. A long rope of mass density 150 g/m is tied at one end. A person holds the oth

Question

. A long rope of mass density 150 g/m is tied at one end. A person holds the other end with a horizontal force of 95 N such that the equilibrium position of the rope is horizontal. The person then shakes the held end of the rope up and down such that sinusoidal travelling waves are generated with a frequency of 1 wave per second and an amplitude of 5.0 cm. (a) What average power must the person holding the rope deliver to the system? (b) If the rope is shaken for 10 sec, how much energy is consumed by the oscillating rope?

Explanation / Answer

given tthat

mass density µ=0.150 kg/m

tension T=95 N

no of waves produced n=1

amplitude A=5.0 cm

now we frequency produced in the rope

f=n/2l[T/µ]^½ =1/2[95/0.150]^1/2=12.6 Hz

so the velocity of rope moved =>Vmax=WA=[2*3.14*f]A=[2*3.14*12.6]*0.05=3.9564 m/s

(a) ans

the average power Pavg=F.V=95*3.9564=375.86 W

(b) ans

the energy is consumed =Pavg*t=375.86*10=3758.6 J

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