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# M3 Circular Motion watch

1. Please could someone explain why they say in this solution that T is greater than or equal to 0 for the string to not go slack? Why isn't it T>0? When T=0 it is slack isn't it?

Thanks for any help
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2. (Original post by PhyM23)
Please could someone explain why they say in this solution that T is greater than or equal to 0 for the string to not go slack? Why isn't it T>0? When T=0 it is slack isn't it?

Thanks for any help
I think that the only reason for it is that it allows them to find a minimum length AB. Without including T=0, they would end up with a strict inequality for the lengths, which would make things messy.

But I agree that it seems to be wrong, strictly.
3. When T=0 the string is not exactly slack as it's length doesn't fall below its maximum length. In other words, when tension is negative, the string is contracted and consequently is slack. At zero, it's just about to go slack.
4. (Original post by oShahpo)
When T=0 the string is not exactly slack as it's length doesn't fall below its maximum length.
Usually in mechanics, the definition of a slack string is T=0. So the mark scheme's wording is inconsistent. Slackness is not defined in terms of the length of the string (not that I've ever seen, anyway).

In other words, when tension is negative, the string is contracted and consequently is slack. At zero, it's just about to go slack.
This makes no sense at all. Part of the definition of a string is that it can't generate compressive forces i.e. it can't have negative tension. Strings can pull, but they can't push. T=0 is the best they can do in that direction, and in that state, they're slack.
5. (Original post by atsruser)
I think that the only reason for it is that it allows them to find a minimum length AB. Without including T=0, they would end up with a strict inequality for the lengths, which would make things messy.

But I agree that it seems to be wrong, strictly.
Yes I thought it was a little strange; thank you very much for clearing that up!

Just another question, why should the length AB depend on the tension? If it's inextensible then won't it always have the same length for any T>0?
6. (Original post by PhyM23)
Just another question, why should the length AB depend on the tension? If it's inextensible then won't it always have the same length for any T>0?
It's not saying that the length changes. You are right in saying that it is inextensible. But this is the sort of problem where it's like "Okay, what's the minimum length we need for this to happen", "okay, cool, it's ABmin", "let's go build a rope with AB_min" now.

Kind of like those M1 questions where it's like "minimum mass for this to happen", the mass is fixed and doesn't change, but what value of this fixed mass/length does it need to be for this to happen.

Geddit?
7. (Original post by Zacken)
It's not saying that the length changes. You are right in saying that it is inextensible. But this is the sort of problem where it's like "Okay, what's the minimum length we need for this to happen", "okay, cool, it's ABmin", "let's go build a rope with AB_min" now.

Kind of like those M1 questions where it's like "minimum mass for this to happen", the mass is fixed and doesn't change, but what value of this fixed mass/length does it need to be for this to happen.

Geddit?
Indeed I do. That's a great way of looking at it actually. Thank you
8. (Original post by PhyM23)
Please could someone explain why they say in this solution that T is greater than or equal to 0 for the string to not go slack? Why isn't it T>0? When T=0 it is slack isn't it?

Thanks for any help
This kind of ******** happens so much in edexcel M3.
Just look at the question and go with whatever they are using as it gets the marks lol, they just uck it up tbh as obviously it can't have T=0 since it is technically incorrect as they teach the opposite in the book. Stupid edexcel piss me right off.

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9. (Original post by atsruser)
Usually in mechanics, the definition of a slack string is T=0. So the mark scheme's wording is inconsistent. Slackness is not defined in terms of the length of the string (not that I've ever seen, anyway).

This makes no sense at all. Part of the definition of a string is that it can't generate compressive forces i.e. it can't have negative tension. Strings can pull, but they can't push. T=0 is the best they can do in that direction, and in that state, they're slack.
A string doesn't have to go slack even if the tension is zero in the string, although I concede that this depends on the definition of the word slack in mechanics. The definition I am accustomed to is that slack corresponds to a string whose axial length (linear length from tip to base) is less than that the string's actual length. I used the term negative tension a bit too loosely, but what I mean is that the force on the string itself is negative, not on the object tied to the string, in the sense that the net force acts to shorten the string's axial length.
10. This reminds me of another weird inequality issue I've had in a previous post. Can you see how I've obtained a minimum value from a strict inequality?
11. (Original post by oShahpo)
A string doesn't have to go slack even if the tension is zero in the string, although I concede that this depends on the definition of the word slack in mechanics. The definition I am accustomed to is that slack corresponds to a string whose axial length (linear length from tip to base) is less than that the string's actual length.
That may be some kind of engineer's definition, but it's not the one usually used in elementary mechanics, so I think that, in this context, your point is moo.
12. (Original post by Ayman!)
This reminds me of another weird inequality issue I've had in a previous post. Can you see how I've obtained a minimum value from a strict inequality?
Well, I guess that you obtained it by a bit of hand-waving in that case. Mathematically, your line of argument would strictly be that 2/3 is the greatest lower bound of the cosine, but I don't think that anyone would ever quibble in an A level context with what you've done.
13. (Original post by atsruser)
Well, I guess that you obtained it by a bit of hand-waving in that case. Mathematically, your line of argument would strictly be that 2/3 is the least upper bound of the cosine, but I don't think that anyone would ever quibble in an A level context with what you've done.
Would that be what is referred to as the infimum? Does it make sense to say infimum if I'm not referencing a specific set?
14. (Original post by Zacken)
Would that be what is referred to as the infimum?
No, I effed up - it should be greatest lower bound, which means the same as infimum

Does it make sense to say infimum if I'm not referencing a specific set?
I don't understand the question. Sorry.
15. (Original post by atsruser)
No, I effed up - it should be greatest lower bound, which means the same as infimum.
Ah, sweet.

I don't understand the question. Sorry.
Does it make sense if I say "the infimum of cosine" or do I need to say "the infimum of the set generated by the values of cosine/range of cosine"
16. (Original post by Zacken)
Ah, sweet.
Not so sweet for me - my cheeks burn with the shame of my error.

Does it make sense if I say "the infimum of cosine" or do I need to say "the infimum of the set generated by the values of cosine/range of cosine"
You can only have the supremum or infimum of a set of numbers, strictly, so the latter not the former, but of course, people say sloppy stuff like the former all the time.
17. (Original post by atsruser)
You can only have the supremum or infimum of a set of numbers, strictly, so the latter not the former, but of course, people say sloppy stuff like the former all the time.
Makes sense, thanks!
18. (Original post by Zacken)
Makes sense, thanks!
At the rate you're learning stuff, you'll be able to skip that whole Cambridge thing, won't you?
19. (Original post by atsruser)
At the rate you're learning stuff, you'll be able to skip that whole Cambridge thing, won't you?
Not quite, I just learn teensy little bits of everything which makes me look clever but I really don't know much of anything.
20. (Original post by Zacken)
Not quite, I just learn teensy little bits of everything which makes me look clever but I really don't know much of anything.
Welcome to the club, Mr Zacken.

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