How Does a Wave Pulse Affect Rope Stretching?

[TwinGemini14]

http://i662.photobucket.com/albums/uu347/TwinGemini14/showme3.gif


The top picture to the right is the picture of the rope before the wave pulse arrives, and the bottom picture to the right is a picture of the rope after the wave pulse has arrived. Notice that the rope has to stretch in order to accommodate this wave pulse.


4) What is the total stretching of the rope (S) as the wave pulse passes by?

A) S = ( L^2 + h^2 )^½ + ( 4L^2 + h^2 )^½
B) S = ( L^2 + h^2 )^½ + ( 4L^2 + h^2 )^½ - 3L
C) S = 2 ( L^2 + h^2 )^½ - L

I believe the answer should be A) because we simply add the hypotenuses of the two right triangles formed by the wave.

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5) What is the work done in stretching the rope? (Hint: Recall that the tension is T, and it acts over the displacement S that you solved for in the previous part.)

A) ST½
B) T½/S
C) ST
D) (S^2)T
E) T/S

Isn't the answer simply ST because Work=Force*Displacement. So the answer is C).
Using dimensional analysis one could already rule out choices B,D and E.
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Can somebody please check my work? I believe these two answers are correct, but if not can somebody help me? Thank you so much in advance!

 

[nickjer]

In problem 4, isn't the total stretching just the difference between the length of the rope during the wave and before the wave? I don't know the definition of stretching for your problem, but it sounds like a change in length. So answer (A) is just the total length of the rope with the wave, and not the change in the ropes length.

But I could be wrong since I don't know your definition of stretching is.

 

[TwinGemini14]

Ah, nice catch. I would agree with you. So it sounds like the answer is B.