Please explain and not just show answer. Thank you: In the arrangement shown in
ID: 2198388 • Letter: P
Question
Please explain and not just show answer. Thank you:
In the arrangement shown in the figure below, an object of mass m = 4.0 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 180 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord?
(b) How many loops (if any) will result if m is change d to 9.00 kg? (Enter 0 if no loops form.)
(c) How many loops (if any) will result if m is changed to 10 kg? (Enter 0 if no loops form.)
Explanation / Answer
Here we have n = 6 so f6 = 130 = 6*v/2L but v = sqrt(T/µ) And T = m*g so 130 = 6*sqrt(T/µ)/2L So µ = (6/130)^2*T/4L^2 = (6/130)^2*m*g/(4L^2) = (6/130)^2*4.0*9.8/(4*2^2) = 5.22x10^-3kg/m b) Now f= 130 = n*sqrt(T/µ)/(2L) So n = 130*2*L/sqrt(m*g/µ) = 130*2*2.0m/sqrt(9.0*9.8/5.22x10^-3) = 4 c) Now f= 130 = n*sqrt(T/µ)/(2L) So n = 130*2*L/sqrt(m*g/µ) = 130*2*2.0m/sqrt(36.0*9.8/5.22x10^-3) = 2