- #1

Gravitino22

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## Homework Statement

You're riding a cable car from Bogota up to Monser-

rate. During your ride there is a small earthquake that

sends vertical, transverse waves propagating along the

cable. The cable's tension is T, its linear mass den-

sity is u, and the wavelength of the wave is [tex]\lambda[/tex]. If the

amplitude of the wave is large enough, the motion of

the cable car will momentarily leave you in free fall.

Show that in order for this to happen the amplitude

must be given by

Y => [tex]\frac{g\lambda^{2}u}{4\pi^{2}T}[/tex]

## Homework Equations

position along a wave: y=Ysin(kx-wt)

string waves speed: v = [tex]\sqrt{\frac{T}{u}}[/tex]

## The Attempt at a Solution

My train of thought is that for free fall to happen the acceleration of the wave must be greater than the acceleration of gravity.

I tried taking the second partial derivate with respect to time of the waves position equation to obtain its acceleration which gave me:

a[tex]_{y}[/tex]=-w[tex]^{2}[/tex]Ysin(kx-wt) that should be => then g

but i don't know where the tension would or the linear mass density would come in.

Any help pointing me in the right direction would be appriciated! thanks :)