# Problem: A 2.1 kg block slides along a horizontal surface with a coefficient of kinetic friction exttip{mu _{ m k}}{mu_k} = 0.31. The block has a speed exttip{v}{v} = 1.4 m/s when it strikes a massless spring head-on.If the spring has force constant exttip{k}{k} = 120 N/m , how far is the spring compressed?What minimum value of the coefficient of static friction, S, will assure that the spring remains compressed at the maximum compressed position?If S is less than this, what is the speed of the block when it detaches from the decompressing spring? [Hint: Detachment occurs when the spring reaches its natural length (x = 0).]Explain why the detachment occurs when the spring reaches its natural length (x = 0).

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###### Problem Details

A 2.1 kg block slides along a horizontal surface with a coefficient of kinetic friction = 0.31. The block has a speed = 1.4 m/s when it strikes a massless spring head-on.

If the spring has force constant = 120 N/m , how far is the spring compressed?

What minimum value of the coefficient of static friction, S, will assure that the spring remains compressed at the maximum compressed position?

If S is less than this, what is the speed of the block when it detaches from the decompressing spring? [Hint: Detachment occurs when the spring reaches its natural length (x = 0).]

Explain why the detachment occurs when the spring reaches its natural length (x = 0).