Question

Q.4 (25pts) The two small spheres A and B have masses 1.5 kg and 2.0 kg respectively, and attached to the rigid rods of negligible mass. Determine the time the torque M=Se º N.m (t is in seconds) must be applied to the rods so that sphere B will attains a speed of 4 m/s. Assume the motion is on a smooth horizontal table, the point is fixed in position and the rigid rods remain perpendicular to each other at all 0.4m 0.3m times. M A

Answer 1

→ | Angular moment of inertia of system about the rotational axis passing through 'O' is. IEE [+mR21 I= s[amri+m82] since_spheres are small, r <<R hence Io ao I= EMR2 :. I[1.5x0.32 + 2x0.42] = 0.455 kg. m2 4 mis 10 rad/s wa VB RB 0.4m 10-0 t-o id=do rad/s2 [assuming spheres dt initially at rest] Using law of conservation of angular momentum Τα= ΣΤ I= 5.0-0.5t [0.455 kg m] [10/4 rad 27 = 5.2 0.5t 0.91 =e •0.5t t using expansion series upto 3 terms] 0.9°= [it 60.5t) + co.ştı?] t 0.1253 – 0.5+2+t -0.91=0 solving, t= 1.8024 S. Note that this is an approximated solution since exact solution cannot be determined.