The figure below shows a 20 kg ladder leaning against a frictionless wall and re

Question

The figure below shows a 20 kg ladder leaning against a frictionless wall and resting on a frictionless horizontal surface. To keep the ladder from slipping, the bottom of the ladder is tied to the wall with a thin wire. The tension in the wire is 29.4 N. The wire will break if the tension exceeds 200 N. (a) If a 78.0 kg person climbs halfway up the ladder, what force will be exerted by the ladder against the wall? In KiloNewtons (b) How far up the ladder can a 78.0 kg person climb? (Measure along the length of the ladder.) in Meters

Explanation / Answer

The length of the ladder, L=sqrt(25+1.5^2) and tan(theta)=5/1.5 summing torque about the bottom of the ladder without anyone on it to check the starting tension T*sin(theta)*L=20*g*cos(theta)*L/2 solve for T T=2*g*1.5=29.43, yup I agree so far Now put a person on t he ladder and repeat the process T*sin(theta)*L= g*cos(theta)*(20*L/2+72*x) set T=200 and solve for x x=sqrt(25+1.5^2)* (200*5/(1.5*9.81)-20/2)/72 x=4.202

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