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. Ignore the spring's mass.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Please Help with #12 only. The answers for 1-11 are: 1 (0), 2 (0), 3 (3.62), 4 (13.10), 5 (3), 6 (9), 7 (point A), 8 (3.20), 9 (10.4), 10 (0), 11 (2).
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.
Ignore the spring's mass.
(1) If the datum for gravitational potential energy is set as shown below, the the gravitational potential energy of the wheel at the state 1 is___ N m(two decimal places)
(2) If the datum for gravitional potential energ is set as shown below, the gravitational potential energy of the wheel at the state 2 is___ N m (two decimal places)
(3) At state 1, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places)
(4) The elastic potential energy of the spring at the potion 1 is_______(N·m) (two decimal places)
(5) At state 2, how long the spring is stretched from its unstretched state (length difference):________(m) (two decimal places)
(6) The elastic potential energy of the spring at the state 2 is_______(N·m) (two decimal places)
(7) The instantaneous center of zero velocity (IC) of the wheel at state 1 is
(8) The mass moment of inertial of the wheel about its mass center G is IG =_________(kg·m2 ) (two decimal places)
(9) The mass moment of inertial of the wheel about its IC center at state 1 is IIC =_________(kg·m2 ) (two decimal places)
(10) The total kinetic energy of the system at the state1 is:________ (N·m) (two decimal places)
(11) Apply the theory of work-energy to the whole system during state 1 and state 2, and calculate the
12) Based on result from (11), the kinetic energy of the wheel at the state 2 is:______ (N·m) (two decimal places)
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