Question

A cable that goes over a frictionless pulley connects two boxes shown below. The coefficients of friction are ui = 0.19 and 42 = 0.6, box 1 sits on an incline 0 of 25 degrees. If the weight of box 1 = 550 kN, determine the minimum weight of box 2 to prevent slipping. frictionless pulley Show all of your calculations and clearly identify your final answers.

Answer 1

step 1 Given dala, Coeffic ient of friction for bo 1 = ,= 0.19 coetticient ot triction for bon a= llz- 0.6 angle of inclination =0= 25° wleight- ote e here given pulley Es tritifondegs of bon 1 t ,- 550 KN Findout minimum weight of boa2 to prevent &lipping (2) atep a : FBD for boa 1 N, = W,c0%O =) E Fy=0; = 550 cO8(25°) 550 X 0.906 N= 498.31KN 10=25 -) F= el,N, = 0.19 x498.3 :94.677KN w,sine- Fp, = T, sso(sin as°) – 94.677 = T, T=137.763KN 080 iswsinoe 'N

step3 FBD of pulley T,=Tz= 137.763KN Ti =) FBD Of bon 2:- =) I Fy=O" N2 N2= klz Tz Tz= Fgg Tz= Mz Nq = ly Wz 137. 763 T2 229.605 K N %3D Weight of boa 2 = W, = 229.605 KN