9) Two geology professors from CSU-LA are taking samples from the bottom of an 8

Question

9) Two geology professors from CSU-LA are taking samples from the bottom of an 80 m deep pit, as shown in Fig.-4. One end of a rope with mass m rope = 2 kg, is attached to a small bag of Olivine specimens with total mass = 20 kg. Also attached is a small seat for one the professors to ride on, as he and the samples are winched up to the surface. Assume he weighs 145 lbs, and that the rope is stretched taut by the weight of the professor, and his prized cash of Specimens. The professor signals to his comrade above, that he is ready to surface, by rapidly jerking the rope sideways. Calculate the speed of the transverse wave that is generated on the rope Choose from the answers provided below 10) Is the wave speed at the top of the rope greater, or less than the speed at the bottom? Choose from the answers provided below. a) greater b) less: or c) the same

Explanation / Answer

linear density u = mrope/L

V = sqrt(T/u)

at top Tension T1 = (145*4.448)+(2*9.8)+(20*9.8) = 860.56 N

at the botton T2 = (145*4.448)+(20*9.8) = 840.96 N

T1 > T2

speed at top is grater than at bottom

at teh bottom v = sqrt(840.96*80)/2 = 183.4 m/s

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