Example 6

Problem: Starting from rest, the 3 kg mass slides 2 m down the smooth incline ( 35 degrees) and across the level floor (where the kinetic coefficient of friction is 0.117). After 1.2 m on the level floor, it encounters a spring of force constant 20 N/m. By how much is the spring compressed before the mass reverses direction?

Solution: The block has gravitational potential energy in its initial position and elastic potential energy when it has fully compressed the spring. In addition, it dissipates heat along the rough surface. Letting x be the amount of compression of the spring...