Question

Chapter D3, Problem D3/067 The small object is placed on the inner surface of the conical dish at the radius shown. If the coefficient of static friction between the object and the conical surface is 0.17, for what range of angular velocities w about the vertical axis will the block remain on the dish without slipping? Assume that speed changes are made slowly so that any angular acceleration may be neglected. +0.40 m - m TITEL 22 Answer: 0 rad/s) SWSCU rad/s)

Answer 1

Answer :

2.31 rad/sec to 3.88 ras/sec.

Solution Given that Ms = 0.17 mase, (m) [ Angular velocisty (wa) Mz 0.40 m) Step I To find out minimum min at which it will not slip When speed will be slove it try to fall inside, that time friction will be outside . FBD af mass in N me wantin Cos (0) f = Ms No P n o my we? (Centrifugal is Lex mg since force ) x 22°50 Emot my cos Cell For Static EFy=0) Ở equilibrium Block (m) mrw.min sin col HSE A S N = mgcos (8)+ mr war in sin (6) LE Fz=o] mg sim(o) = els N +more.com col mong sim( 22)=0:17 (0) C0516) + marunon sinco)]t whir Wing Carlos Cutrin = 5:3706 W mém. = 2.31 viele Answer

Step II For (umaa :) it will try to I go outside that time friction force will be inside as in FBD. mrw.corcol my mimos como & Fy=0 Na mg C95 (@) + mrwan Bincas els wa S heo mr we ma mocasco, ing o Eft=0) orw?resinto Mis nt og sin (s = mrw.das con los 0:17 Erg Cos(22) + n/20-4 ka asin(22)] + mig sinai); [mx xo: 4 Wired Cox (22)] winnaa = 15.116 W men = 3.887 radi sec] 12-31 z we 3.887 rad 1sec Anguer seadis