(Solved): Please Solve A and B, Civil Engineering Dynamics Learning Goal: To set up and analyze equations of m ...

Learning Goal: To set up and analyze equations of motion in a cylindrical coordinate system. The mechanism shown in the figure below rotates about the vertical axis. The collar has mass $m=3.85\mathrm{kg}$. The spring has an unstretched length of $735\mathrm{mm}$ and the spring constant is $k=150\mathrm{N}/\mathrm{m}$. The distance $d=400\mathrm{mm}$, and the collar is required to stay a fixed distance $r=960\mathrm{mm}$ from the vertical axis.(Figure 1) Figure 1 of 1 Part A - The angular velocity for a smooth shaft If there is no friction between shaft $AB$ and the collar, what angular velocity $\dot{\theta }$ must the mechanism have to keep the collar at $r=960\mathrm{mm}$ from the vertical axis? Express your answer to three significant figures. Incorrect; Try Again; 2 attempts remaining Part B - The minimum required angular velocity when there is friction Consider the same mechanism again, with $m=3.85\mathrm{kg},d=400\mathrm{mm},k=150\mathrm{N}/\mathrm{m}$, only now, instead of being smooth, the collar and shaft have a maximum coefficient of friction of ${\mu }_s=0.711$. What is the minimum angular velocity required to keep the collar at a constant distance $r=960\mathrm{mm}$ from the axis of rotation? Express your answer to three significant figures. Incorrect; Try Again; 5 attempts remaining