A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The la

Question

A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a 57.0° angle with the horizontal.

(a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 810-N firefighter has climbed 4.20 m along the ladder from the bottom.
Horizontal Force

Vertical Force

(b) If the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, 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[16 sin 57] - 490[(16/2)cos57] - 810[4.2 cos57] = 0
Rw = 297.185 N

Sum horizontal forces to zero shows that the horizontal floor reaction is 252 N toward the wall
Sum vertical forces to zero to find the floor vertical force

Fv - 490 - 810 = 0
Fv = 1300 N upward

b) Using the same logic to find the horizontal reactions when the firefighter is higher
Rw[16sin57] - 490[(16/2)cos57] - 810[9.1cos57] = 0
Rw = (490[(16/2)cos57] + 810[9.1cos57]) /[16sin57]
Rw = 458.279 N

The vertical reaction remains the same
Fv = 1300 N upward

coefficient of friction is the ratio of the maximum horizontal force to vertical force
= Fh / Fv
= 458.279 / 1300
= 0.3525

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