Shown above is the motion of the system made up of blocks A and B, with the velocities of A and B shown in the plots at the top. A is initially moving to the right, and B is initially moving to the left. As A slides on B, friction is generated at the contact of A and B. This friction slows down the motion of A with respect to B to the point where A is no longer moving to the right, and instead A begins moving to the left. You are asked to find the mutual speeds of A and B when sticking occurs.
STEP 1 - FBD: Draw a SINGLE free body diagram (FBD) of the system including Blocks A and B. Note that for this choice of system, the friction force between A and B is internal.
STEP 2 - Kinetics: From your FBD above, there are no external forces acting on the system in the horizontal direction. What is the implication of this in terms of the linear momentum of the system? (HINT: It says that the linear momentum is conserved for the system of A + B. This becomes your kinetics equation. Note that energy is NOT conserved for this problem due to friction.)
STEP 3 - Kinematics: Note that when slipping ceases between blocks A and B, we have vA2 = vB2.
STEP 4 - Solve. Your final answer should be in terms of vA1 and vB1.
- Should the final answer depend on the coefficient of friction? Does yours?
- Could you have worked out the problem by using two systems: A and B, individually? [Answer: Yes, but it requires more effort since you need to deal with the force of friction.]
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