Classical Mechanics
# 1D Dynamics

Paul wants to hang a picture frame on his wall. To mark out the dimensions, he applies a horizontal force to the middle of the frame. If the wall is perfectly smooth, what is the minimum force that Paul has to exert to keep the frame in equilibrium?

**Details**

- The coefficient of friction \(\mu\) between Paul's hand and the frame is equal to 1.

Paul keeps his luggage box (denoted by B in the image) on frictionless ground and goes to the restroom. When he returns, he finds that someone has tied their luggage box (denoted by A) with a horizontal rope to a wall and put it on his luggage box B as shown in the diagram. The surface between boxes A and B is rough. Paul applies a force \(F\) in the horizontal direction to take out his luggage.

How does the minimum horizontal force \(F_\textrm{min}\) he needs to apply to remove box B depend on the mass of the boxes?

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