A 10.8-kg monkey climbs a uniform ladder with weight w = 1.29*10^2 N and length

Question

A 10.8-kg monkey climbs a uniform ladder with weight w = 1.29*10^2 N and length L = 3.15 m as shown in the figure below. The ladder rests against the wall and makes an angle of ? = 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N.

(a) Find the normal force exerted on the bottom of the ladder.

(b) Find the tension in the rope when the monkey is two-thirds of the way up the ladder.

(c) Find the maximum distance d (along the ladder) that the monkey can climb up the ladder before the rope breaks.

 

 

 

Explanation / Answer

Mass of the monkey is m = 10.8 kg weigth of the ladder is w = 1.29*10^2 N Length of the ladder is L = 3.15m a ) Normal force exerted on the bottom of the ladder is         N = w + mg              = 1.29*10^2 N + 10.8 kg * 9.8 m/s^2              = 234.8 N b ) Tension in the rope when the monkey is two thirds of the way of the ladder is       T_1 cos 60  = 129  *( 3.15/ 2 )*sin 60 + ( 2/3 ) * 3.15 * 10.8kg   * 9.8 sin 60       T_1 = 387.6 N c ) Maximum distance     80.0N cos 60 = 9.8* (3.15/2 )*sin 60  +  d * ( 3.15) * 10.8 kg * 9.8 sin 60     d = 3.46*10^-3m

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