# Two objects attached with a spring

1. Feb 22, 2016

### giokrutoi

1. The problem statement, all variables and given/known data
on frictionless surface there are two objects m1 = 0.9 kg m2 =1.6 kg
at first these two are held by person an spring is shrined L = 10 cm . After that first objet is released and when this object is in it's equilibrium moment another object is released . Find maximal acceleration that can be reached by second objet
2. Relevant equations

3. The attempt at a solution
mv2/2= kx2/2 m1v1/m1+m2 = v2 v2 is the velocity of the center of mass (m1+m2)a=kx1 k1 is found by conservation of energy mv12 = (m1+m2)v22/2 + kx12/2 are my conclusion write?

2. Feb 22, 2016

### BvU

I don't think so. Perhaps you want to work more systematically:
• name all variables and make clear how you derive the unknowns from the knowns
• check dimensions for every equation
• clearly list all the relevant equations

Last edited: Feb 22, 2016
3. Feb 22, 2016

### giokrutoi

relative equations: Kx12/2=m1v12/2

4. Feb 22, 2016

### giokrutoi

oh I forgot k is also given

5. Feb 23, 2016

### giokrutoi

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6. Feb 23, 2016

### BvU

I decipher
• now $(m_1+m_2)a = kx_1\quad(2)$
What is $x_1$ and what is $a$ ?

Then: "I guess..."
No need to guess: you already calculated the velocity of the center of mass.
But it seems to me you are still in the dark about where you are going and how you want to go there ?

7. Feb 23, 2016

### giokrutoi

a is acceleration of center of mass and I think that initial energy - energy of the center of mass should be potential energy of spring which has it's new x1

8. Feb 23, 2016

### BvU

And how would the center of mass be able to undergo acceleration ?

9. Feb 23, 2016

### giokrutoi

it should be because net force on system isn't zero

10. Feb 23, 2016

### giokrutoi

it's motion should be linear but It can also gain acceleration

11. Feb 23, 2016

### haruspex

What external forces are there on the system?

12. Feb 23, 2016

### haruspex

What, exactly, do x1 and v1 represent there? (There is no value in being able to quote equations if you cannot say what the terms in it represent.)

13. Feb 23, 2016

### giokrutoi

ok guess that only external force is kx which cause objects to move with acceleration
but it can also be that I don't understand their motion too well

14. Feb 23, 2016

### giokrutoi

this formula meant to be in general but in this cases all variables are given

15. Feb 23, 2016

### giokrutoi

I can't figure out how do they move and I don't have to find system acceleration but maximal of the second objet

16. Feb 23, 2016

### BvU

Can you see that $kx$ is NOT an external force ? According to Isaac the force one exercises on the other is opposite and equal to the force the other exercises in the one. So for the motion of the center of mass this has no significance !

17. Feb 23, 2016

### haruspex

You have not understood what I asked. Even though you have not stated it, I'm happy to guess that x1 is a spring compression (or extension) and that v1 is a velocity. But what compression and what velocity? Hint: it does not give you the velocity of an attached mass when the extension is x1.
As BvU notes, in the system consisting of the two masses and the spring, forces between those entities are internal to that system. What forces act on that system from outside it?

18. Feb 23, 2016

### giokrutoi

i don't understand what forces are from outside

19. Feb 23, 2016

### haruspex

Exactly, there aren't any. So would the common mass centre accelerate?

20. Feb 24, 2016

### giokrutoi

you're write I understand what you're saying but. How can I calculate m2 acceleration

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