Question

16-96. Due to slipping, points A and B on the rim of che disk have the velocities shown. Determine the velocities of the center point C and point D at this instant. UB= 10 ft/s B D AN I A 450 0.86 Ес A = 5 ft/s 1 16-100. The square plate is confined within the slots at Hand B. When = 30°, point A is moving at va = 8 m/s. Determine the velocity of point C at this instant. TOR 8 m/s

Answer 1

16-96 Given- R = oooft Vas 10 ft/sec Á VA= 5ft/sec due to slippling weget different velocities at points A e B. we can solve this problemy using I center Method. is due to slippling the I-center of body does not lie at the point of contact it lie along the common normal due to for bothe given velocilies this COMMOD normal is the only perpendicular line and, to find I center we doraw other line which passes through both arrow heads of the belocities The point of intersection this line and nor -ral drawn is the I center of rotation

is at this instant the body is inpure wouling about this point i Wikim let bocky votate with an angulcor irelocity w about I at this instant then . VA = JAx W 2) w: VA NB : 2B*w :) W: VB 13 -> equailing born x ZR-x 1.6-x . ) 8-5= 10x 2 g C x x: 8 35,0-533ft | 7) Wita Sos = 9.375 vad/sec. > 16-4.375 rad/sec To find Vo wehave to find the distance blo Ild taking that geometry with enlarged figure shown below

Joy - 0-8 sinuso, e 018 cosus! churo og =) from gle IJD 30%= (1j3 +5032 Ig? =(0.267 + 0-8COSAS) +(6.8 sinust 2) 10% = 1.01336 ft -)|10 = 1.0066f81 i velocity of point o at this sostant is Vo = 10xw 310066* 9.375 Vo = 9.39576 ft/sec c' for velocity at center Vc = Icro = 0.267* 9.375 z> TVC = 2.503125 ft/sec i velocity of center cis Ne= 2.50325 ft/sec relocity of point Dis Voz 9-39576 ft/sec

16-100 Given! 0:3 03 BI 2.0:30 160 KY 10.39int 3:1 AVA= smis 4. In this probleme leke vo be the velocity of point B and this can be solved byusing I center Method. in draw line perpendicular to velocities VAL VB their intersection point is I center » Lucot let wis angulas velocity of pure NAZ rolling at this instanc 27 VA = IAxw => wr NB = I By Co is W2 VB a) equaling both NA ha es consindo o costo VB 030056 TA 013 Sinbo 2) Vg: 8 cot 60.

» Vas wcl 68 m/s ? Wie : 30:14 var dere » [103 3079 reduce IA 0.35100 to calculate Velocity cat c we need to fiore tc for that we use forowing diagro, 1 300 10.32 05601 V . from gleBDC >> Biz bo't BC=100-3? (O3)2 BC=0.3x82 is angle blw Bu lif w BC & cf is 75 zs from ale BFC Costjº. E l sin 45" DE » FC=Bccos 75 >> BF: Brinq;" ) Fc 10138 .20575 | BF: 0.34 12:4 sinas" TFC = 0.1098 m || JBF = 0.logem |

* BF can be written as BFBI+IF >> Bia BF - IF BJ = 0.4098 - IF » IF = 0.4098- 0-3x c0560 IF : 0-2598 m from all IFC Ic²= I F² t Fc? = (0-2593;?+ 0.109812 ac² :o:07955604 ,/3030.282_m ) velocity of point cis Vco Ic vue 20-79 202824.37074 Ne= 8.683 m/s i velocity - of point cis The = 8.683 m/s