The figure below shows a spring with a force constant 300 [Nm−1] compressed by a 2.5[kg] block held at rest initially. The compression is 18.0 [cm]. The block is then released and slides freely across a smooth surface until it reaches a rough patch 10 [cm] long with μ = 0.72 Figure 2: Mass on spring. a - Find the speed of the block before it reaches the rough patch. b - Find the speed of the block after crossing the rough patch.
![The figure below shows a spring with a force constant 300 [Nm−1] compressed by a 2.5[kg] block held at rest initially. The compression is 18.0 [cm]. The block is then released and slides freely across a smooth surface until it reaches a rough patch 10 [cm] long with μ = 0.72 Figure 2: Mass on spring. a - Find the speed of the block before it reaches the rough patch. b - Find the speed of the block after crossing the rough patch.](https://www.doubtrix.com/uploads/editor/6842514473sqZuaFADmh.jpg)
![A 30 kg mass is held against a spring of stiffness 600 N/m on a smooth horizontal surface compressing it by an amount d. When the mass is released from rest (from point A ), the spring accelerates it until it reaches its relaxed length, after which the mass moves away from the spring. It then encounters a rough horizontal patch of length 3.25 m (beginning at point B), with a coefficient of kinetic friction of 1/9. After leaving the rough patch (at point C) the mass continues to move horizontally until it reaches x = 0, after which it moves along the smooth vertical surface described by: y(x) = x3 9 (with x and y in m, for x > 0 ). When the mass reaches x = +2.0 m along the cubic curve (labelled point D on the diagram), its speed is measured to be 2.50 m/s. Ignore air resistance throughout this problem, and take g = 10 m/s2 (in −y direction). a) [5] What initial compression d in the spring was required so the mass arrives at point D moving at 2.50 m/s? b) [5] At point D, what is the instantaneous i) magnitude of the normal force the curve exerts on the mass and ii) the mass' rate of change of speed? (Note: Since you've been given the speed at D, parts a and b are completely independent of each other.)](https://www.doubtrix.com/uploads/editor/1276136357XvOVXovqvl.png)
