Question

Determine the velocity of the 60-1b block A if the two blocks are released from rest and the 40-16 block B moves 2 ft up the incline. The coefficient of kinetic friction between both blocks and the inclined planes is 0.10. B 60° 30°

Answer 1

Given WA = 60 eb WB - 40 eb u-o-l. Drawing FBD of A & B. T AA op MARA NB a' DY PUNA 4 B, mBaB 30 PLNB 160 WB since block 'i is double stringed & block B is single stringed. AB QA 2 ap ver VA - Now From FBD of (B) E fy'= (*) ". NB We cos (30)=0. NB = 40 cos(30)= 34.64 eb {Fx'=0 ( **). :. T-MNB - mBaB - WBsin (30) =

qu 3 2.2 T-o.1 x 3 4.64 4o Sin ( 30 )=0. AB :, T-1.24229B = 23.464 lb Now! AB=29A 23.464 ebl :. T- 1.2422 (204) 23.464 -0 T- 2.484 AA- : From FBD of A: {Fzy=0 (4+) -. NA - WA Cos (6)=0. NA=30 + ) E fx=0 C- 2T +UNA+ MA QA - WA Sin (61)=0. i, 2T to.lx30 + ) aa- Gusin (Gos=0. 322- :: 12T + 1.8634 AA - 48.962 From ¢ ¢ (2) T-24, 2db QA = 0.298 ftis? dB = 20 A = 0.5g6 ft/s?

time taken by B to Now, cover 2ft up the inclined (t): SB - 2 FE - not + Žast? { ugru initial velocity of 6) :. 2. x 0.596x+? : t=2-59 sec In the same time for Ä : VA = MAT ant { UA su}, :. VA= 0.2988 2.59 VA = 0.7718 ft is Ans.).

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