A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter .4m and hangs vertically, as shown. The rotational inertia of the wheel is .5kg.m^2. When the block is released and the cord unwinds, find the acceleration of the block?
Could you please help me with this problem?
Thank you
Could you please help me with this problem?
Thank you
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Free-body analysis of the forces on the 16 Kg block gives
mg - T = ma
and a torque analysis around the flywheel
T R = I α
From the kinematics of the system we have that
α R = a
substituting into the expression for torque and solving for T we get
T = I a / R^2
substituting into the forces of the free body diagram
mg - Ia/R^2 = ma
solving for a
a = mg / (m + I/R^2) = 16*9.8/(16+0.5/0.4^2) = 8.19 m/s^2
mg - T = ma
and a torque analysis around the flywheel
T R = I α
From the kinematics of the system we have that
α R = a
substituting into the expression for torque and solving for T we get
T = I a / R^2
substituting into the forces of the free body diagram
mg - Ia/R^2 = ma
solving for a
a = mg / (m + I/R^2) = 16*9.8/(16+0.5/0.4^2) = 8.19 m/s^2