Question

Chapter 3, Problem 3/119 The two springs, each of stiffness k = 1.24 kN/m, are of equal length and undeformed when 0 = 0. If the mechanism is released from rest in the position 0 = 35°, determine its angular velocity O when 0 = 0. The mass m of each sphere is 4.0 kg. Treat the spheres as particles and neglect the masses of the light rods and springs. m 0.29 m Answer: 0 = rad/s The number of significant digits is set to 3; the tolerance is +/-1 in the 3rd significant digit

Answer 1

Here undeformed de l, a la length of the springs o Beformed length of the spring om, don-1,-6 4- length of the spring S60=412 - (24.6in (10 =35) = 2240:29 - Faxo.aq bin 2759] boy = 0.14226 m Simi Varly don = 128 - [axa_ sin (10135) =-3x0.29 + [exo-29 x Gin 6s] = 0.10434M calculate the angular velocity wing conservation of energy equation: Initial Kine ilii energy is zela, P.E yoi sphere A4 B is zud inutiley Therefore Ev = K dog + koon - mg riscoso) ->(1) olt position 2, polential energy at B,C,D is ze10 1. Ea = 3 1 mwit- mgr = [2 mlrój - mga] → 12) K OB + Kdor - mg (rcoso) = 3 mko - mgr - 479.87X0.29 (12.0x o: 1421) 4 (1440 x 9 09- (48781x0298684 36 2 x4202x6 12.547+ 6.744 – 9.321 = 0.504602- 11.3796 10 > 6.504 sad/s]