Figure represents a painter in a crate which hangs alongside a building. When the painter of mass 100kg pulls the rope, the force exerted by him on the floor of the crate is `450N`. If the crate weighs 25 kg. find the acceleration (in `ms^(-2)`) of the painter.

Answer

2

Explanation

Let M=mass of painter `= 10kg`
m=mass of crate = 25 kg
Let `F_(A)` be the action force exerted by painter on create, reaction force exerted by crate on man
`N=F_(A) =450 N`
The free body diagram of painter is shown in fig.

Therefore, equation of motion of painter is
`N+T-Mg = Ma` ...(i)
The equation of motion of whole system is
`2T-(M+m)g = (M+m)a` ...(ii)
Multiplying (i) by 2, we get
`2N + 2T - 2Mg = 2Ma` ...(iii)
Substracting(ii) from (iii) , we get
`2N-2Mg+(M+m)g = (2M-M-m)a`
`a=(2N-(M_m)g)/(M-m)`
`=(2 xx 450 - (100 - 25) xx 10 )/(100 -25) = (900-750)/(75)= 2ms^(-2)`.