if in atwood machine m1=1.30kg and m2=2.80kg at t=o.m1 starts losing the mass at a rate of .200kg/s due to leakage.at what rate does the acc. of the container changes at t=0sec and t=3 sec.when dos the acc. reach max. value

what is an atwood machine.

Approved

dm₁/dt = -0.2kg/s           ( given)

dm₁ = -0.2dt

integrating both sides

m₁ = -0.2t + c

at t=0 , m₁=1.3

therefore  ,  c=1.3

now , m₁ = 1.3 - 0.2t ...............1                                      (mass of m₁ at any time)

now accleration (a)= g(m₂-m₁)/(m₂+m₁)

     a = g{m₂ - (1.3-0.2t)}/{m₂+(1.3-0.2t)}                        (putting m₁ from eq 1)

    a =g(1.5+0.2t)/(4.1-0.2t)           ...................2              (after putting value of m₂)

 da/dt = g(1.12)/{4.1-0.2t)²  ................3

at t=0 ,

da/dt = 0.652m/s²

at t=3

da/dt = 0.896m/s²