Physics 121
posted by Bob .
Two block are connected by a rope that runs over a pulley. The block on the tables has mass 4kg, the hanging block has mass 2kg, and the pulley has mass 0.5kg and radius 0.25m. Assume that the table is frictionless. If the block are released from the rest, determine their speeds after the hanging block has dropped 0.75m.

m1 =4 kg, m2 = 2 kg, m = 0.5 kg, R = 0.25 m, h= 0.75 m.
Projections on the horizontal and vertical axis:
m1•a = T1
m2•a =m2•gT2,
I•ε =M.
If the pulley is the disk (cylinder) I =m•R²/2 ,
M = torque = (T1T2) •R,
ε = a/R,
I•ε =M => m•R²•a/2•R =(T1T2) •R =>
m•a/2 = (T1T2).
m1•a + m2•a = T1 + m2•g T2 = m2•g + (T1T2) = m2•g +m•a/2,
a = m2•a/[m1+m2m(m/2)] = 2•9.8/(4+2+0.125)=3.336 m/s^2,
a = v^2/2•h ,
v=sqrt(2•a•h) = sqrt(2•3.336•0.75) = 2.2 m/s^2