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Unformatted text preview: homework 33 HETTIGER, CHRISTOF Due: Apr 19 2008, 4:00 am 1 Question 1, chap 16, sect 2. part 1 of 2 10 points A steel piano wire is 0 . 7 m long and has a mass of 70 g. It is stretched with a tension of 300 N. What is the speed of transverse waves on the wire? Correct answer: 54 . 7723 m / s (tolerance 1 %). Explanation: Let : F = 300 N , L = 0 . 7 m , and m = 70 g = 0 . 07 kg . The speed of transverse waves on the wire is given by v = radicalBigg F = radicaltp radicalvertex radicalvertex radicalbt F m L = radicalbigg F L m = radicalBigg (300 N) (0 . 7 m) . 07 kg = 54 . 7723 m / s . Question 2, chap 16, sect 2. part 2 of 2 10 points To reduce the wave speed by a factor of 2 without changing the tension, what mass of copper wire would have to be wrapped around the steel wire? Correct answer: 210 g (tolerance 1 %). Explanation: Let : v v = 2 , and m = 70 g = 0 . 07 kg . The new wave speed will be v = radicalbigg F L m radicalbigg 1 m , so v v = 2 = radicalbigg m m m = 4 m. The amount of copper wire required is m = m  m = 3 m = 3 (0 . 07 kg) = 210 g . Question 3, chap 16, sect 2. part 1 of 1 10 points Tension is maintained in a string as in the figure. The observed wave speed is 24 m / s when the suspended mass is 3 kg . The acceleration of gravity is 9 . 8 m / s 2 . 3 kg What is the wave speed when the suspended mass is 2 . 7 kg? Correct answer: 22 . 7684 m / s (tolerance 1 %). Explanation: Let : m 1 = 3 kg , m 2 = 2 . 7 kg , and v 1 = 24 m / s . The linear density is v 1 = radicalBigg F , so = F v 2 1 (1) = m 1 g v 2 1 homework 33 HETTIGER, CHRISTOF Due: Apr 19 2008, 4:00 am 2 = (3 kg) (9 . 8 m / s 2 ) (24 m / s) 2 = 0 . 0510417 kg / m . The velocity is v 2 = radicalBigg F , so v 1 = radicalbigg m 2 g (2) = radicalBigg (2 . 7 kg) (9 . 8 m / s 2 ) . 0510417 kg / m = 22 . 7684 m / s . Alternate Solution: Plugging from Eq. 1 into Eq. 2, we have v 1 = radicalbigg m 2 g (2) = radicalBigg m 2 g v 2 1 m 1 g = v 1 radicalbigg m 2 m 1 (3) = (24 m / s) radicalBigg (2 . 7 kg) (3 kg) = 22 . 7684 m / s ....
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This note was uploaded on 05/09/2010 for the course PHYSICS PHY 301k taught by Professor Turner during the Spring '10 term at University of TexasTyler.
 Spring '10
 Turner
 Physics, Mass, Work

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