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Discussion and hints
The four-step plan:
- FBD: It is recommended that you draw a free body diagram of the plate and cart combined.
- Kinetics: Your FBD should show that the summation of forces in the direction of motion for the cart (call that the x-direction) is zero; therefore, linear momentum in the x-direction is conserved for ALL time. Also note that energy is conserved up to the point of impact. During impact, energy is not conserved; however, you are given the coefficient of restitution (COR) for the impact.
- Kinematics: Write down the rigid body velocity equation relating the motion of points O and the plate's center of mass G. Here you will use the fact that the cart moves only in the x-direction.