A 20 kg mass is hanging at the end of a rope passing over a pulley. The other en

Question

A 20 kg mass is hanging at the end of a rope passing over a pulley. The other end of the rope is tied to a mechanical oscillator that makes the string vibrate (as shown below). For everything you calculate, write clearly the equation you are using. a. On the figure, draw all the forces acting on the hanging block and calculate the tension in the string. Use g = 9.81 m/s^2. b. The mass per unit length for the string is 8 g/m. Find the speed of the waves in the string. c. What is the wavelength of the standing wave shown in the figure? d. What is the frequency of oscillation of the mechanical oscillator? e. The frequency of the mechanical oscillator cannot be changed. A different mass M is now hanging at the end of the string and the string vibrates in the third harmonic, as shown below What is the wavelength of this third harmonic?

Explanation / Answer

only two force is acting on the 20 kg block

one is tension in the upward direction and weight in the downward direction

tension = weight of 20 kg block =

tension is T= 20*9.8 = 196 N

b) speed v = sqrt(T/mu) = sqrt(196/(8*10^-3)) = 156.52 m/sec

C) wavelength is lamda

length of the string is L = lamda/2

lamda = 2*L = 2*50 = 100 cm = 1 m

d) v= lamda*f

frequency is f = v/lamda = 156.52/1 = 156.52 Hz

e) L = 3*lamda/2

lamda = 2L/3 = 2*0.5/3 = 0.33 m

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