Question

The mass of the symmetrical wheel shown below is m = 4 kg and its radius of gyration about its center is kg = 0.25 m. The outer radius of the wheel is r2 = 0.4 m. The radius of the inner hub, where a cable is wrapped around it, is rı = 0.2 m. The wheel rolls without slipping. The force P, applied to the cable, is increased slowly according to the linear relation P = at, where P is in Newtons, a is an unknown coefficient, and is the time in seconds after P is first applied. The average force P during the first 5 sec is 5 N. The wheel is rolling to the left with a velocity of its center of v. = 1 m/s at time t= 0. Answer the following questions. A. Draw an FBD with all externally applied forces to the wheel, also indicate in the figure the coordinate you will use in your solution. B. Determine the unknown parameter a. C. Find the angular velocity o of the wheel 10 sec after P is applied. D. Compute the average value of the rolling friction during this period. Vo=1 m/s 0.2m

Answer 1

Soli values girem in the question are: m=qkg radius of gyration (KG) = 0.25 mm Outer radius (22) = 0.4 m innes hub radius (r) = 0.2m Forcell) = at at t= 55ce, P= 5W dorimis at t=0 tas my t weight {force of gravitation] mg fs friction rolling 7.(* force Ng Normal reaction force py Applied force orion & Twis

(b) value of a : P = at 5:9.5 =(Q:1 Ot t= 10 sele IP= 1x10=10N] (€8d) Apply force equation moment of gnerijala) T = m kg 2 = GX 1202 = 0.25 P-Hsz ma or Efzama ma 8 69= TL on 15.6-pira = - 109 No sipping condo ginen) [Q: Mix] Fmmi si| At t: logee, P: 10N 10- fs = GXGd ::fQ=7,8] 09 310-45 =1.6~0 § 5.109)-1010.2) : 0.250 or ys= 0.6290

aftes Solding, Q = 2.26 yad/52 8lfs = 6:4NW O At mo slipping, rem = Ro ro Eri Do 1 = 0.4 X Do Wo = 2.5 rades & Dean on to that, w =Dotat DE 2.5 +2.25X10 i o = 25 vad75] cdAcesage noiling force 14's) = 6.40