Newton Laws of Motion and System of Particles
A ladder of mass `20 kg` is hanging from ceiling as shown in figure. Three men A,B and C of masses `40 kg, 60 kg` and `50 kg` are climbing the ladder. Man A is climbing with upward retardation `2m/s^(2)`, B is climbing up with a vonstant speed of `0.5m/s` and C is climbing with upward accelaration of `1 m/s^(2)`. FInd the tension in the string supporting the ladder.

Explanation

External forces acting on the system are weights of the men, weight of the ladder and tension supporting the ladder. Denotingmasses of men A,B,C and ladder by `m_(A), m_(B), m_(C) and m_(L)`, accelaration due to gravity by g, tension in the string by T and accelarations of the men A,B,C and ladder by `a_(A), a_(B), a_(c)` and `a_(L)` respectively, we can write the following equation according to equation.
`Sigma vec(F)_(1) = sigma(m_(1)vec(a)_(1))rarr" " T-m_(A)g - m_(B) g - m_(C ) g - m_(L)g = m_(A)a_(A) + m_(B)a_(B) + m_(C )a_(C ) + m_(L)a_(L)`
Substituting given values of masses `m_(A) = 40 kg, m_(B) = 60 kg, m_(C ) = 50 kg, m_(L) = 20kg`, given values of accelarations `g=10m//s^(2), a_(A) = -2m//s^(2),a_(B)=0m//s^(2), ac=1m//s^(2)`, and `a_(L) = 0m//s^(2)`, we obtain `T-400-600-500-200=-80+0+50+0`
`T=1670N`