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# Conservation of Energy in a Sliding Block

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A 2.0 kg block slides along a horizontal surface with a coefficient of friction µk = 0.30. The block has a speed of v = 1.2 m/s when it strikes a massless spring head-on (as in Fig. 8-18).

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

(b) What minimum value of the coefficient of static friction, µs, will assure that the spring remain compressed at the maximum compressed position?

(c) If µs 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).]

(d) Explain why detachment occurs when the spring reaches its natural length.

(Please see attachment for diagram)

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#### Solution Preview

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

(1/2)*m*v^2 = (1/2)* K *x^2

x = sqrt(m/K)*v = sqrt(2/120) * 1.2 = 0.155 m

(b) What minimum value of the coefficient of static friction, µs, will assure that the spring remain compressed at the maximum compressed position?

Spring Force = Static Frictional force for the spring to ...

#### Solution Summary

The solution explains, in a mixture of words and formulae, how to find values such as the minimum coefficient of static friction and speed at certain points of a block sliding along a horizontal surface as described in the question in a methodical, easy-to-follow manner.

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