Question 4

Author Message   Lau Kai Kwong Username: lkk Registered: 04-2003 Posted on Sunday, April 13, 2003 - 12:36 am:    A uniform ladder rests on rough horizontal ground with its top against a smooth vertical wall. If the angle of friction is l, find the least possible inclination of the ladder to the horizontal. Please post your solution.   Ho Ka Wai Username: 971066 Registered: 04-2003 Posted on Tuesday, April 15, 2003 - 12:40 am:      Ho Ka Wai Username: 971066 Registered: 04-2003 Posted on Tuesday, April 15, 2003 - 12:49 am:    Let q be the angle of inclination, 0< q <p/2 . Let 2L be the length of the ladder. when q is min. F=R2 tan l In equilibrium condition, R1=F and R2=mg By the conservation of moment, R2(L cos q) = (F + R1)(L sin q) R2 cos q = (F + F) sin q R2 cos q = 2R2 tan l sin q q = tan-1 [(1/2) cot l]   Lau Kai Kwong Username: lkk Registered: 04-2003 Posted on Tuesday, April 15, 2003 - 10:47 am:    Good. Actually, you should state where you take the moment. Anyway, it is better to take moment at the point where the largest number of forces intersect.