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 61.0 degree angle with the horizontal. Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.20 m along the ladder from the bottom. Horizontal Force magnitude N direction Vertical Force magnitude N direction If the ladder is just on the verge of slipping when the firefighter is 8.90 m from the bottom, what is the coefficient of static friction between ladder and ground?

Explanation / Answer

L = 16.0 m, weight w = 490 N, = 61.0o, F = 850 N, d = 4.20 m

a) horizontal force Nh

M = 0 (about the lowest point)

Nt*Lsin = w*(L/2)cos + F*d*cos, where Nt is the force on the ladder by the wall

Nt = (wL/2 + Fd)/(Ltan) = 259 N

F = 0 (horizonatl)

Nh = Nt = 259 N

Vertical force Nv

F= 0 (vertical)

Nv = w + F = 1340 N

b) d'= 8.90 m

Nt' = (wL/2 + Fd')/(Ltan)

s = Nt'/Nv = 398/1340 = 0.297

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