First slide

mechanical equilibrium

Question

A 13 m ladder is placed against a smooth vertical wall with its lower end 5m from the wall. What should be the minimum coefficient of friction between ladder and floor so that it remains in equilibrium.

Difficult

A

0.36
B

0.72
C

0.21
D

0.52

Solution

$v e r t i c a l d i r e c t i o n d o w n w a r d f o r c e m g a n d n o r m a l r e a c t i o n o n t h e f l o o r c l o c k w i s e t o r q u e a b o u t t h e o r i g i n i s m g x (\frac{5}{2}) a n d a n t i c l o c k w i s e t o r q u e μ m g (12) [12 i s t h e h e i g h t o f t h e l a d d e r] a s i t i s i n e q u i l i b r i u m m g (\frac{5}{2}) = μ m g (12) μ = \frac{5}{24} \approx 0.21$

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