Solving for Spring Stretch with Two Blocks of Mass m/2

[tiny-tim]

if you pull a spring on one side only, it will not stretch

it will simply move in that direction (and it will oscillate a little)

a spring will stretch only if you pull it on both sides

also, you have to pull it equally on both sides

(if you don't, it will move as well as stretch)

usually when we stretch a spring by pulling (or pushing) it from one side, we don't bother to mention the equal force on the other side … but that equal force is always there … usually a force that keeps the spring near the wall or ceiling, or a reaction force that stops the spring moving any further

does that help? ​

 

[thonwer]

Ohhh so, if the block pulls the spring of the ceiling it stretches x because mg produces it, but if it is mg/2 who produces it then it's half the length. In (i) the force is mg up and down, and in (ii) it's mg/2 left and right. So the answer is x/2 right? What I wasn't taking into account was that you need 2 forces to stretch a spring :)

 

[tiny-tim]

Ohhh so, if the block pulls the spring of the ceiling it stretches x because mg produces it, but if it is mg/2 who produces it then it's half the length. In (i) the force is mg up and down, and in (ii) it's mg/2 left and right. So the answer is x/2 right?

yes!

you got it!

What I wasn't taking into account was that you need 2 forces to stretch a spring :)

exactly! (and this is why it's so important to do a full analysis of the external forces on anything!)