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?
kN

(b) How far up the ladder can a 78.0 kg person climb? (Measure along the length of the ladder.)
m

Explanation / Answer

The length of the ladder,
L=sqrt(25+1.5^2)
and tan(theta)=5/1.5

a)T*sin(theta)*L= g*cos(theta)*(20*L/2+78*L/2)

T=144.06 N

b)

Now put a person on t he ladder and repeat the process
T*sin(theta)*L= g*cos(theta)*(20*L/2+78*x)

set T=200 and solve for x
x=sqrt(25+1.5^2)*
(200*5/(1.5*9.81)-20/2)/78

x=3.8788326085 m

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