The spring has an un-deformed length of 100mm and its stiffness k=800N/m. If the collar is released from rest at A, Determine its velocity i) as it passes through B. ii) as it reaches C.

It passes through B (A to B)

$x_1=250-100=150mm=0.15 \\ x_2=200-100=100mm=0.1 \\ W.D= ∆ K.E \\ \dfrac 12 K (x_1^2-x_2^2 )+ mgh=\dfrac 12 m(V_2^2-V_1^2) \\ \dfrac 12 ×800 (0.15^2- 0.1^2 ) + 2×9.81×0.2=\dfrac 12 ×2×(V_2^2-0) \\ V_2=2.98 m/s $

It passes through C (A to C)

$x_1=250-100=150mm=0.15 \\ x_2=150-100=50mm=0.05m \\ W.D= ∆KE \\ \dfrac 12×K(x_1^2-x_2^2 ) = \dfrac 12 m (V_2^2-V_1^2) \\ \dfrac 12 ×800 (0.15^2- 0.05^2 )= \dfrac 12 ×2×(V_2^2-0)\\ V_2=2.83 m/s $

Velocity of collar as it passes through B= 2.98 m/s

Velocity of collar as it passes through C = 2.83 m/s