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Discussion
Shown above is the motion of particle B as it moves through the circular slot in A.
- Consider an FBD of a system made up of A and B together. Since there are no forces acting in the horizontal direction (x-direction), then linear momentum for the system of A+B is conserved in the x-direction. We see evidence of this as we watch the motion above: as the velocity in the x-direction for B increases to the right, then the velocity in of A increases to the left.
- From the above FBD, we can also say that energy is conserved for the system of A+B since there are no external non-conservative forces acting on the system that do work. A consequence of conservation of both energy and linear momentum is that as B reaches its maximum height in the circular slot the total kinetic energy for the system goes to zero since both momentum and kinetic energy was initially zero. You can readily see this in the above animation.
HINTS:
STEP 1 - FBD: Draw a SINGLE free body diagram (FBD) of the system of A+B.
STEP 2 - Kinetics: Based on the above FBD (and the discussion above), you can use conservation of both energy and linear momentum in the x-direction. Write down both of these equations for the system of A+B.
STEP 3 - Kinematics: At Position 2, the velocity of B is strictly in the x-direction; that is: vB2 = vB2x.
STEP 4 - Solve.