In the arrangement shown in the figure below, an object of mass m = 2.0 kg hangs

Question

In the arrangement shown in the figure below, an object of mass m = 2.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (Ignore the mass of the vertical section of the cord.)

(a) When the vibrator is set to a frequency of 170 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord?
____ kg/m

(b) How many loops (if any) will result if m is changed to 72.0 kg? (Enter 0 if no loops form.)
___ loops

(c) How many loops (if any) will result if m is changed to 14 kg? (Enter 0 if no loops form.)
___ loops

Explanation / Answer

a) f = 1/2L)*sqrt(T/u) = (1/2L)*sqrt(mg/u)

170 = (1/4)*(sqrt(2*9.8)/u)

u = 42.3875e?6 kg /m

b) f = (n/2L)*(sqrt(T/u)

170 = (n/4)*sqrt(((72*9.8)/42.3875e?6))

n = 1 loop

c) f = (n/2L)*(sqrt(T/u)

170 = (n/4)*sqrt(((14*9.8)/42.3875e?6))

n = 0 loop

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