A 15.5 m uniform ladder weighing 480 N rests against a frictionless wall. The la
ID: 1787023 • Letter: A
Question
A 15.5 m uniform ladder weighing 480 N rests against a frictionless wall. The ladder makes a 63.0° angle with the horizontal (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 850 N firefighter is 4.10 m from the bottom Magnitude of the horizontal force XN Direction O away from the wall towards the wall Magnitude of the vertical force XN Direction up O down (b) If the ladder is just on the verge of slipping when the firefighter is 9.40 m up, what is the coefficient of static friction between ladder and ground?Explanation / Answer
Sum moments about the floor contact to find the wall reaction horizontal force.
Rw[15.5sin63] - 480[(15.5/2)cos63] - 850[4.1cos63] = 0
Rw = 236.8 N
Sum horizontal forces to zero shows that the horizontal floor reaction is 236.8 N toward the wall
Sum vertical forces to zero to find the floor vertical force
Fv - 480 - 850 = 0
Fv = 1330 N upward
b) Using the same logic to find the horizontal reactions when the firefighter is higher
Rw[15.5sin63] - 480[(15.5/2)cos63] - 850[9.4cos63] = 0
Rw = Fh = 384.94 N
The vertical reaction remains the same
Fv = 1330 N upward
coefficient of friction is the ratio of the maximum horizontal force to vertical force
= Fh / Fv
= 384.94 / 1330
= 0.289
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