Help with Mechanical Waves? (Physics)?

Question

A rope with length L = 1.0 m and mass m = 0.50 kg hangs from the ceiling. Attached to the bottom of the rope is a small rock with mass M = 0.40 kg The rock is given a small tap which creates a pulse that travels up the rope. How long does the pulse take to travel the length of the rope?
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Here is my try:

where v = sq root(F/mu);
         F = Tension = 0.40 * 9.8 = 3.92N
       mu = m/L = .5/1 = .5

v = sq root(3.92/.5) = 2.8m/s
1/2.8 = .35714s for the pulse to travel the length of the rope.

However the answer is .29s ... where was my mistake(s)?

hello · Accepted Answer

It's tricky because the tension is changing as you go up the rope. At the top the tension is holding up the weight of the rope and rock, so T top = 0.9 g
At the bottom the tension is just holding up the rock so T bottom = 0.4 g. This means there are two v's (actually infinte v's between the two values)  and you should probably take the average of the two. the average of your value 2.8 and that calculated by the previous answer of 4.2 is 3.5 m/s. This gives a t of 1m/ 3.5 m/s or 0.29 s !!

Matt · Answer

Using your formulas I get:

F = T = (0.40 + 0.5) * 9.8
.
.
.
v = 4.2 m/s
1 m/(4.2 m/s) = 0.238095 s

I used 0.4 + 0.5 kg for my calculation, you used 0.5, the solutions used 0.6 kg. [EDIT] So the average of our two should account for both the movement upward (where the tension is less) and the movement downward (where the tension is more). Good job hello!

Help with Mechanical Waves? (Physics)?

2 個解答