# A 7.9 m, 231 kg uniform ladder rests against a smooth wall. The coeﬃcient of static friction between the ladder and the ground is 0.527, ?

A 7.9 m, 231 kg uniform ladder rests against a smooth wall. The coeﬃcient of static friction between the ladder and the ground is 0.527, and the ladder makes a 31.7◦ angle with the ground. How far up the ladder can a 924 kg person climb before the ladder begins to slip? The acceleration of gravity is 9.8 m/s2 . Answer in units of m.

### 1 Answer

- FiremanLv 71 month agoFavorite Answer
let the vertical & horizontal reaction force is By & Bx Newton respectively at the base of the ladder & The horizontal reaction force at the top is Tx Newton. Let the 924 kg person climb L meter before the ladder begins to slip, by balancing the vertical & horizontal forces:

=>By = 231g + 924g = 11319 N ---------------(i)

& Bx = Tx ---------------------------------(ii)

As Bx = µ x By

=>Bx = 0.527 x 11319 = 5965.11 N-------(iii)

Now by taking the torque at the bottom:

=>231g x (7.9/2) x cos31.7* + 924g x (L) x cos31.7* = Tx x 7.9 x sin31.7*

=>7607.94 + 7704.27L = 4.15 x 5965.11 {as Tx = Bx}

=>L = 2.23 m