The figure below shows a 20 kg ladder leaning against a frictionless wall and re
ID: 1556037 • Letter: T
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 71.0 kg person climbs halfway up the ladder, what force will be exerted by the ladder against the wall? kN (b) How far up the ladder can a 71.0 kg person climb? (Measure along the length of the ladder.) 3.6 m Draw an extended free-body diagram showing the forces acting on the ladder. Apply the conditions for translational and rotational equilibrium.Explanation / Answer
Given Data:
Mass of the ladder, M = 20 kg
Mass of the person, m = 71 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
91 * 9.8 * ( 1.5 / 2 ) = Fw * 5
Fw = 133.77 N
Force exerted by ladder against the wall, Fw = 133.77N
(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) + (71 * 9.8 * 1.5 * f) = 200 * 5
147 + 1043.7f = 1000
f = 0.8172
Length of the ladder L = [ (1.5)^2 + (5)^2 ]
= 5.22 m
Climbed length = f * L
= 0.8172 * 5.22
= 4.26m
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