How Do Pulley Motions Influence Particle Dynamics?

[f(m)]

I was helping my friend with some questions regarding motions of pulleys and i am came up with the following question which i couldn't think of an argument... please check

Two particles A and B of masses M and m respectively are connected by an inelastic string which passes over a smooth pulley. Initially A is at rest on a smooth horizontal table and B hangs at a height h above the table. B is then raised through an extra height H and allowed to fall.
i. Show that if (m²/(M²-m² ))H<h, B does not reach the table.
ii. If (m²/(M²-m² ))H≥h show that, during the motion, A rises to a maximum height m{2(M+m)h+mH}/(m+M)

can anyone explain how the motion happens and what is the condition i need start to prove the above questions

thanks...

 

[aditya~]

solving the first part
click here

 

[aditya~]

the second part can also be proved:
after m hits the table ,the string becomes lose
find the velocity of M at that instant using work energy theorem
and then equate this K.E of M to its max potential energy(that corresponds to max height )

 

[f(m)]

thanks for the reply aditya..
it did help but i am wondering is there any other way of proving it rather using conservation of energy theorem, can't we prove only using the Newton's laws of motion and with other required theorem

 

[aditya~]

i think the work energy theorem itself is a manifestation of Newton's secomd law

we write

F(net)=ma

say the motion is 1 dimensional in the x-axis

F(x)=mvdv/dx
take the dx to the other side and integrate

integral(F(x)dx) =delta kinetic energy


so if u have done by work energy theorem ..u are indirectly doing by Newton's laws