A ladder (L = 7.90 m) of weight WL = 350 N leans against a smooth vertical wall.

Question

A ladder (L = 7.90 m) of weight WL = 350 N leans against a smooth vertical wall. The term "smooth" means that the wall can exert only a normal force directed perpendicular to the wall and cannot exert a frictional force parallel to it. A firefighter, whose weight is 867 N, stands 6.00 m up from the bottom of the ladder (this distance goes along the ladder, it is not the vertical height). Assume that the ladder's weight acts at the ladder's center, and neglect the hose's weight. What is the minimum value for the coefficient of static friction between the ladder and the ground, so that the ladder (with the fireman on it) does not slip? (Assume ? = 48.0

Explanation / Answer

? = 48
Height of top ofladder= 7.90sin(48) = 5.87 m
Horizontal distance from centre ofladderto base ofladder= (7.9/2)cos(48) = 2.64 m
Horizontal distance from firefighter to base ofladder= (6)cos(48) = 4.01 m
At the bottom of the ladder, the vertical normal force on the ladder (upwards) is NV
Resolving vertically:
NV = 350 + 867 = 1217 N
At the top of the ladder the horizontal normal force on the ladder is NH
Taking moment about the bottom of the ladder:
NH*5.87= 350x2.64+ 867x4.01
NH = 749.68 N
At the bottom of theladderthe horizontal frictional force, F, acts towards the wall
Resolving horizontally
F = NH =749.68 N
Suppose theladderis on the point of slipping, then 799.3N is the limiting frictional force
? = F/NV =749.68 /1217 = 0.616

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