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A uniform ladder of mass m and length ℓ leans at an angle θ against a wall, Fig. 12–101. The coefficients of static friction between ladder-ground and ladder-wall are μG and μW, respectively. The ladder will be on the verge of slipping when both the static friction forces due to the ground and due to the wall lake on their maximum values. (a) Show that the ladder will be stable if θ ≥ θmin, where the minimum angle θmin is given by
(b) “Leaning ladder problems” are often analyzed under the seemingly unrealistic assumption that the wall is frictionless (see Example 12–6). You wish to investigate the magnitude of error introduced by modeling the wall as frictionless, if in reality it is frictional. Using the relation found in part (a), calculate the true value of θmin for a frictional wall, taking μG = μW = 0.40. Then, determine the approximate value of θmin for the “friction-less wall” model by taking μG = 0.40 and μW = 0. Finally, determine the percent deviation of the approximate value of θmin from its true value.
FIGURE 12–101 Problem 95.
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