# Ball on String, Calc V with mass, answer by "accident?"

Hi all, concerned Dad here - looking for a validating opinion on the following and would be eternally grateful with some guidance/help. The attachment, Unit4ExamAQ7c is from one of my son's honor's exams. He gets #7c CORRECT with the answer v=2.29 m/s. However, the teacher grades him WRONG as he claims the answer was achieved "by accident." I asked an engineer friend to review the answer and his response was "the grader got it wrong due to laziness." his response is in the attachment ReviewofPhysicsExams. Thank you VERY much!!

#### Attachments

• Unit4ExamAQ7c.pdf
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• ReviewofPhysicsExams.pdf
56.2 KB · Views: 157

mfb
Mentor
Where did the angle get introduced? In the way it is used, it is apparently between the string and the vertical, but you should never make others guess that.
The formula works, but where does it come from? Certainly not from the wrong ##F_T = \frac{mv}r^2## to the left of it (and you need the correct version of it to arrive at the formula with the speed). If it was provided somewhere else on the page, things might be different.

Where did the angle get introduced? In the way it is used, it is apparently between the string and the vertical, but you should never make others guess that.
The formula works, but where does it come from? Certainly not from the wrong ##F_T = \frac{mv}r^2## to the left of it (and you need the correct version of it to arrive at the formula with the speed). If it was provided somewhere else on the page, things might be different.
The formula is provided at the top of the page - I mistakenly cut it off. the new attachment contains Question 7 with the formula.

and therefore, The angle θ ("theta") is in introduced by the formula provided on the exam. Its true that it would've been more clear to have labeled it on the diagram, but he used it correctly regardless, and got the correct answer.

Because of the fact that the formula was provided at the top of the page, you could argue that the onus was on the writer of the test to label θ on the diagram, and that the common convention of θ being the angle between the string and the vertical was already implied in the context of the problem.

#### Attachments

• q7wformulas.pdf
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mfb
Mentor
It is strange to have such a specific formula there, but if it is given, then I don't see why you shouldn't use it.

It is strange to have such a specific formula there, but if it is given, then I don't see why you shouldn't use it.

Apparently he did use it: The question remains, why would the teacher claim that the correct answer was achieved "by accident?" This is still what I need to determine as the teacher seems to be simply wrong - and, I need credible help to prove it.

Apparently he did use it: The question remains, why would the teacher claim that the correct answer was achieved "by accident?" This is still what I need to determine as the teacher seems to be simply wrong - and, I need credible help to prove it.
It is strange to have such a specific formula there, but if it is given, then I don't see why you shouldn't use it.

MFB - if you can please assist me privately I would be forever grateful.. Its extremely important to our family, thank you.

mfb
Mentor

I'm not that teacher, and I cannot read his mind. Speaking with him is the only option to influence the grade in any way. I would point out that the formula used was given at the top of the page, and applies to the problem with the proper definition of theta, and apparently was included in the list with this problem in mind, because it fits directly to it. And your son figured out where theta has to be = which quantity goes into numerator and denominator.

vela
Staff Emeritus
Homework Helper
I think the formula was intended for the problem of a car on a banked, frictionless road. You happen to get the same formula for this problem, but the teacher probably didn't realize the coincidence and expected students to derive it for this problem.

mfb
Mentor
Ah, good point, but it really is the same thing. Arguing that the student understood the relation might work. The wrong (b) suggests otherwise, but ...

I'm not that teacher, and I cannot read his mind. Speaking with him is the only option to influence the grade in any way. I would point out that the formula used was given at the top of the page, and applies to the problem with the proper definition of theta, and apparently was included in the list with this problem in mind, because it fits directly to it. And your son figured out where theta has to be = which quantity goes into numerator and denominator.

So, let me ask you a straightforward question, is the problem solved correctly/validly?

So, let me ask you a straightforward question, is the problem solved correctly/validly?
..and would you concur with
So, let me ask you a straightforward question, is the problem solved correctly/validly?

also, here is his tutor's explanation, do you concur?

#### Attachments

• Question7bc response.pdf
56.2 KB · Views: 115
mfb
Mentor
is the problem solved correctly/validly?
It does not matter what I think. I think it is certainly possible to argue that the solution is correct.
though he reused some of the work he did in part (b)
Here I would highlight that the velocity was not used in part (b). The calculations might be written at the same height of the answer to part (b), but they belong to the answer to (c).

haruspex