As the figure shows, a 0.50 kg block is pushed against a spring of constant 3.5 N/m and held at 0.60 m away from equilibrium position. The block then released from rest and starts sliding on a rough horizontal ground with coefficient of kinetic friction 0.3 and the spring returned to its relaxed length. How far will the block slide before it stops?
![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)
