- #1
DavidDante
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Homework Statement
The usual configuration of an Atwood's Machine.
Two masses: m1, m2
Accelerations (unknown): a1, a2, ap (Pulley)
Rope Tension: T (Unknown)
BUT:
Massive pulley: mp
Upwards force acting on pulley (i.e the pulley is not in equilibrium): F
NOTE: Consider that all the pulley's mass in concentrated at the center of the pulley, so as not to consider the moment of inertia. (Is this ok?)
Question: Find the tension T, and the accelerations a1, a2.
Homework Equations
Newton's Second Law
The Attempt at a Solution
So this is what I tried:
Analyzing the pulley.
F - 2T - mp . g = mp . ap.........(I)
Analyzing the whole System as a unit:
F - (mp + m1 + m2) . g = (mp + m1 + m2) . ap....(II)
Analyzing m1:
T - m1 . g = m1 . a1..........(III)
From (II) I derived ap in terms of known constants, then I replaced ap (in terms of the constants) in (I) and I found T in terms of known constants. Finally I replaced the equation for T in (III).
So this is what I've got. Did I miss anything? Any feedback would be greatly appreciated.
Thanks-