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Gotejjeken
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Homework Statement
The two blocks in the figure are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.55 N * m.
If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?
Homework Equations
Taking mass 1 (m1) to be on the left, and mass 2 (m2) to be on the right:
m1 = 4.0 kg
m2 = 2.0 kg
r = 0.06 m
Mp = 2.0 kg
f = 0.55 N * m
a(m2) = -a(m1)
T1 = m1 * a(m1) + m1 * g (T1 = Tension on mass 1)
T2 = m2 * g - m2 * a(m1) (T2 = Tension on mass 2)
Net Torque = T1 * r - T2 * r - f
alpha = Net Torque / I
I = 1/2 * Mp * r^2 (where Mp = Mass of Pulley)
a(m1) = -alpha * r (negative acceleration and positive rotation)
y = 1/2 * a * (delta)t^2
The Attempt at a Solution
Using the above equations I get:
Code:
alpha = 2*r(T1 - T2) - f
------------------
Mp * r^2
Substituting that alpha into the a(m1) = -alpha * r equation and then solving for a(m1), I get a(m1) = -2.14 m/s^2. Then substituting this value for acceleration into the above kinematic equation and solving for time, I get the time to be 0.97s, which is wrong.
I'm not sure if my issue is just an issue of messing up the signs, or if I am approaching the problem wrong. Any help would be appreciated.
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