Sir Lancelot climbs a ladder. The ladder has total length I and mass m₁, and makes an angle with the horizontal. There is no friction between the ladder and the wall; between the ladder and the ground there is static friction with static friction coefficient μg. Sir Lancelot has mass ms = 5 my: the acceleration of gravity is g. The ladder has 10 rungs with mutual distance L/10; the bottom rung is on distance L/20 from the bottom. See right figure. When Sir Lancelot is positioned on rung n (with n <10), the situation is still stable. When he steps on rung n+ 1 the ladder slips and he falls to the ground. Calculate the minimum value μs,min and the maximum value μs,max of the static friction coefficient (so, μs,min Hs

International Edition---engineering Mechanics: Statics, 4th Edition
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Chapter7: Dry Friction
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Problem 7.50P: The block of weight W is pulled by the force P inclined at the angle to the horizontal. Find the...
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x(n)
y(n)
Frictionless
wall
L
11/20
L/10
L/20
Sir Lancelot climbs a ladder. The ladder has total length I and mass m₁, and makes an angle with the
horizontal. There is no friction between the ladder and the wall; between the ladder and the ground there is
static friction with static friction coefficient μg.
Sir Lancelot has mass ms = 5 m₁; the acceleration of gravity is g.
The ladder has 10 rungs with mutual distance L/10; the bottom rung is on distance I/20 from the bottom.
See right figure.
When Sir Lancelot is positioned on rung n (with n <10), the situation is still stable. When he steps on rung
n+ 1 the ladder slips and he falls to the ground.
Calculate the minimum value μs,min and the maximum value μs,max of the static friction coefficient (so, μs,min<
Hs<s,max).
Hints:
o use that standing on rung n, there is still equilibrium to calculate μs,min.
o use that standing on rung n+1, there is no equilibrium any more to calculate μs,max-
o first, write down expressions for (n) and y(n) (see figure).
o use the point where the ladder touches the ground as point of rotation (if necessary).
Transcribed Image Text:x(n) y(n) Frictionless wall L 11/20 L/10 L/20 Sir Lancelot climbs a ladder. The ladder has total length I and mass m₁, and makes an angle with the horizontal. There is no friction between the ladder and the wall; between the ladder and the ground there is static friction with static friction coefficient μg. Sir Lancelot has mass ms = 5 m₁; the acceleration of gravity is g. The ladder has 10 rungs with mutual distance L/10; the bottom rung is on distance I/20 from the bottom. See right figure. When Sir Lancelot is positioned on rung n (with n <10), the situation is still stable. When he steps on rung n+ 1 the ladder slips and he falls to the ground. Calculate the minimum value μs,min and the maximum value μs,max of the static friction coefficient (so, μs,min< Hs<s,max). Hints: o use that standing on rung n, there is still equilibrium to calculate μs,min. o use that standing on rung n+1, there is no equilibrium any more to calculate μs,max- o first, write down expressions for (n) and y(n) (see figure). o use the point where the ladder touches the ground as point of rotation (if necessary).
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