You must determine the length of a long, thin wire that is suspended from the ce
ID: 1489860 • Letter: Y
Question
You must determine the length of a long, thin wire that is suspended from the ceiling in the atrium of a tall building. A 2.00-cm-long piece of the wire is left over from its installation. Using an analytical balance, you determine that the mass of the spare piece is 14.5 g. You then hang a 0.400-kg mass from the lower end of the long, suspended wire. When a small-amplitude transverse wave pulse is sent up that wire, sensors at both ends measure that it takes the wave pulse 21.7 ms to travel the length of the wire.
(A) Use these measurements to calculate the length of the wire. Assume that the weight of the wire has a negligible effect on the speed of the transverse waves.
(B) Discuss the accuracy of the approximation made in the previous part. Choose the correct statement.
The mass of the wire is equal to 0.37 g. It is negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 0.037 kg. It is not negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 0.037 g. It is negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 3.66 g. It is not negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 0.37 g. It is negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 0.037 kg. It is not negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 0.037 g. It is negligible compared to the mass of the 0.400-kg.
The mass of the wire is equal to 3.66 g. It is not negligible compared to the mass of the 0.400-kg.
Explanation / Answer
A) Use equation ,
v= sqrt(T/)
L/t = sqrt(T/)
L= sqrt(T/)*t = sqrt[(mg)/]*t
Where v= velocity of the transverse wave along the wire , T = tension due to weight , = linear density of the wire, Length of the wire , t= time
= (14.5*10^-9)/(0.02) = 7.25*10^-7 kg/m
t=21.7*10^-3 s
Plugging values,
L= sqrt[(0.4*9.8)/(7.25*10^-7)]*(21.7*10^-3) = 50.46 m
B) Mass of the wire = linear density*length = *L = 7.25*10^-7*50.46 = 0.037kg
Which is negligible as compare to mass that is hanged.
The mass of the wire is equal to 0.037 g. It is negligible compared to the mass of the 0.400-kg.
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