A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. the coefficient of static friction between the floor and the ladder is 0.28. what distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

Question

Nora Escobar

Physics

1 August, 05:17

A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. the coefficient of static friction between the floor and the ladder is 0.28. what distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

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Butterfinger · Answer 1

First establish the summation of the forces acting int the ladder

Forces in the x direction Fx = 0 = force of friction (Ff) - normal force in the wall (n2)

Forces in the y direction Fy = 0 = normal force in floor (n1) - (12*9.81) - (60*9.81)

So n1 = 706.32 N

Since Ff = un1 = 0.28*706.32 = 197,77 N = n2

Torque balance along the bottom of the ladder = 0 = n2 (4 m) - (12*9.81*2.5 m) - (60*9.81 * x m)

X = 0.844 m

5 / 3 = h / 0.844

H = 1.4 m can the 60 kg person climb berfore the ladder will slip