Box a in on a table with box B on top of it. A horizontal rope is putting box A

Question

Box a in on a table with box B on top of it. A horizontal rope is putting box A to the right with a force F an shown. There is between the boxes and between the lower box and the surface it is traveling along. The top box B is at rest relative to the bottom box and both boxes are accelerating to the right. A student draws separate free-body diagram for boxes A and B and defines all the forces as shown below. There is at least one thing wrong with these free-body diagrams. Please identify and explain how to correct.

Explanation / Answer

In the second diagram force applied by box A on box B is not shown

So the diagram must be corrected as below,   

Where FBA is force on box B due to motion of box

By Newton’s second law on box B

FBA- E = mB*aB

Since aB = 0 => FBA= E

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