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Classical Mechanics

# 1D Dynamics Warmup

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 is at an airport and has to pass through a security check. He places his luggage on a conveyor belt, which is initially stopped to scan another passenger's bag. When the conveyor belt starts to move to the right, what can be said about the friction force acting on the luggage?

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?

A man of mass m is standing in a hanging cage of mass M. The cage is made from a lightweight material, so $$M < m$$. A rope is attached to the cage, passed over a smooth light pulley, and the man holds the other end of the rope. The man pulls the rope, such that the entire system is suspended in equilibrium. If the man is standing on a weighing machine, what do we know about the reading of the weighing machine?

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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