### Challenging questions for in friction - for physics and mechanics: A Level and IB

1)

If the section of the rope that hangs down is about to move on the table, find and expression for x in terms of the coefficient of friction and the length of the rope.

2)

The mass of a book is 2kg and is pressed against a wall by a horizontal force to stop it from sliding down. Find the minimum value of the force if the coefficient of the friction between the book and the wall is 1/3.

3)

A horizontal force is applied at a right angle to the top edge of a rectangular box with a length 60cm and a height 20cm to
move it. What should the coefficient of friction between the
box and the surface it is placed on so that the box moves without toppling.

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