# [Mechanics] Resolving Tensions

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#1
Here is the question:

My current workings:

I have tried to resolve vertically and I found the vertical component of T1 but with The inextensible string since it doesn’t extend at all its tension I said is 0 therefore I found the upwards component and let it equal 2g because the system is at equilibrium and tried to solve for the extension x and I got 2m which isn’t the correct answer. The solution bank resolved diagonally however I don’t understand what mistake I’ve made resolving vertically.

Any help would be appreciated thanks
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11 months ago
#2
(Original post by BrandonS15)
The inextensible string since it doesn’t extend at all its tension I said is 0
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#3
(Original post by RDKGames)
It says inextensible: not extensible; incapable of being extended or stretched so extension (x) = 0 so using T = (lambda * x )/ l if x= 0 then T = 0 through that string? So it won’t have a vertical component?
Last edited by BrandonS15; 11 months ago
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11 months ago
#4
(Original post by BrandonS15)
It says inextensible: not extensible; incapable of being extended or stretched so extension (x) = 0 so using T = (lambda * x )/ l if x= 0 then T = 0 through that string? So it won’t have a vertical component?
Im with rdkgames on this one.
Inextensible simply means it wont change its length. Hookes law is not valid (spring), but it does transmit forces (tension).
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#5
(Original post by mqb2766)
Im with rdkgames on this one.
Inextensible simply means it wont change its length. Hookes law is not valid (spring), but it does transmit forces (tension).
So how would I find the tension in the inextensible string or do I have insufficient information so I have to resolve horizontally?
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11 months ago
#6
(Original post by BrandonS15)
It says inextensible: not extensible; incapable of being extended or stretched so extension (x) = 0 so using T = (lambda * x )/ l if x= 0 then T = 0 through that string? So it won’t have a vertical component?
Hookes applies only to extensible objects.

You resolve vertically and horiztonally. Two eqns in two tensions. Solve them.
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#7
(Original post by RDKGames)
Hookes applies only to extensible objects.

You resolve vertically and horiztonally. Two eqns in two tensions. Solve them.
And when resolving horizontally how do I find the vertical component of T2 if T2 doesn’t equal 0?
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11 months ago
#8
(Original post by BrandonS15)
And when resolving horizontally how do I find the vertical component of T2 if T2 doesn’t equal 0?
T2 * sin(60) is vertical

T2 * cos(60) is horizontal
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#9
(Original post by RDKGames)
T2 * sin(60) is vertical

T2 * cos(60) is horizontal
I resolved horizontally and found an equation solvable for x and I still get x = 2, I don’t see what I’m doing wrong:
Working:
Last edited by BrandonS15; 11 months ago
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11 months ago
#10
(Original post by BrandonS15)
I resolved horizontally and found an equation solvable for x and I still get x = 2, I don’t see what I’m doing wrong:
Working:
When you resolve horizontally and vertically you should get
t_1 cos(30) = t_2 cos(60)
t_1 sin(30) + t_2 sin(60) = 2g

If you resolve diagonally D must be less than 2g. Multiply by cos() rather than divide and you should get x=1/2 which agrees with the horizontal and vertical analysis.

The original force (2g) is always the hypotenuse and the perpendicular components in the directions of t_1 and t_2 are the other two sides, so must both be less than 2g.
Last edited by mqb2766; 11 months ago
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#11
(Original post by mqb2766)
When you resolve horizontally and vertically you should get
t_1 cos(30) = t_2 cos(60)
t_1 sin(30) + t_2 sin(60) = 2g

If you resolve diagonally D must be less than 2g. Multiply by cos() rather than divide and you should get x=1/2 which agrees with the horizontal and vertical analysis.

The original force (2g) is always the hypotenuse and the perpendicular components in the directions of t_1 and t_2 are the other two sides, so must both be less than 2g.
Also if the string PB is inextensible, how does it have tension when its extension is 0?
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11 months ago
#12
(Original post by BrandonS15)
Also if the string PB is inextensible, how does it have tension when its extension is 0?
Imagine a single steel rod (inextensible string) from which the 2kg mass is hanging vertically. That would have an upwards force (tension) of 2g and no extension.
https://physics.stackexchange.com/qu...ensible-string
Last edited by mqb2766; 11 months ago
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