Question re interpreting MarkScheme - Moments (Edexcel A-level)

[rsk]

Attached is a Q from an AS mechanics paper. I'm perplexed about part (c) in which we are told that the tensions in the two cables are equal.
My physics brain says take moments about the CoM of the beam so eliminating the mass of the beam and making the moments of the two cables equal and opposite, which reduces the problem to a very simple one, and gives the correct answer.

Markscheme warns about 'correct' answers which ignore the mass of the beam and offers 4 different options for taking moments, none of them around the CoM of the beam. Can anyone tell me why this method is invalid?

 

[kuruman]

How is the warning exactly phrased? It may be an indirect warning not to ignore the mass of the beam. If the system is in equilibrium, the sum of the moments will be zero with reference to any point. No matter where you choose your reference, you will end up with two equations and two unknowns. Another possible reason for the warning is that if you take the reference point at the CoM of the rod, you will answer part (b) before part (a) and they don't want you to do that.

 

[vela]

Your method is fine. The simplest explanation would be that whoever wrote that warning had a brain fart.

I just noticed on the requirements for the moments equation that "all terms required." Perhaps your method is acceptable but the solution requires you to explicitly include the term $100 g(0)$. That, however, would seem inconsistent with the provided expressions as they don't include a term for the moment due to the tension when the lever arm is 0.

 

[kuruman]

Your method is fine. The simplest explanation would be that whoever wrote that warning had a brain fart.

I just noticed on the requirements for the moments equation that "all terms required." Perhaps your method is acceptable but the solution requires you to explicitly include the term $100 g(0)$. That, however, would seem inconsistent with the provided expressions as they don't include a term for the moment due to the tension when the lever arm is 0.

I tried to be charitable but, after digesting your comments, I'll go with "brain fart."

 

[rsk]

Thanks both.
I suppoe my method doesn't include those lines above where the vertical forces are balanced - but that's completely unnecessary when we don't need to know T.
I don't like to think that students would be penalised for this - for spotting the most efficient solucion - in an exam.

@kuruman - the warning is just what you see there on the bottom of the markscheme "watch out for "correct" answers which ignore the 100g" - so in other words it's a warning for the markers and not for the students.

 

[kuruman]

Let's hope that this scheme provides just guidelines in an attempt to achieve uniformity and that the markers would recognize a correct solution when they see one. Am I correct in assuming that the takers of this test see just their scores but not the marked papers?

 

[rsk]

Schools do have the right to request the papers (or copies) if they want to appeal grades but it's not the norm and there's a fee involved.

I also hope that a decent marker would accept this (or raise it up the chain of command) but the worry is always over who is marking - there are often too few experienced teachers willing to give up their holidays for this and the worry that it's someone else just applying the MS to the letter (that's why they are often so detailed).

I'll try not to worry about it. I must be in a good place at the moment if I can find time to worry about hypotheticals which will probably never happen.

 

[rsk]

An update. So concerned was I about good students possibly losing marks that I got in touch with the exam board.

They reply that the CoM method is indeed the best, but that some students don't see the best method so other methods have to be included in the MS.

I still think that the CoM method is so simple that the 6 marks are in no way justified and that whoever wrote the paper didn't spot that solution but I have at least been reassured that, at the marking stage, students would not have been penalised.

 

[kuruman]

There has to be a level of trust in the markers and in the belief that if a student obtains the correct numerical answer, one has to examine the solution carefully to determine if it is correct outside the marking criteria. By the same token, students need to document their solutions carefully. Here is an example of a simplified solution to part (c) that eliminates quite a bit of algebra and does not look like any of the suggested solutions.

1. The ropes are symmetrically disposed about the CoM of the rod and have equal tensions.
2. This means that if the ropes are removed and replaced by a pivot at the CoM of the rod, the assembly will remain at equilibrium.
3. The 60g gymnast is 2 m from the pivot whilst the 48g gymnast is at (x - 4) m from the pivot.
Thus, the moment balance equation is $$60g~\text{[N]}\times 2 ~\text{[m]}=48g~\text{[N]} \times (x-4~\text{[m]})\implies x=6.5~\text{m}.$$It is the marker's responsibility to override the various suggested solutions and give full marks for this one with perhaps a bonus for thinking outside the box. However, it behooves the student to provide statements 1 and 2 to justify the equation in 3.

 

[rsk]

Yes, and I can't see students giving statements 1 and 2 as you write them.
However I will ensure that from now I encourage to show this kind of thinking, albeit briefly
ie take moments about CoM: eliminate 100g force as moment =0; moments of Ts are equal and opposite.

In fact, I will keep this question to use as an example with them of why explicitly stating the steps in the reasoning is so important.