# Measure of spring in system with roller

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1. Jun 11, 2017

### Aireve

1. The problem statement, all variables and given/known data
m1= 0,05 kg, m2= 0,03 kg, mass of spring is omitted. We look at movement after spring stopped vibrate. How long does the spring measure during the movement if not stretched spring measure 0,1 meter and if we use force 0,1N elongation measures 0,02 meter.
(sorry, English isn't my main language, I've never learn scientific words so I'm not quite sure if my translation is right)

I know the answer is 0,174 meter.
2. Relevant equations

3. The attempt at a solution
m1*a = m1*g - Ft (Ft is thread tension)
m2*a = Ft + Fs - m2*g

0,1 = k*0,02
k=5

Don't know what next and if it's even right.

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2. Jun 11, 2017

### Jamison Lahman

3. Jun 11, 2017

### Aireve

Hym, I can solve problems when there is no spring. That spring is real problem since I don't know how to mark forces at that device. Is Fs=Fg? My friend tried to solve that without Fs but I'm not sure...

4. Jun 11, 2017

### Jamison Lahman

Why would Fs be Fg?
Is the spring applying force in either direction? what does Newton's third law tell us?

Last edited: Jun 11, 2017
5. Jun 11, 2017

### Aireve

I'm not sure but aren't second mass applying force? Can't Fg be force of action and Fs force of reaction?

6. Jun 11, 2017

### Jamison Lahman

Is there any effect from mass 1?

7. Jun 11, 2017

### Aireve

Well, because of mass 1 that system is moving to the left.

8. Jun 11, 2017

### Jamison Lahman

I think you have the right idea. Translation may be a little off. Because of mass 1, the force on mass 2 does not equal the the force of gravity on mass 2.
With that being said, because the spring is without mass it does not contribute to the acceleration of mass 1. The tension in the string, Ft , is therefore also the same force acting on the spring, Fs .

9. Jun 11, 2017

### Aireve

So...
0,1 = k*0,02
k=5

m1*a = m1*g - Ft
m2*a = Ft - m2*g

a(m1 + m2) = g(m1 - m2)
a = 0,2/0,08 = 2,5 m/s^2

Ft = m2(a + g) = 0,03*12,5 = 0,375 = Fs

0,375 = 5*x
x = 0,075 m

x+0,1 = 0,175 m = 17,5 cm

Is it correct?

10. Jun 11, 2017

### Jamison Lahman

Looks like it

11. Jun 11, 2017

### Aireve

Ok, thank you!
But can I have one more question? How should I draw those forces at that picture? Should I draw Fs and Ft or only one of them? They should "touch" mass 2 or spring?

12. Jun 11, 2017

### Jamison Lahman

You could explicitly show all of the forces (so that the spring looks like the green to the side):

But I think that would be messy and overly complicated. I personally would only draw forces on objects with mass.

13. Jun 11, 2017

### Aireve

Right, I don't think I have to do that much.
To be 100% sure, it's ok?

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14. Jun 11, 2017

### Jamison Lahman

Looks fine to me

15. Jun 11, 2017

### Aireve

Ok, thank you. :)