Question

Problem 4. A pivoted beam has mass mį suspended from one end and an Atwood's ma- chine suspended from the other with masses m2 and mz suspended on either side. The frictionless pulley has negligible mass and size. (a) Find the relation between mı, m2, m3, li, and l2 which will ensure that the beam has no tendency to rotate just after the masses are released. (b) What would you predict the relation would be in the case that all three masses are equal? Does your answer from part (a) agree with that prediction? -l1 * -l2 mi |m3| m2

Answer 1

l2 li mi ma M a) As beam is not rotating so pulley will behave if hanging to ceiling as alio ms a be acc -T= mza = mza M2+ M3 yet I be tension and writing equation for me mag-T- writing equation for ms Toming Sulving equations T= 2ma mo fouce acting on beam = 2T Balancing Torque about poins o 2Tl2 = migli 4 m2 m3 gle_mge, On beam M2+ m3 4 m2 m3l2 mil, is relation Matma

of all mili b) thele masses are equal ie me m2 = m3 m allation in 2 m2 m3 lz Putting 2 m² lg = me m2 + m3 2m li= l2