| Problem statement Solution video |
DISCUSSION THREAD
Ask and answer questions here. You learn both ways.
DISCUSSION and HINTS
Initially Block A slides to the right along Block B which is traveling to the right. However, with friction acting between A and B, both A and B slow down. At some point, A instantaneously comes to rest, and the starts to move to the left. Once the speed of A to the left matches that of the speed of B to the left, the two stick and move together. You can see this in the animation that follows.
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw single free body diagram (FBD) for the entire system (A+B). Do NOT consider A and B in separate FBDs because you will need to deal with the friction force acting between A and B (which you do not know).
Step 2: Kinetics (linear impulse/momentum)
Consider all of the external forces that you included in your FBD above. If there are no external forces acting in the horizontal direction (x-direction) on your system, the linear momentum in the x-direction is conserved.
Step 3: Kinematics
As described above, A comes to rest with respect to B when vA = vB.
Step 4: Solve
Combine your kinetics equation from Step 2 with your kinematics that you found in Step 3, and solve for the velocity of B.
QUESTION: Are you surprised that your answer for the final speed of B (and A) does not depend on the coefficient of friction acting between A and B? I was the first time that I worked the problem. 🙂
Can your answer for this problem be in terms of Va1 and Vb1? Since we aren’t given numerical values?
Yes, your final symbolic answer will be in terms of vA1 and vB1.
Yeah, in terms of Va1 and Vb1.
Do we include gravity in this problem?
I would assume gravity is present but there is a way to solve this problem that doesn’t involve gravity in your final answer. The problem hints should give you a better idea of how to solve this problem. Friction force (influenced by gravity) is not needed to solve this problem.
Please include gravity.
It is true that the value of the friction coefficient does not influence this particular answer; however, the blocks will NOT come to rest with respect to each other if friction is not present, and friction will not be present without gravity.
Would the only forces in the single free-body diagram be gravity and normal force? I assume friction wouldn’t be included in the whole system.
You are correct. The important part of that observation is that there are no external forces acting in the direction of motion.
Friction is present for the individual FBDs, but when considering the entire system, the FBD would not include friction because the friction forces acting on Block A and Block B are equal in magnitude and opposite in direction, meaning they cancel each other out.
Can it be assumed that this is a rolling without slipping problem when looking at the bottom block? We haven’t had a rolling with/without slipping problem recently but I feel like this would impact the problem.
I assume that you are referring to the two supports on the bottom block that contact the smooth horizontal surface on which that block moves?
If so, each support provides a single-point contact with the surface on which the block moves. The supports insure smooth contact; that is, no friction forces to oppose the motion of the lower block.
Should we provide our final answer as a vector?
I’m not exactly sure what the instructors want, but it’s probably a safe bet to leave the final answer as a vector.
Velocity is a vector. Please write your velocity answer as a vector.