Extending Newton's Law to real life. No more ideal systems

[flyingpig]

Extending Newton's Law to real life. No more "ideal systems"!

Homework Statement

Newton's Laws in reality, applying all forces 10 pts?
A block of mass m is hung on a pulley that is at the end of a table. The pulley connects the hanging block m and another block M that is on the table. The friction between the block and the surface is u. In this system, the pulley has a mass and there is friction in the pulley. The mass of the pulley is unknown, but it is assumed to be smaller than the blocks.

In this question, assume that the hanging mass m < M, the block on the table. As the hanging mass is let go, the hanging mass drops to the ground and the block on the table follows. Using your knowledge of physics, explain how the pulley's mass, friction, can make this unideal situation possible?

Homework Equations

F = ma

Ffric = uFnormal

The Attempt at a Solution

I used M as the heavy mass and m as the lighter mass

(1) mg - T = ma

(2) T - uMg = Ma

(1) + (2)

g(uM - m) = a(M + m)

g(uM - m)/(M + m) = a

For a to go downwards, then a>0

g(uM - m)/(M + m) > 0

g(uM + m) > 0

uM - m > 0

u > m/M

Is this right? But even so, how do i account for the friction and mass of the pulley? I need to explain this "nonideal system"

 

[hnikol]

Is this right? But even so, how do i account for the friction and mass of the pulley? I need to explain this "nonideal system"

The way than I imagine the whole system, the friction of pulley means that tension isn't T
the same on both sides of the pulley. The equations I would use are:(1) mg - T₁ = ma => T₁ = mg - ma

(2) T₂ - uMg = Ma => T₂ = Ma +uMg

Since it's moving at the side where m mass is hanging, it must be T1 > T2...