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 put his luggage box (denoted by A) on top of his luggage such that his luggage box is tied with a horizontal rope to a wall. 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?

The person who is able to pull the other across the middle line is declared the winner. If the rope is massless and inextensible, who will win the tug of war?

**Assume** that both people are wearing identical shoes that have an identical coefficient of friction with the ground.

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