Question

Question 3 Member AB has the angular motions shown. Using the vector and acceleration analytical method, 2 m 4 rad/s 5 rad/s2 А 0.5 m Figure 3 a) Write down an equation relating the Velocity of point B from A [3 marks) b) Write down an equation relating the Velocity of the slider Cfrom B [3 marks c) Using the equation obtained in b), determine the angular velocity of BC and the velocity of the slider [6 marks d) Write down an equation relating the acceleration of point B from A [3 marks] e) Write down an equation relating the acceleration of the slider Cfrom B [3 marks) f) Using the equation obtained e), determine the angular acceleration of BC and the acceleration of the slider [6 marks

Answer 1

ay VB VA + WAB K x 8 AB + 4k X 2 x 21 VB 81 s by ve - Ve + WBC k xr Be A 8 é twee kx -0.5 **-0.5 - 2] = -84 + (-0-5wBej + 2W Be 1 Eq. (1) Also, ve = (4 v) i + ( 3 Ve) j Eq. (2) Equate i coeff. of Eq. (1) 4 (2) 3 ve 5 -0.5 w Be = compare i coeff. e ve + 2 WBC 5 I 8

solve above two equations Vc Vc 2.5 m/sec. Д- WBC 3 rad sec , 2 dy AB = а2 + KAB K" X8AB - (WAB VAB ОР 5k x2 – (4)* 2 ј То, щ.(3) О) 32 i , el a Чg + TBCkxr BC- (WBC XBc ар — 5 -б•S ( - Квск 4 -0.5 4 L — 21 - 2ј ac = AB o 5 * Bej + 2 каве і + 4.5 + 18 і = (3 чај (5 Fa: (4) А) 50, ac Eq (5)

(4) { (5) compare i coeFF OF Eq. + 2 TBC +4.5" a B i ac 4. 5 10+ 2 TBC + 4.5 4 ac 5 Rearrange 2 TBC 14.5 = 4 ac 5 ac compare i coeff. asj' 40.5 Be j' + 18 = Rearrange to.5 TBC 3 5 3 ac 32 +18) 5 Solve above two equations f de = - 12.9688 m/s² -ve. 3 HT qckt TBC rad - 12.4375 -ve D see?