A block has a mass of 500 g, another block has a mass of 460 g. Both are attached to a pulley with a frictionless wire that does not slip. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 seconds. What is the magnitude of the blocks' accleration? What is the magnitude of the pulley's angular acceleration?
Torque = Moment of Inertia * Angular Acceleration
Force = Mass * Acceleration
Acceleration = Angular Acceleration / Radius
Moment of Inertia = (1/2)MR^2
The Attempt at a Solution
T=tension; W=weight; A=accleration; R=radius; I=moment of inertia
M(1) = left box; M(2) = right box; M(3) = pulley
A(1) = A(2) = a/R = A
1. T(1) - W(1) = m(1) * A; T(1) = W(1) + M(1) * A
2. T(2) - W(2) = -m(2) * A; T(2) = W(2) - M(2) * A
3. T(1)R - T(2)R = I * A / R
T(1) - T(2) = M(3) * A
W(1) + M(1) * A - W(2) + M(2) * A = M(3) * A
Solved for A.
Well, I started plugging things in and stuff, but I can't solve the problem because the mass of the pulley is unknown. I'm pretty sure I did it wrong so can someone point out my mistake or show me how to do it if I did it completely wrong? Thanks!
answer: a) 6.00 cm/s^2 b) 1.20 rad/s^2