Wave Pulse Travel Time on 24m Nylon Rope

[StephenPrivitera]

A 24m nylon rope has a tension of 1.3x10⁴N. The total mass of the rope is 2.7kg. If a wave pulse starts on one end, how long does it take to reach the other end.
I get 0.07s
$$v=\sqrt{\frac{T}{\mu}}$$
$$t=d/v=d\sqrt{\frac{\mu}{T}}$$
$$\mu=\frac{m}{l}=\frac{2.7kg}{24m}$$
$$t=d/v=d\sqrt{\frac{m}{Tl}}=0.07s$$
Book has 1.6s

 

[Norman]

one thing you may be doing incorrectly is not taking into account the tension in the rope due to the mass of the rope. This is a little tricky though. Does the question say to disregard the mass of the rope when calculating the total tension?
good luck,
Norm

 

[himanshu121]

HOw the string is situated may also help

Is it Vertical

 

[arcnets]

Stephen, I think you are correct and the book is wrong.

 

[Doc Al]

Originally posted by Norman
one thing you may be doing incorrectly is not taking into account the tension in the rope due to the mass of the rope. This is a little tricky though. Does the question say to disregard the mass of the rope when calculating the total tension?

If the rope were oriented vertically, the added tension due to the weight of the rope would only be about 270 N at the top (zero at the bottom). I don't think this will make much of difference, compared to the given tension of 1.3x104N. In any case, additional tension would reduce the time.

The book is wrong (again).

 

[harsh]

It seems to me that the book has worded the question terribly. I think the only Force they want us to use is the weight of the rope. If you try that in, you get something very close to 1.6 sec for the time.

Harsh