Energy and a spring

[NickStar]

Homework Statement:

In two cases two weights are tied using a string, and one of them is also tied to a spring(k=50N/m). Two weights are released when the spring is not compressed.
1) What is the maximum strain of the spring
2) What is the speed of the weight which is tied to the spring when the strain is 10cm

I need to solve this for two cases

I solved the first one using energy laws(but I couldn't solve this using Hooke's Law and I didn't understand why) if you could solve the first one using Hooke's Law, I would be really thankful)
And I have no clue how to solve the second one

Everything there is written in Hebrew

Relevant Equations:

K=1/2kx^2
deltaE=W

 

[Orodruin]

Why would you use Hooke’s law? Is the problem asking you explicitly to use Hooke’s law? Please also show your solution to 1 using energy laws.

 

[NickStar]

Why would you use Hooke’s law? Is the problem asking you explicitly to use Hooke’s law? Please also show your solution to 1 using energy laws.

No, it's not. But I just can't understand when do we have to use Hooke’s law and when energy equations. And the most important is the second part(with speed) (I can't even get something close to the right answer)

 

[Orodruin]

Generally, it is going to be easier to use conservation laws whenever you can get away with it.

Please type out your attempts (with your steps explained) instead of attaching rotated images of questionable quality. (See the homework guidelines)

 

[NickStar]

Generally, it is going to be easier to use conservation laws whenever you can get away with it.

Please type out your attempts (with your steps explained) instead of attaching rotated images of questionable quality. (See the homework guidelines)

I solved the first one so It doesn't really matter. But I really need to solve the second one(I have no clue how to do it) Here is my attempt:

 

[haruspex]

But I just can't understand when do we have to use Hooke’s law and when energy equations

Mostly, you want to use forces when the situation of interest is zero acceleration. That means forces are in balance.
When the situation is zero velocity, as here when the spring is under maximum strain, energy conservation is useful because you know the KE is zero.

Energy is also useful for the second part because you want to find a velocity, not an acceleration.

 

[Orodruin]

I solved the first one so It doesn't really matter.

This is not a constructive answer. In order to guide you to be able to solve the second, you need to show us how you have solved the first because (obviously) they are related to each other as they relate to the same system and the considerations necessary are very much alike. When we ask you to provide something, it is for your own benefit and for us to be able to help you better, please keep this in mind.