In the figure a 1.5 kg block is held at rest against a spring with a force constant k = 700 N/m . Initially, the spring is compressed a distance d . When the block is released, it slides across a surface that is frictionless except for a rough patch of width 5.0 cm that has a coefficient of kinetic friction ? k = 0.40. Find d such that the block\'s speed after crossing the rough patch is 2.4 m/s . Express your answer using two significant figures. Solution spring PE = friction work + final KE ½kd² = µmgx + ½mv² ½ * 700N/m * d² = 0.40 * 1.5kg * 9.8m/s² * 0.05m + ½ * 1.2kg * (2.4m/s)² 350N/m * d² = 3.75 J d = 0.010 m = 1 cm .

1. In the figure a 1.5 kg block is held at rest against a spring with a force constant k = 700 N/m .
Initially, the spring is compressed a distance d . When the block is released, it slides across a
surface that is frictionless except for a rough patch of width 5.0 cm that has a coefficient of
kinetic friction ? k = 0.40.
Find d such that the block's speed after crossing the rough patch is 2.4 m/s .
Express your answer using two significant figures.
Solution
spring PE = friction work + final KE
½kd² = µmgx + ½mv²
½ * 700N/m * d² = 0.40 * 1.5kg * 9.8m/s² * 0.05m + ½ * 1.2kg * (2.4m/s)²
350N/m * d² = 3.75 J
d = 0.010 m = 1 cm