Spring with 2 forces at both end

[MechaMZ]

Homework Statement

Hooke's law describes a certain light spring of unstressed length 33.0 cm. When one end is attached to the top of a door frame and a 8.80 kg object is hung from the other end, the length of the spring is 46.50 cm.
(a) Find its spring constant. (639.4667N/m)
(b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 170 N. Find the length of the spring in this situation.

The Attempt at a Solution

For the part B, the spring with two 170N at both end should be equal to 340N at one end and the other end fixed.

since the K = 639.4667N/m
F=kx
340 = (639.4667)x
x = 0.531m

then the total length should be 0.33m + 0.531m isn't?
but my answer is wrong =(

Homework Statement

A light spring with force constant 3.25 N/m is compressed by 5.00 cm as it is held between a 0.300 kg block on the left and a 0.600 kg block on the right, both resting on a horizontal surface. The spring exerts a force on each block, tending to push them apart. The blocks are simultaneously released from rest. Find the acceleration with which each block starts to move, given that the coefficient of kinetic friction between each block and the surface is the following values. Let the coordinate system be positive to the right and negative to the left.

The Attempt at a Solution

I don't understand why we could assume the spring forces apply on both blocks are equally the same?

 

[Delphi51]

For the part B, the spring with two 170N at both end should be equal to 340N at one end and the other end fixed.

This seems sensible, but it is not. Consider part (a) again. Gravity pulls down on the mass and spring with 86 N. But the spring does not accelerate according to F = ma. Something must be holding it up and cancelling out the 86 N force, because the acceleration is zero. The spring is attached to a door frame, and that door frame is holding it up with a force of 86 N upward.

The same holding force is acting in (b). One of the 340 N forces is just preventing the spring from accelerating away. Only the other 340 N counts in the F = kx formula.