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A spring with spring constant k = 40 N/m and unstretched length of L0 is attached to the ceiling. A block of mass m = 2 kg is hung gently on the end of the spring.

a) How far does the spring stretch? dL = 0.49

Now the block is pulled down until the total amount the spring is stretched is twice the amount found in part (a). The block is then pushed upward with an initial speed vi = 2 m/s.

|v|max = ?

A spring with spring constant k = 40 N/m and unstretched length of L0 is attached to the ceiling. A block of mass m = 2 kg is hung gently on the end of the spring.

a) How far does the spring stretch? dL = 0.49

Now the block is pulled down until the total amount the spring is stretched is twice the amount found in part (a). The block is then pushed upward with an initial speed vi = 2 m/s.

|v|max = ?

**F=ma. W=Fd, W = ΔKE, U = mgh, Fs = -Kx**

**Part a was easy, weight equals spring force so mg = kx => x=mg/k = 0.49.**

Part b is where I'm really stuck. Since (U + KE)final = (U + KE)initial then

mgh + 1/2mv^2 = mgh + 1/2mv^2 + Uspring => 2(9.81)(0.981) + 1/2(2)(2^2) = 40(0.981) + 1/2(2)(vmax^2) + 0 so vmax = 4.05 but that's not right. HELP PLEASE!

Part b is where I'm really stuck. Since (U + KE)final = (U + KE)initial then

mgh + 1/2mv^2 = mgh + 1/2mv^2 + Uspring => 2(9.81)(0.981) + 1/2(2)(2^2) = 40(0.981) + 1/2(2)(vmax^2) + 0 so vmax = 4.05 but that's not right. HELP PLEASE!