Question

7.0 m long uniform ladder,weighing 210 N rests against a smooth vertical wall with its foot on a horizontal floor.The ladder makes an angle 60° with the horizontal and the coefficient of static friction between it and the floor is 0.33.How far along the ladder can a 20kg load be hung without the ladder slipping​

Answer 1

Answer:

Ch 12.3 #13

A 15 m uniform ladder weighing 500 N rests against a frictionless wall. The ladder makes a 60° angle with the horizontal.

(a) Find the horizontal and vertical forces that the ground exerts on the base of the ladder when an 800 N firefighter is 4 meters from the bottom.

(b) If the ladder is just on the verge of slipping when the firefighter is 9 m up what is the coefficient of static friction between the ladder and the ground?

a) SFx = 0 (not moving)

SFx = Ffriction – Nwall

Nw = Ffriction

SFy = Nground – Wfire - Wladder = 0

Ng = 800 N + 500 N

Ng = 1300 Newtons

Remember, the lever arm is ALWAYS perpendicular to the force.

Torque applied by the ladder, the center of mass of the ladder is at 7.5 meters …so the lever arms is 7.5 (sin q). (I’ve chosen the pivot point at the base of the ladder.)

Stccw = Stcw in equilibrium

twall = tfirefighter + tladder

Nw cos 30° 15 m = 800 N 4 m sin 30° + 500 N 7.5 m sin 30°

Nw = 268 N to the left

Ff = 268 N to the right Ng = 1300 N up

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b)

cos 30° Nw 15 m = 800 N 9 m sin 30° + 500 N 7.5 m sin 30°

Nw = 421 N to the left

Nw = Ff (where Ff = m Ng)m

1300 N = 421 N

m = 0.324

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