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mechanics of a point mass

3. Series 9. Year - 1. a gnawed prism

A gnawed prism (see pic.) of mass $M$ was put on a smooth horizontal plane. Small cubes of masses $μ$ and $m$ are situated in the lowest part of the pit and on the right slope respectively. There's no friction both between the prism and the surface and the cubes and the prism.

Determine the relations between masses $M$, $m$, $μ$ necessary for the cube $m$ to start to move when the cube $μ$ gets loose.

3. Series 9. Year - 3. Pinoccio's hat

Papa Carlo made a hat for Pinoccio from a thin metallic plate in the form of cone of height 20 cm with top angle of 60 degrees. Will this decoration keep itself on his head that could be imaged as a perfectly smooth ball of 15 cm diameter?

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