Problem statementSolution 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 *f**our-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 v_{A} = v_{B}.

**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. ðŸ™‚

Is the velocity of V_A1 relative to the ground or the cart? In the future homework, if nothing specific assumed, do we assume that the velocity of the object is relative to the ground?

All given velocities are absolute. That seen by a fixed observer.

Do we need to include a negative sign for the velocity of v_b when performing our calculations? For example I have 2*m*v_b1 as the initial momentum of block B but it is moving to the left, so should I plug in the velocity as -v_b1?

The problem refers to v_b1 as the "speed" at which B is moving. This is a scalar quantity. If you want to use that to find a velocity vector, you will have to add a directional component. The sign of the term will ultimately depend on your arbitrary coordinate system. but because A and B are moving in opposite directions, their velocity vectors should also be opposite, so one of the terms should have a negative sign.