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A Little Physics Problem

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elpaw

the rod is also extensible now?

No, just the wires. I'm still stuck :mad:

:mad:

:frown:

.

OP

Nylex

No, just the wires. I'm still stuck :mad:

:mad:

:frown:

.

Yes, just the wires.

No one actually answered my question!

RobbieC

No one actually answered my question!

There was stuff about extensible strings in Edexcel's M3, but I dunno about the modules after that as I didn't do them.

another question....

are the wires fixed in place to the support and the rod?

OP

elpaw

another question ... are the wires fixed in place to the support and the rod?

Yep.

Nylex

There was stuff about extensible strings in Edexcel's M3, but I dunno about the modules after that as I didn't do them.

Eww, thats sick. Thanks for the warning.. Maybe I shall avoid it like the plague then!

RobbieC

Eww, thats sick. Thanks for the warning.. Maybe I shall avoid it like the plague then!

IIRC, the stuff in the 'Strings & Springs' chapter isn't too difficult. If you're taught it, it should be easier anyway.

Nylex

IIRC, the stuff in the 'Strings & Springs' chapter isn't too difficult. If you're taught it, it should be easier anyway.

Part of the problem. I have elected to teach myself a further maths module or two, as it is not offered at my school in any other form. Then again I am being advised against taking on more maths, but it is finally making sense and becoming less of a chore, more interesting!

RobbieC

Part of the problem. I have elected to teach myself a further maths module or two, as it is not offered at my school in any other form. Then again I am being advised against taking on more maths, but it is finally making sense and becoming less of a chore, more interesting!

I taught myself M3 and didn't do very well. If you can do it though, that's good :smile:

:smile:

.

Depends the textbooks you use and whether you're ok with teaching yourself. Personally, I am.

Just come across this one. It's been a while since I did any physics, but this just looks like a mechanics problem ???

Anyway, I've had some thoughts about it and I offer the following soluition. Not too sure if it's right though!

Looking at Fig1 first of all.

Sum of vertical forces

T1 + T2 + T3 = 4W ------------(1)

Moments about A

2T2L + 4T3L = 4WL
T2 + 2T3 = 2W ----------------(2)

Moments about B

T1L = T2L + 3T3L
T1 = T2 + 3T3 ------------------(3)

Now consider the extension in the vertical wires.

Fig2 shows the extension in the three wires schematically.
There is obviously a linear relationship between the extensions ∂1, ∂2 and ∂3, and ∂2 is just the average of ∂1 and ∂3, i.e.

∂2 = ½(∂1 + ∂3)
∂1 + ∂3 = 2∂2 ------------------(4)

I can't remember the proper notation for elastic extension and stuff, but I'm putting it down as,

extension = (something) * Force

∂ = η*T

applying this to (4),

ηT1 + ηT3 = 2ηT2
T1 + T3 = 2T2 ----------------(5)

using (5) and (3),

T1 + T3 = 2T2
T1 - 3T3 = T2

giving,

4T3 = T2
T2 = 4T3 ---------------------(6)
======

substituting for T2 from (6) into (2),

4T3 + 2T3 = 2W
6T3 = 2W
T3 = (1/3)W ---------------(7)
==========
and
T2 = (4/3)W ---------------(8)
==========

substituting for T2 and T3 from (8) and (7) into (1),

T1 + (4/3)W + (1/3)W = 4W
T1 = (4 - 5/3)W
T1 = 2(1/3)W
==========

Edit: corrected the force from 4Wg to 4W.

shiny2.gif2.6KB

Fermat

Just come across this one. It's been a while since I did any physics, but this just looks like a mechanics problem ???

...

==========

the problem as far as i can see is that it is impossible for the wires to be acting parallel. because they are fixed to both the rod and the support, they will be 2L apart at both ends. and so they will be slightly skewed wrt each other (see image for crude example)

elpaw

the problem as far as i can see is that it is impossible for the wires to be acting parallel. because they are fixed to both the rod and the support, they will be 2L apart at both ends. and so they will be slightly skewed wrt each other (see image for crude example)

Oh yes, but since the extensions will by very small compared to the other dimensions (basic assumption) can't we just simplify matters by saying that the three wires remain vertical and use my Fig3 as a reasonable approximation?
Even in the skewed condition, d2 will still be approximately the average of the other two extensions, and the difference in the ratios of the extensions will be insignificant compared to the ratios of the three tensions.
If the skewed condition is taken as the working state, then evaluation of the vertical (and horizontal) forces wull now mean the the three tension will have to be resolved horizontally and vertically - for minimal effexct on the final results.
However, if the exact answer is required then the natural lengths of the three wires (in terms of L) will be needed to work out a relationship among the three extensions.
Shiny was asked to write out the complete question wilth all the relevant info, but didn't - suggesting all the info was there ??
We usually neglect air resistance unless it is specifically mentioned. Can't we just make the assumptions I've made?
Hey shiny, do you have the answer? - or was this a prob that you made up?

OP

Rep on its way to you Mr Fermat! :biggrin:

:biggrin:

Fermat

Oh yes, but since the extensions will by very small compared to the other dimensions (basic assumption) can't we just simplify matters by saying that the three wires remain vertical and use my Fig3 as a reasonable approximation?
Even in the skewed condition, d2 will still be approximately the average of the other two extensions, and the difference in the ratios of the extensions will be insignificant compared to the ratios of the three tensions.
If the skewed condition is taken as the working state, then evaluation of the vertical (and horizontal) forces wull now mean the the three tension will have to be resolved horizontally and vertically - for minimal effexct on the final results.
However, if the exact answer is required then the natural lengths of the three wires (in terms of L) will be needed to work out a relationship among the three extensions.
Shiny was asked to write out the complete question wilth all the relevant info, but didn't - suggesting all the info was there ??
We usually neglect air resistance unless it is specifically mentioned. Can't we just make the assumptions I've made?
Hey shiny, do you have the answer? - or was this a prob that you made up?

Are you really 57 years old?

integral_neo

Are you really 57 years old?

Yes, he is.

Invisible

Yes, he is.

you are bono arent u?

y did u change ur name?

Invisible

Yes, he is.

if he is then he shouldn't be allowed to take part in maths competition in maths thread i think coz its unfair with others.. he is doing maths degree and most of the poeple in maths have only done A2, so if he is to be allowed to take part then age/experience should count in the final mark... i am gonna tel this to mik1a as well

shiny

Rep on its way to you Mr Fermat! :biggrin:

:biggrin:

muchos gratias :biggrin:

:biggrin:

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