PLEASE HELP!! PROVIDE DETAILED SOLUTION FOR NUMBERS PROVIDED!! Will rate lifesav

Question

PLEASE HELP!! PROVIDE DETAILED SOLUTION FOR NUMBERS PROVIDED!! Will rate lifesaver!

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.)

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.) 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? How many loops (if any) will result if m is changed to 144 kg? (Enter 0 if no loops form.) How many loops (if any) will result if m is changed to 10 kg? (Enter 0 if no loops form.) is NOT 0.272 kg/m or 9.07e-4 kg/m or 6.8e-4 kg/m.

Explanation / Answer

Tension in the rope is T=mg=4g=4*9.8N=39.2N

a)

see tension is 39.2N and at f=180hz 6 loops are formed , so L=2m and wavelenght =2/3=2/3m

so speed =wavelenght *frequency=180*2/3=120 m/s=sqrt(T/u)

so

u= mass per lenght=T/(120^2)=39.2/(120^2)=0.0027222 kg/m

b)if m=144kg , then T=144g=1411.2 N

speed is then v=sqrt(1411.2/(39.2/(120^2)))=720m/s

if f=180Hz then wavelnght=720/180=4 m

so , L=2m

thus 1 loop is formed as then 1 loop =wavelenght/2=2m

c) if m=10kg

if T=10g=98N

so speed=sqrt(98/(39.2/(120^2)))=189.736 m/s

189.736=180*wavelenght

wavelenght=1.05409 m

so ,0 loop as it doesnot form any loop

wavelenght cannot be divided into a integer among rope

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.