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A metal cylinder of mass ? = 5 kg with a coaxial hole is sliding horizontally...

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Physics

A metal cylinder of mass ? = 5 kg with a coaxial hole is slidinghorizontally on a metal rod. A spring with spring constant ? = 500N/m is attached to the cylinder. The other end of the spring isattached on a table at a vertical distance of â„Ž = 0.3 m below thecylinder. The spring has an equilibrium length of ?_0 = 0.5 m.

a) What is the horizontal position ?0 of the cylinder when thespring is at its natural equilibrium length of ?0 = 0.5 m? Definethe attachment point of the spring on the table as position ? =0.

b) What is the length ? of the spring when the cylinder is atany given position ??

c) Draw a free-body diagram of the cylinder.

d) Show that the horizontal force from the spring on thecylinder is: ?? = −?? (1 − ?0 √? 2 + ℎ 2 )

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