In the figure, a ladder of weight 200 N and length 10 meters leans against a smo

Question

In the figure, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip?

In the figure, a ladder of weight 200 N and length 10 meters leans against a smooth wall (no friction on wall). A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of friction between the ladder and the floor is 0.5. What is the maximum value of x if the ladder is not to slip?

Explanation / Answer

Ff -Fn Ff = Fn 1) Gn = Mg + mg Gn = 200+600=800 2) Ff = mu*Gn Ff = 0.5 * 800 = 400 3) x = (Ff*L*sin50 - Mg(L/2)sin40) / (mg*sin40) [40 deg is 90-50; the 90 is perpendicular to the ladder] x=[(400*10*sin50)-(200*5*sin40)] / [600*sin40] x = 6.28m

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