Question

Va rolling sliding string rod In the figures above, (a) shows a ball rolling without slipping on a track; (b) shows the ball sliding on a frictionless track; (c) shows the ball on a string; (d) shows the ball attached to a rigid massless rod attached to a frictionless pivot. In all four figures the ball has the smallest velocity at the bottom of its circular trajectory that will suffice for the ball to reach the top while still moving in a circle (note that the velocities are not drawn to scale). Correctly ordinally rank these minimum velocities, for example va = Vb < ve < vd is a possible (but probably incorrect) answer.

Answer 1

Selution A ling Moment iuenta ball ball is tlin) (sie ta V Rw 글씨V2 hinetc enery KE = 프 w 7 MU2 /0 AE-M MR) 2 nseroing energy f hall at top and hattom (rA) Z Mv 금씨님 2 Mgr Mu2 Mv2 NM r-R Y N Mg Fon ninimum speed V, N =o V = (vg) 느그 M3Y J O Migr) 2 MAY MUa 11 Jo \\W (49) 274r (skding KE - Kinetic eney 1

snserving energy at p and at batt om MV M 2Mgr NMA=Mv2 V =(vg) tor N huvi um V, 54r (541) string (C) Kinetic enagy KE = MV onderring energ at top and at bati om Mv 2 MGr 2 Mv2 T+ MA fon minimam U, T-0 v ニレ Vc- (5gr)

Aigid mars less wd kinetic KE = MV eneryy enserving enengy ttp and at hattm MU2MgY AT Mg-T Mv2 MJ Far v minimum, T MA and V O 2 V Va(49 (1) Va- 4gr)