Question

A 520 lb uniform disk with center G and radius r = 3 ft is connected by a pulley system to a counterweight A weighing 75 lb. The system is initially at rest when A is allowed to drop, thus causing the disk to roll without slipping to the right. Neglect the inertia of pulley B and the cord, but model pulley C as a uniform disk with radius r_C = 0.8 ft and weight W_C = 50 lb. Assume the cord does not slip relative to pulley C.

Determine the speed of G after A has dropped 2 ft.

Required information A 520 lb uniform disk with center Gand radius r=3 ft is connected by a pulley system to a counterweight A weighing 75 1b. The system is Initially at rest when A is allowed to drop, thus causing the disk to roll without slipping to the right. Neglect the Inertia of pulley B and the cord, but model pulley Cas a uniform disk with radius rc=0.8 ft and weight Wc= 50 lb. Assume the cord does not slip relative to pulley C. B 4 Determine the speed of Gafter A has dropped 2 ft. The speed of GIS 3.4244 ft/s.

Answer 1

wc NG P given disc mass (ma) = 152016 A r = 3ft WA h - 75W с pulley mass m = 506 Xe = 0.qft when h=2ft. Vo = ? tension X velocity = power transmitted through rege = constant Тva – Т. 1 V6, 2 T₂ = 2T2 TV A- Tatry 1 - 2 v A Wd 11 Vos 2/6 We = rad see Vog We = re og radell using energy conservation magh - I'm 2 + I I W? + 1 mv too? te = math 1p med

g= 32.2 tu See2 :. 754 32.2x2 = - 1 x 75 xV 2 2 + 35101(a)? Cia 75x64.4 = 37.5 4V 0-8 va 3.42 ft sec Ang
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