The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m. (1) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 1 is___ (two decimal places) (2) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 2 is___ (two decimal places) (3) The stretched spring length of the spring at the state 1 is________(m) (two decimal places) (4) The elastic potential energy at the potion 1 is_______(N·m) (two decimal places) (5) The stretched spring length of the spring at the state 2 is _______(m) (two decimal places) (6) The elastic potential energy the state 2 is ___ (N·m ) (two decimal places) (7) The instantaneous center of zero velocity (IC) is (8) The mass moment of inertial about the mass center G is IG =_________(kg·m2 ) (two decimal places) (9) The mass moment of inertial about the IC center is IIC =_________(kg·m2 ) (two decimal places) (10) The kinetic energy at the state1?________ (N·m) (two decimal places) (11) The angular velocity at the state 2?_______(rad/s) (two decimal places) (12) The kinetic energy at the state 2?______ (N·m) (two decimal places)
The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration kG=0.4 m. The spring’s unstretched length is L0=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is θ=30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is θ=0°. The spring’s length at the state 2 is L2=4 m.
(1) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 1 is___ (two decimal places)
(2) If the mass center G is set as the origin (datum), the gravitational potential energy at the state 2 is___ (two decimal places)
(3) The stretched spring length of the spring at the state 1 is________(m) (two decimal places)
(4) The elastic potential energy at the potion 1 is_______(N·m) (two decimal places)
(5) The stretched spring length of the spring at the state 2 is _______(m) (two decimal places)
(6) The elastic potential energy the state 2 is ___ (N·m ) (two decimal places)
(7) The instantaneous center of zero velocity (IC) is
(8) The mass moment of inertial about the mass center G is IG =_________(kg·m2 ) (two decimal places)
(9) The mass moment of inertial about the IC center is IIC =_________(kg·m2 ) (two decimal places)
(10) The kinetic energy at the state1?________ (N·m) (two decimal places)
(11) The angular velocity at the state 2?_______(rad/s) (two decimal places)
(12) The kinetic energy at the state 2?______ (N·m) (two decimal places)
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