NOTE: Has to be solved withOUT using kinematic equations. Please show all work a

Question

NOTE: Has to be solved withOUT using kinematic equations. Please show all work and formula's used. Thanks!

It's Atwood's machine, again! Atwood's machine consists of two masses joined by a rope (which in this case we will assume is massless) that is passed over a single pulley (which we assume is frictionless). In this case, assume the masses m and M as given. At the moment shown in the diagram, they are currently at rest. Note that M m. Using the concept of energy conversion, with what speed does M hit the ground?

Explanation / Answer

Applying energy cosnervation,

PEi + KEi = PEf + KEf

(m g H + M g H) + 0 = (M g 0 + m g (2H)) + (m + M) v^2 / 2

g H (M - m ) = (M + m) v^2 / 2

v = sqrt[ 2 g H (M - m) / (M + m)]

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