Question

# Problem 15. Consider the mechanism shown in the figure below that is constructed from two identical slender bars of mass m and length 21 pinned together; a roller of radius r, mass M, and radius of gyration R about its axis; and a spring with spring constant k. The mechanism sits in the vertical plane with the left end of Bar 1 pinned to the pivot at O and the right end pinned to Bar 2 at A. The other end of Bar 2 is pinned to the roller (see figure below). Assume all joints in the mechanism are frictionless. The system is initially at rest at position theta =theta 0with the spring in its natural unstretched equilibrium position. When the system is released from rest, it is assumed to roll without slipping on the fixed horizontal support 0. [5 pts] (a) Determine the angular velocity of the bars at the instant they become horizontal theta = 0. 5 pts](b) Find a condition on the parameters that is necessary for the bars to reach the final horizontal position (i.e., it's spring force versus gravity!).  Fig: 1  Fig: 2  Fig: 3  Fig: 4