Question

A uniform plank of mass m and length L is connected to a wall by a wire of mass my attached to the plank at L/3 as shown. The wire is perpendicular to the wall. The plank rests on the junction of the floor and wall at an angle as shown. A wave with amplitude A and wavelength A propagates along the wire. Disregard reflections. 1/3 L A. (5 points) Draw an extended free-body diagram of the plank. B. (20 points) Find the maximum speed of a particle in the wire. C. (5 points) Calculate the maximum displacement of a particle in the wire, assuming that its maximum speed is 76 m/s, the mass of the plank is 1.3 kg, the mass of the wire is 0.00025 kg, the length of the rod is 0.86 m, the wavelength is 0.28 m and the angle is 52°.

Answer 1

7 Tension in wou Solution Given data; A uniform plank of mass 'm length "L wire of mass mwi The wire is perpendicular to the wall. - The plank rests on the Junction the floor and o lo! Wall at an angle 43 o ra): puce body diagram of the plank!- D B Ang At. AC = l-12 -243

Maximum speed in wire. The maximum speed 0ے a partick in the wire: At Equilibrium EMATO mgal, sino - Tkzl.co coso = 0 Tension in wire T = 3ng tano 4 7 - 33 toe Vmax = 1 Ime length of wire memase per unit mw -> Mass wice g me a mw length of wire length of ware = al sino mo mda al sino me 3mo 218ing. max = V m). 3mgtano u Bmw 218ma.

INmax mg Itano sing amw Vanay = 76m/s warelength x=0.28m Angle 0-52° mw = 0.00095kg 1.3 kg. length 1= 0.86m. V=fX Vnan fo X 76 Hz 0.28 f = 271.428543 Nmax mgltano sino amw maximum displacement - Amare mgltanesing f "max amw 1.349.8180-86x tansa'sinsaº 971.4285 x Ymar 2 x 0. 00025 Amaz 0. 55m