Physics question

[Ingested Banjo]

Ok, I wasn't sure where to post this, but I figured as it's vaguely about theme parks, being a roundabout question, it could just about fit in here



So, we have a roundabout. This roundabout is comprised of a solid ring, held up by 8 (presumed light) ropes.

In the first question, you are asked to calculate the tension in each string - simple, just do a bit of trig and divide it by 8 because there's 8 strings.

However, part b) is the question I'm confused about, and this topic isn't asking you to give me the answer: I've seen the 'answer' already. However, I think it's wrong

Part b) says that the disc is spun so that it reaches a constant speed (assuming no losses of friction/air resistance). It asks you if there is any change in tension within the rope now that it's at a constant speed.

The official answer is that yes - there is a change in tension due to centripetal force counterbalancing the momentum pulling it round in a circle.

However, whilst I think this would be true were you to spin a single particle, such as a conker, around in a circle, this question is different because it asks about a disc, not a single particle.

The disc is being pulled inwards not by the tension in the string, but by the fact that it is a solid itself, and can't change its shape. The disc does not change its overall position apart from rotating, so there is no tension change in the string.

2 analogies of the situation:

Take a block of wood and staple it to a desk, with string attached at an angle out of it. Now, pull the block in any direction along the desk, and since it is stapled, it will not move, so the string is neither lengthened or shortened, so there in no change in string tension.

Take the disc, and put it into space where there is (assumed) no gravity to pull it to earth. This means that there is no string required to hold the disc up. Obviously, when the disc is spun, there is no change in the tension of the string because there is no string.

So in conclusion, the only causes for change in tension in the string are:
A) The disc changes its position outside of the space in which it rotates
B) There is more mass added to the disc, so the vertical component of the tension of the string changes.

The force required to keep the disc from not flying outwards would come from a tension within the disc itself, NOT tension in the string.

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Sorry for writing such a long essay, I just get excited by things like this, because I've shown it to my parents, both of whom studied maths, my dad studied physics too, and they weren't sure about it, so it means that if I'm correct, not only have I beaten the exam board, I've also outsmarted my parents

And so I have to be sure that I'm right

 

[Hixee]

I think you're wrong in your assumptions about the ring.

Take a block of wood and staple it to a desk, with string attached at an angle out of it. Now, pull the block in any direction along the desk, and since it is stapled, it will not move, so the string is neither lengthened or shortened, so there in no change in string tension.

No. There is increased tension in the string, just not enough to pull the staple out. If you pulled hard enough, with enough force, the block would move.

Whilst I can see your point, I think you'd have to argue that, under enough force, the ring would deform. The tension in the strings would increase as they tried to keep the ring in the same shape and balanced. However, you would probably have to spin the ring fairly quickly and have a fairly soft material for this effect to be noticed.

I'm sure someone here can give a proper explanation. See how your exam board argue the answer, that should give a clue as to their reasoning (assuming this is a numerical question).

 

[Gazza]

^I think Hixee is spot on...

But to add a bit more, the string and block analogy is incorrect because the string would be lengthened, just by a degree that is not readily visible.....
This is true of any material. Imagine a heavy concrete footing. If you were to stand on it, it would be deforming under your weight, but by a microscopic degree.

The other error with the string analogy is saying that the tension does not increase....of course it does! Lets say you have a string and suspend 1kg of weight from it...You then decide to suspend 2kg from it. Ok, the string might not appear to be lengthened or shortened, but clearly the increase in weight hanging from it would put it under higher tension.

 

[Ingested Banjo]

^ Yes, I agree that practically, no material will stay exactly un-stretched by force, but I think the exam board were arguing that the tension would change by a significant amount compared to the original tension.

And yes if you hang string vertically downwards, and add a kilogram of mass to it, then it will increase the tension in the string. Likewise if you added mass to the disc, there would be more tension in the string because the string is holding up the disc, therefore the vertical component of the tension has changed.

However, the centripetal force only affects the horizontal component of the disc, and what I'm saying is that the disc probably takes a lot more of the strain of the horizontal component, obviously depending on how stretchy the disc is - if the disc has 0 coeff of restitution (really stretchy) then the string will take all of the strain, if the disc is very in-flexible, then the disc will take most of it.

I've got it all sorted in my mind now, so please don't tell me I'm completely wrong now

 

[jayjay]

if the disc has 0 coeff of restitution (really stretchy) then the string will take all of the strain, if the disc is very in-flexible, then the disc will take most of it.

Just a bit of help so you don't get your technical terms mixed up, coefficient of restitution only applies to bouncing objects. coefficient=0 means that an object will not bounce off a surface. coefficient=1 means that it will bounce off at the same speed as it approached.

I'd say that if you assumed this ring was rigid then the speed would not affect the tension. What reasoning does the exam board give for their answer?

 

[neo]

Your exam is correct, although it’s hard to imagine. Say you’re riding The Claw in Dreamworld Australia:

http://www.coasterforce.com/The_Claw

If they spin the seats without the swing, you’d feel centripetal force pulling you inwards and so would the restraint mechanisms. As you can see, the ride gondola is engineered very much like your exam question. If the gondola was spun in zero gravity, you’d still feel the centripetal force, even if the central spokes were removed.

The ring in your exam question and indeed other scenarios simply cause their own centripetal force within their construction.

As another analogy, if you spun a particularly elastic loop of material (again in zero gravity), then increased its RPM, you’d notice a change in diameter (which of course is again due to centripetal force).

 

[Ingested Banjo]

^^ Yeah sorry I meant the one to do with springs... spring constant?

^ I know, that's what I was arguing, not the exam board, that the ring would become more tense, whereas the ropes would keep a constant tension no matter how fast the rotation.

 

[jayjay]

^^ Yeah sorry I meant the one to do with springs... spring constant?

Young's Modulus?

 

[neo]

I know, that's what I was arguing, not the exam board, that the ring would become more tense, whereas the ropes would keep a constant tension no matter how fast the rotation.

Mathematically there should be a change in rope tension. The acceleration of centripetal force and gravity will produce a resultant phasor diagram that produces a larger resultant force.

I’m sure if you’ve ever ridden a Huss Enterprise that you will have noticed a steadily increasing g-force as the ride accelerates and the gondolas swing outward. The resultant acceleration/g-force of an Enterprise gondola will clearly increase the tension of the rides structure.

It’s no different with ropes at an angle. Although there is probably a point where the resultant phasor is linear with the rope angle and therefore any further centripetal acceleration would only be placed upon the tension of the ring itself.

A bit like an Enterprise increasing its velocity when the gondolas are linear with the ride structure, the ride structure tension would increase and the effects of gravity would become less apparent. But in the case of angled ropes, the tension distribution would be transferred onto the ring itself, like you suggest, and not onto the ropes.

 

[Ingested Banjo]

^Yeah. Except remember with your enterprise and frisbee analogies, the gondolas/seats are on the ring itself, so you do feel a change in force, but you're on the ring, which was my point anyway