A ladder is hanging from ceiling as shownin figure. Three men A, B and C of masses 40 kg, 60 kg, and 50 kg are climbing the ladder. Man A is going up with retardation `2m//s^(2),` C is going up with an acceleration of `1m//s^(2)` and man B is going up with a constantg speed of `0.5` m/s. Find the tension in the string supporting the ledder. `[g=9.8m//s^(2)]`

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`