Engineering Calculating Tx and Inertia at Break and After Break | Simple Physics Formulas

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The discussion focuses on calculating tension and inertia before and after a cable break using physics formulas. Key equations include Tx=ma for tension and inertia calculations involving mass and radius. Participants question the relevance of the speed of sound in the cable to its movement after snapping, suggesting it may relate to how quickly tension dissipates. Theoretical considerations indicate that the break can occur at any distance from the winch, and the cable's behavior post-snap is influenced by its tensile strength. Overall, the conversation emphasizes the importance of defining terms and using proper mathematical notation for clarity.
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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)
 
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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?
 
Baluncore said:
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
 
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)?
 
MarcoClement said:
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.
 
MarcoClement said:
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 ?
 
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