Two objects attached with a spring

[giokrutoi]

Homework Statement

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

Homework Equations

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?

 

[BvU]

Homework Statement

on frictionless surface there are two objects $m_1 = 0.9$ kg, $m_2 =1.6$ kg

at first these two are held by a person and the spring is shrinked over a distance $L = 10$ cm.

After that, the first object is released and when this object is in its equilibrium position the other object is released .

Find the maximum acceleration that can be reached by the second object.

Homework Equations

There is nothing here ?​

The Attempt at a Solution

$mv^2/2= kx^2/2 \qquad$ In general, or at some specific point ?
$m_1v_1/m_+m_ = v_2$ $v_2$ is the velocity of the center of mass Can't be: dimensions do not match

$(m_1+m_2)a=kx_1$ k1 is found by conservation of energy Don't know. What is a ?

$mv_1^2 = (m_1+m_2)v_2^2/2 + kx_1^2/2$ How do you derive that ?

are my conclusion right ?

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

 

[giokrutoi]

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

relative equations: Kx₁²/2=m₁v₁²/2

 

[giokrutoi]

oh I forgot k is also given

 

[giokrutoi]

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

 

[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 ?

 

[giokrutoi]

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 ?

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

 

[BvU]

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

 

[giokrutoi]

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

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

 

[giokrutoi]

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

 

[haruspex]

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

What external forces are there on the system?

 

[haruspex]

relative equations: Kx₁²/2=m₁v₁²/2

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.)

 

[giokrutoi]

What external forces are there on the system?

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

 

[giokrutoi]

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.)

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

 

[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

 

[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 !

 

[haruspex]

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

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?

 

[giokrutoi]

i don't understand what forces are from outside

 

[haruspex]

i don't understand what forces are from outside

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

 

[giokrutoi]

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

 

[giokrutoi]

maybe m1a1=m2a2

 

[giokrutoi]

so center has no acceleration

 

[haruspex]

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

If you find the velocity of the common mass centre then you can consider the motions of the masses relative to that. When m2 is at its maximum acceleration, what can you say about the acceleration of m1 and the relative velocities of the masses?

 

[giokrutoi]

maybe relative velocity of m1 due Tue center of mass is v-vcenter and we can calculate v2 which is velocity of m2 from cocervation of energy

 

[haruspex]

maybe relative velocity of m1 due Tue center of mass is v-vcenter

Sorry, but I have no idea what you mean. Maybe it will make sense if you post some equations.

 

[giokrutoi]

what about this

 

[BvU]

Are we going full circle ?
$mv^2/2= kx^2/2 \qquad$ was in post 1 as well. My question was "In general, or at some specific point ?"

Now you post (I deduce) $$m_1 v_1^2/2 = (m_1+m_2) v_{\rm\, c.o.m.}^2 /2 + m_2 v_2^2/2 $$
What relevant equation can possibly lead to this ? Any idea yourself what you mean with these variables ? Or at what time ?

Why don't you start over and present a complete problem statement with a complete list of symbols/variables/given/known data (plus explanation what they mean) and the relevant equations (not that many anyway). Very helpful and instructive. Just coming up with ever more new "what about this" isn't going to solve this exercise for you !

 

[giokrutoi]

Are we going full circle ?
$mv^2/2= kx^2/2 \qquad$ was in post 1 as well. My question was "In general, or at some specific point ?"

Now you post (I deduce) $$m_1 v_1^2/2 = (m_1+m_2) v_{\rm\, c.o.m.}^2 /2 + m_2 v_2^2/2 $$
What relevant equation can possibly lead to this ? Any idea yourself what you mean with these variables ? Or at what time ?

Why don't you start over and present a complete problem statement with a complete list of symbols/variables/given/known data (plus explanation what they mean) and the relevant equations (not that many anyway). Very helpful and instructive. Just coming up with ever more new "what about this" isn't going to solve this exercise for you ![/ to you QUOTE]
i have question to you
do you know Russian

 

[giokrutoi]

do you know Russian

 

[giokrutoi]

?

