What is wrong with this equation ?

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The equation presented for the system of two blocks connected by a pulley is incorrect because it fails to account for the moment of inertia of the pulley. The dynamics of the system must include the rotational effects of the solid disk pulley, which affects the overall acceleration and tension in the string. Additionally, the equation does not properly incorporate the forces acting on both blocks, including friction and the gravitational components. To accurately solve for the acceleration and tensions, the moment of inertia must be included in the equations of motion. Properly addressing these factors will lead to the correct analysis of the system's behavior.
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A block of mass m1 ϭ 2.00 kg and a block of mass
m 2 ϭ 6.00 kg are connected by a massless string over a pul-
ley in the shape of a solid disk having radius R ϭ 0.250 m
and mass M ϭ 10.0 kg. These blocks are allowed to move
on a fixed block-wedge of angle ␪ ϭ 30.0° as in Figure
P10.37. The coefficient of kinetic friction is 0.360 for both
blocks. Draw free-body diagrams of both blocks and of the
pulley. Determine (a) the acceleration of the two blocks
and (b) the tensions in the string on both sides of the
pulley.

[PLAIN]http://img820.imageshack.us/img820/9199/36360522.jpg

(m1 + m2)a = m2gSin30 - \mum1g - \mum2gcos30

what is wrong with this equation ?
 
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ManishR said:
what is wrong with this equation ?

You neglect the momentum of inertia of the pulley.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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