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    Just a question of mine:

    You have a string, natural length l.
    Particle fixed in middle of string.
    You stretch the string and attach it to two points, you stretch it so that total length = l + x where x is extension.

    How do you calculate the tensions acting on the particle?

    I know you need to consider the system as two seperate strings and go from there but I'm a little confused.

    Thanks 4 help.
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    because the pratical is fixed. ther treat as 2 individual strings.
    so the natural length of each is l/2 and extension is x/2

    Energy in each string =[λ(x²/4)]/2.(l/2)

    oh i jus read ur post again. u said tension

    T = λ(x/2)/(l/2) = λx/l

    so each of the tensions are equal and opposite. if still in middle.
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    Right, that's what I thought, but here's a Q that confused me a little.

    Elastic string stretched between C and D, 1m apart. P, mass 2kg, fixed to midpoint of string and rests on surface. l =0.8m, Lambda = 40N.

    Particle set in motion.

    Show: d2x/dt^2 = -100x

    Now obviously this is F = ma = m(d2x/dt^2) and go from there, but the problem is calculating the resulting tensions acting on the particle.

    Scheme says: F = (40/0.4)(0.1 - x) - (40/0.4)(x + 0.1)

    I get the 40 and 0.4, that's just Lambda and l/2 when considering the string as 2 seperate strings, but the bracketed terms confuse me.

    Cheers
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    Ah if the particals are set in motion thats completely different, the tensions are now not equal.
    One sec ill work it through.
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    It's ok I get it now.

    It's travelling along line CD. Tension = (Lambda.x)/l.

    Consider the whole string as 2 seperate strings, of length 0.4m and each extended by 0.1m (Half of tot. extension of 0.2m).

    For 1 string, you have original extension extension plus the displacement of the particle causing further extension; this is x + 0.1. So: T = (40/0.4)(x + 0.1).

    For other string, the displacement is in direction of extension thus effectively reducing it. Hence: T = (40/0.4)(0.1 - x). Resultant = (40/0.4)(0.1 - x) - (40/0.4)(x + 0.1)

    Where I took Tension in direction of motion of particle as +ve.
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    yeah. Nice question i think feel free to share to rep for tranna help
 
 
 
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