 

[giokrutoi]

hey I guess I found solution I realized that I had to choose reference frame on center of mass
are my conclusion write

 

[haruspex]

hey I guess I found solution I realized that I had to choose reference frame on center of mass
are my conclusion write

Those images are simply unreadable. Please make the effort to type your equations in. Use parentheses, superscript (X²) and subscript (X₂) as appropriate.
Diagrams would be good, but draw them in black and try to get the lighting even on the page.

 

[giokrutoi]

I rewrote it
is it readable?

 

[haruspex]

I rewrote it
is it readable?

Yes, this readable.
Check the signs in the first equation on the right hand page.
Some places you write "due to centre of mass" where I think you mean "relative to centre of mass".
Other than that, you seem to be on the right track now.

 

[giokrutoi]

I think all signs are write
in relation to center of mass I think i have to subtract velocity of center of mass

 

[haruspex]

I think all signs are write
in relation to center of mass I think i have to subtract velocity of center of mass

Actually, it's not a sign issue, but something is wrong.
You defined v₁ as the velocity of the mass centre after releasing m₂, and v as the velocity of m₁ at the moment of release. Thus you should have m₁v=(m₁+m₂)v₁.
v and v₁ are fixed, but v₂ varies, so the equation cannot be right. Do you use that equation?

 

[ehild]

do you know Russian

I understand Russian. Show the original problem, please.

 

[giokrutoi]

if both v and v1 is fixed v2 should also be fixed but it varies so it's magnitude derived from formula of conversation of momentum it may be maximal

 

[giokrutoi]

here is Russian version

 

[haruspex]

if both v and v1 is fixed v2 should also be fixed but it varies so it's magnitude derived from formula of conversation of momentum it may be maximal

Wrong conclusion. Since v₂ varies the equation is wrong. If you want to change the equation by replacing the reference to v₂ to a reference to v_{2, max} then that could be OK, but you should show some justification. At the moment I cannot see where the equation comes from.

 

[giokrutoi]

as the initial momentum is zero it may stay constant so m1(V-v1)-m2v2=0 v2 is vmax and minus in formula is because they are moving in opposite way from each other

 

[giokrutoi]

are my conclusion write

 

[ehild]

here is Russian version

Thank you.

Two blocks connected by a spring are placed on a horizontal table. m1= 0.9 kg, m2= 1.6 kg, the spring constant is k=20 N/m.
Initially the spring is held compressed by 10 cm. Then the first block is released and when the spring gets relaxed, the second one is also released. What is the maximum magnitude of acceleration of the second block during the further motion of the system?

 

[giokrutoi]

I have stated that before
what can you say about solution

 

[ehild]

maybe m1a1=m2a2

That is right, for the magnitude of accelerations. And ma=F. What is the force acting on the blocks?

 

[giokrutoi]

kx

 

[giokrutoi]

That is right, for the magnitude of accelerations. And ma=F. What is the force acting on the blocks?

aren't solutions by momentum and center of mass write?

 

[ehild]

Do you mean "right" when you write "write"?
I can not follow your argument. The momentum of the whole system is constant after both blocks has been released, but it is zero in the center of mass frame of reference only. The spring force and the accelerations are the same in all inertial frames of reference. You have to give the maximum acceleration of block 2.
The center of mass moves with constant velocity and the blocks perform simple harmonic motion with respect to the center. During that motion, the spring gets compressed, gets relaxed and gets stretched. What is the maximum compression, and what is the spring force then? What are the accelerations of the blocks?

 

[giokrutoi]

maximal compression may be 10 centimeters and if that's true force should be 10 centimeter multiplied by k and acceleration of second mass should be this magnitude divided by m2
and yes I mean right when I write write

 

[ehild]

maximal compression may be 10 centimeters and if that's true force should be 10 centimeter multiplied by k and acceleration of second mass should be this magnitude divided by m2

Yes, but you need to calculate the compression in meters, and that should be multiplied by k=20 N/m.