) won’t be bothered with that kind of bureaucratic nonsense.

When my older daughter was in 7th grade, her class was studying DC circuits. The teacher called her up in front of the class and questioned her about her - I forget…homework? test? project?

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.

So, my wife went to ask the teacher about it. Teacher wouldn’t talk to her. I went to talk to the teacher. Teacher wouldn’t talk to me. To this day, we have no idea what the problem was, and we were willing to assist the teacher in increasing her understanding of the topic.

As it happens, working as a volunteer, I had started a science olympiad team at that school (a small private school in Ohio) and had been spending a great deal of time at the school, and had turned that group of kids into state-level contenders. My wife had been working with me. Probably the only thing she ever worked WITH me on…but that’s a different story…

So, when the teacher stonewalled us, we went to the school board about it. We didn’t have to go very far to establish our “expert” credentials; they knew who we were and what we were doing. We described the situation, showed the papers that were under dispute, and told the school board - very flatly and without equivocation - that our daughter was objectively and provably correct, the teacher was objectively and provably wrong, and we didn’t appreciate at all how this was being handled.

The teacher’s contract was not renewed.

Teaching science is very, very important. Getting qualified people to teach is very, very difficult given the environment. And the kids suffer.

Don’t back down. You did it right.

edit. Oh, also. After this event in class, at a science olympiad team meeting, we built the circuit that the teacher had claimed had the short circuit. It worked, of course. I did this simply because so many of the team were my daughter’s classmates. I was defending her, I suppose, but I was also teaching the kids…many things. And this was a good lesson.

10

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)

11

Right, but the mass isn’t 230 rounded down, it’s 260 kg, right? In other words, the total mass that has to be accelerated includes the boulder and the car, not just the boulder. (Otherwise, it would accelerate infinitely fast if it weren’t attached to the car)

12

In any case, it is wrong to round before doing the calculations.

13

Superscripts. :wink:

14

Yes. Maybe her teacher subtracted instead of adding, giving 230-30 = 200. Because it can’t just be coincidence that you’ve got 30 and 230. They’re just begging to be subtracted, giving that nice round 200…

The important thing is your daughter understands she did it right.

15

Right. Having evidence in hand that you know something about how to teach children, when your job will involve teaching children—that’s “beaurocratic nonsense.” :rolleyes:

Because of what a student’s parents said about the correctness of that student’s homework?

I will assume they spoke with some other expert before making that drastic decision. (And I will assume this teacher had a record of other incidents.) If not, this is a bad story, not a good one.

16

Look at Figure 30 of this link.

If I understand correctly, this is essentially the system under study. The corresponding acceleration is:

a = g*m_2 / (m_1 + m_2)

a = [9.80665 m/s^2* 30 kg] / [260 kg] = 1.1315 N

The teacher probably derived an incorrect formula for the acceleration, probably this:

a = g*m_2 / (m_1 - m_2)

Allowing g ~ 10 m/s^2, we have:

a = [10 m/s^2* 30 kg] / [200 kg] = 300/200 N = 1.5 N

Let me emphasis that this solution is wrong. The original solution is correct.

17

I just tried the problem to confirm, I think I found her (meaning the instructor’s) error, maybe.

Assume the coordinate system grows upwards (y) and rightwards (x). A subscript of “c” means car and “b” means boulder.

Since this is an ideal pulley we know the magnitude of acceleration (a) and the magnitude of the force of tension (T) on both objects is equal.

ΣF[sub]c,x[/sub] = m[sub]c[/sub]a = T
ΣF[sub]b,y[/sub]= m[sub]b[/sub]a = T - m[sub]b[/sub]g
=> T = -m[sub]b[/sub]a+m[sub]b[/sub]g

=> m[sub]c[/sub]a = m[sub]b[/sub]a + m[sub]b[/sub]g
=> m[sub]c[/sub]a - m[sub]b[/sub]a = m[sub]b[/sub]g
=> (m[sub]c[/sub] - m[sub]b[/sub])a = m[sub]b[/sub]g
=> a = (m[sub]b[/sub]g)/(m[sub]c[/sub]-m[sub]b[/sub]) = (30kg * 9.8m/s[sup]2[/sub])/(230kg - 30kg) = 1.47m/s[sup]2[/sup]

Do you see the error? It’s tiny. Not only did we assume the MAGNITUDES of the accelerations were the same, we assumed the (one-dimensional) DIRECTIONS (i.e. sign) were the same. I actually made the exact same mistake doing the problem the long way until I caught myself halfway through. If the teacher did the problem the “long way” to confirm it was correct, she probably made the same error I did.

As soon as you realize that, given the coordinate system we set up, that it’s not m[sub]b[/sub]a, but rather m[sub]b/sub, it works correctly.

18

Er, take out the negative on this line, I changed my mind several times on whether to type the actual solution or the incorrect solution and accidentally left the correct version of this line in.

19

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

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.

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.

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. And requiring a teaching certificate says that this person has to pay money and spend time to go back to school to get a piece of paper that “qualifies” him to teach a subject he knows thoroughly so he can make a fraction of what he can make in industry. It is a very substantial disincentive.

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.

20

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.”

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.