The figure below shows a 20 kg ladder leaning against a frictionless wall and re

Question

The figure below shows a 20 kg ladder leaning against a frictionless wall and resting on a frictionless horizontal surface. To keep the ladder from slipping, the bottom of the ladder is tied to the wall with a thin wire. The tension in the wire is 29.4 N. The wire will break if the tension exceeds 200 N.
(a) If a 72.0 kg person climbs halfway up the ladder, what force will be exerted by the ladder against the wall?


(b) How far up the ladder can a 72.0 kg person climb? (Measure along the length of the ladder.)

Explanation / Answer

Given Data: Mass of the ladder, M = 20 kg
Mass of the person, m = 72 kg
Tension T = 29.4 N Maximum tension, Tmax = 200 N Vertical height, h = 5 m
Horizontal distance, d = 1.5 m Let Fw be the Force exerted by laddeer against the wall. (a) about the bottom of the ladder = 0
( M + m ) * g *( d/2 ) = Fw * h 92 * 9.8 * ( 1.5 / 2 ) = Fw * 5 Fw = 135.24 N Force exerted by ladder against the wall, Fw = 135.24 N
(b)
Let f be the Fraction of the total length climbed
about the bottom of the ladder

= 0

M * g *( d/2 ) + m * g * d * f = Tmax * h
(20 * 9.8 * 0.75) + (72 * 9.8 * 1.5 * f) = 200 * 5
147 + 1058.4 f = 1000
                      f = 0.8059
Length of the ladder L = [ (1.5)^2 + (5)^2 ]
                                        = 5.22 m

Climbed length = f * L
                             = 0.8059 * 5.22
                             = 4.2 m

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