(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The tansverse displacemrnt of a rope, is given by a function of x and t ( in m and sec) by:

y(x,t) = 0.04 sin(0.21x - 8t)

if the rope is 7m long and has a mass 0.4kg

Find:

a. the tension in the rope

b. the maximum transverse component of the tension

2. Relevant equations

[tex]y=Asin(kx-\omegat)[/tex]

3. The attempt at a solution

part a.

we know that:

[tex] v = \frac{\omega}{k} = \sqrt{\frac{F}{\mu}}[/tex]

and [tex] \mu = \frac{0.4}{7}=0.057[/tex]

so [tex] Tension = F = 82.93N[/tex]

i have checked this, and this is correct so far.

part b.

find the maximum transverse tension.

i think you have to find the se3cond time drivative of the given function and maximise it to find the acceleration then use F=ma, this is how far i got:

second time derivative = a

[tex] a = - 0.04 \times 8^2 sin( 0.21x - 8t)[/tex]

so acceleration is maximum when periodtic part sin is +/- 1

so [tex] a(max) = 0.04 \times 8^2 = 2.56 m/s^2[/tex]

i think using f=ma with this acceleration should give the transvese component of tension but i'm unsure as to what m is, any ideas?

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# Homework Help: Find the maximum transverse tension in a rope supporting a travelling wave

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