The restroom door is equipped with a torsional spring and a torsional viscous damper so that it automatically returns to its closed position after being opened. The door has a mass of 60 kg and a centroidal moment of inertia about an axis parallel to the axis of the door’s rotation of 7.2 kg m 2 . The torsional spring has a stiffness of 25 Nm/rad. a. What is the damping coefficient such that the system is critically damped? b. A man with an armload of packages, but in a hurry, kicks the closed door to cause it to open. What angular velocity must his kick impart to cause the door to open 70 0? c. How long after his kick will the door return to within 5 0 of completely closing?
The restroom door is equipped with a torsional spring and a torsional viscous
damper so that it automatically returns to its closed position after being opened. The door has a
mass of 60 kg and a centroidal moment of inertia about an axis parallel to the axis of the door’s
rotation of 7.2 kg m
2
. The torsional spring has a stiffness of 25 Nm/rad.
a. What is the damping coefficient such that the system is critically damped?
b. A man with an armload of packages, but in a hurry, kicks the closed door to cause it to open.
What angular velocity must his kick impart to cause the door to open 70
0?
c. How long after his kick will the door return to within 5
0 of completely closing?
D. Repeat parts a through c if the door is designed with a damping ratio, ζ = 1.3.
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