Refer to the figure. Will have to open it in a new window. Part A A uniform cabl

Question

Refer to the figure. Will have to open it in a new window.

Part A

A uniform cable has a mass of .3 kg and a lengh of 5 m. (Tension is maintained in the cable by suspending a ball B with 2 kg mass from a beam. The ball is struck from the side with a hammer.

1) find the speed (velocity) of a pulse traveling up this cable.

2) find the time it takes the pulse to travel from the 2 kg mass to the beam.

Part B

Two cables are made of the same sample of wire rope as above, cable A having twice the length of cable B.

1) they are given the same tension (2kg) and then plucked. Compare their frequencies.

2) compare frequencies when the tension of A is four times that of B (8kg). show caluculations for both

Part C

If the beam in the figure is vibrating left to right at frequency f, what will happen to the ball B? If it will remain stationary, state the conditions and reason why. If it will move, state the conditions and reason. If it can do either, state the conditions for each.

Explanation / Answer

Part(a)

1) velocity of pulse = sqrt(T/mu)

T = 2*g

mu = 0.3/5 = 0.06 kg/m

so velocity = 18.074 m/s................Answer

2) time = 5/18.074 = 0.2766 s.............Answer

Part(b)

1) frequency = (1/L)*sqrt(T/mu)

La = 2*Lb, Ta=Tb, muA=muB

so freqA = 0.5* freqB....................Answer

2) Ta = 4*Tb

so freqA = freqB..................Answer

Part(c)

If the beam is oscillated horizontally, longitudinal oscillations are produced in the rope.

If it matches with the previous frequency , then stationary waves are produced....if not, then even the rope will vibrate simply

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