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# Mechanics Elastric Strings Energy Stuff. watch

1. 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.
2. 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.
3. 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
4. Ah if the particals are set in motion thats completely different, the tensions are now not equal.
One sec ill work it through.
5. 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.
6. yeah. Nice question i think feel free to share to rep for tranna help

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