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You are asked to investigate the dynamics of this system during the time from release through to the time of immediately after when A strikes B.
- Divide this time of investigation into two segments: 1 to 2, and 2 to 3.
- From times 1 to 2, A slides outward on the arm until it almost impacts B. During this time, angular momentum of A+B+arm is conserved, as well energy for that same system is conserved.
- From times 2 to 3, A impacts B. During this time, angular momentum of A+B+arm is conserved; however, due to the impact, energy is NOT conserved. Instead, we will use the coefficient of restitution relating the change in radial velocity for A as the second equation.
HINTS:
STEP 1 – FBD: Draw a SINGLE free body diagram (FBD) of the system of A+B+arm.
STEP 2 – Kinetics: The only force that you will see acting on this system during the full range of time from 1 to 3 is the support force at O. Because this forces acting through point O, angular momentum about O is conserved throughout. During the pre-impact time of 1 to 2, also write down a conservation of energy equation. During the impact time of 2 to 3, write down the COR equation involving only the radial components of velocity for A.
STEP 3 – Kinematics: At Instant 1, A and B have only eθ components of velocity. For Instants 2 and 3, A has both er and eθ components of velocity, and B has only eθ components of velocity.
STEP 4 – Solve.