In Figure 12-5, a ladder of length L = 11 m and mass m = 42 kg leans against a s

Question

In Figure 12-5, a ladder of length L = 11 m and mass m = 42 kg leans against a slick (frictionless) wall. The ladder's upper end is at height h = 8.2 m above the pavement on which the lower end rests (the pavement is not frictionless). The ladder's center of mass is L/3 from the lower end. A firefighter of mass M = 70 kg climbs the ladder. Let the coefficient of static friction ?s between the ladder and the pavement be 0.54. How far (in percent) up the ladder muct the firefighter go to put the ladder on the verge of sliding?

Explanation / Answer

Fpy = Mg + mg = 70*9.8 + 42*9.8 = 1097.6 N
Fpx = Fr = 0.54*1097.6 = 592.704
Fw = 592.704

a= (11^2- 8.2^2)^0.5
a = 7.33 m
now balancing moment
42*9.8* 7.33/2 + 70*9.8*x = 592.704*8.2
x = 4.89 m

tan = 8.2/7.33

= 48.2 deg
along length of ladder = 4.89 / cos48.2 = 7.336

% of ladder = 7.336/11 *100 = 66.7%

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