Question 5

Author Message   Lau Kai Kwong Username: lkk Registered: 04-2003 Posted on Sunday, April 13, 2003 - 12:38 am:    A uniform ladder rests with one end against a rough wall and the other end on rough horizontal ground. When the ladder is inclined at a to the vertical it is on the point of slipping. The coefficient of friction between the ladder and the wall and the ladder and the ground is m. Find the value of m. Please post your solution.   961093 Username: 961093 Registered: 04-2003 Posted on Tuesday, April 15, 2003 - 11:42 pm:    Let 2L be the length In equilibrium condition F2 + R1 = mg and R2 = F1 F1 = R1£g => R2 = R1£g F2 = R2£g Take the moment about the centre of gravity, (F1 + R2) Lcosa + F2 Lsina = R1sina 2R2cosa + R2£gsina = R2sina / £g 2tan£g + £g^2tana = tana £g^2 + 2cot£g ¡V 1 = 0 £g = (-2cota +- ¶}¤è4cot^2a + 4) / 2 = -cota +- csca = -1/tana +- csca = -cosa/sina +- 1 / sina = (-2cos^2 (1/2)a) / (2sin(1/2)acos(1/2)a) (reject) or (2sin^2 (1/2)a) / (2sin(1/2)acos(1/2)a) = tan(1/2)a   961093 Username: 961093 Registered: 04-2003 Posted on Tuesday, April 15, 2003 - 11:58 pm:      961093 Username: 961093 Registered: 04-2003 Posted on Wednesday, April 16, 2003 - 12:10 am:      Lau Kai Kwong Username: lkk Registered: 04-2003 Posted on Wednesday, April 16, 2003 - 12:14 pm:    Some typing mistakes in the third paragraph: Line 4 : 2m + m^2tana = tana Line 5 : m^2 + 2mcota ¡V 1 = 0 Besides, you would better reject the -ve root in an earlier step.