Tension and inertia of a cylinder before and after fracture

[MarcoClement]

Homework Statement

Work out the speed at what a cable attached to a winch will move if it snaps(meaning the tension force exceed the tensile strength ).Work out as well the distance the rope will travel after it breaks.

Relevant Equations

F=ma
I=mr^2

At break
Tx=ma
a(initial)=Tx/pi.r^2.density

After break
Ix=m/12.(3r^2+h^2)
Iy=same as above
Iz=mr^2/2T(inertia)=Iz/a=mr^2/a=0at 1 second
delta L=v(initial).delta t+1/2at^2
=1/2a(1)^2
=a/2T(inertia)=[(a/2)(pi.r^2)(density)r^2]/a
=(pi.r^4.density)/2
T(inertia)=ma
a=(pi.r^4.density)/2 multiply by 1/pi.r^2.(a(initial)/2)
=r^2/a(initial)

 

[Baluncore]

Welcome to PF.
How far from the winch does the cable snap?
Does the speed of sound in the cable have anything to do with the speed of the cable after the snap?

 

[MarcoClement]

Welcome to PF.
How far from the winch does the cable snap?
Does the speed of sound in the cable have anything to do with the speed of the cable after the snap?

Any distance from the winch. Its theoretical so any distance from winch or any weight of rope or any pulling power from winch.I don't think speed of sound is necessary

 

[erobz]

So how quickly does the tension go to zero (I suspect that is why @Baluncore is pointing you toward the speed of sound in the rope)?

 

[berkeman]

Homework Statement:: Work out the speed at what a cable attached to a winch will move if it snaps(meaning the tension force exceed the tensile strength ).Work out as well the distance the rope will travel after it breaks.
Relevant Equations:: F=ma
I=mr^2

At break
Tx=ma
a(initial)=Tx/pi.r^2.density

After break
Ix=m/12.(3r^2+h^2)
Iy=same as above
Iz=mr^2/2T(inertia)=Iz/a=mr^2/a=0at 1 second
delta L=v(initial).delta t+1/2at^2
=1/2a(1)^2
=a/2T(inertia)=[(a/2)(pi.r^2)(density)r^2]/a
=(pi.r^4.density)/2
T(inertia)=ma
a=(pi.r^4.density)/2 multiply by 1/pi.r^2.(a(initial)/2)
=r^2/a(initial)

Please make it a habit to define your terms when posting your work. What is "I"? What is "L"? Yoiks.

Also, please read the LaTeX Guide link at the bottom of the Edit window so you can post your math reasonably. Thank you.

 

[Baluncore]

Any distance from the winch.

With the winch at the origin, if the cable snaps at x, what is there to stop the accelerated cable end before it gets to -x ?