A 5.50 kg block free to move on ahorizontal, frictionless surface is attached to

Question

A 5.50 kg block free to move on ahorizontal, frictionless surface is attached to one end of a lighthorizontal spring. The other end of the spring is fixed. The springis compressed 0.100 m from equilibrium and is then released. Thespeed of the block is 1.10 m/s when itpasses the equilibrium position of the spring. The same experimentis now repeated with the frictionless surface replaced by a surfacefor which µk = 0.300. Determine the speedof the block at the equilibrium position of the spring.
1 m/s

Explanation / Answer

The energy stored in the spring is the same in both cases. Theonly difference between the first and second situation is thatfriction does work, taking away kinetic energy, in the secondsituation. So... .      KE in situation 2 = KE insituation 1 - work done by friction .          (1/2) mv22   = (1/2) mv12    -    m g d .               v22   =  v12   - gd = 1.102 - 0.300 * 9.80 *0.100    = 0.916 .        v2 =    0.9571 m/s

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