Proving Acceleration of A ≤ Acceleration of B

[rohitarura]

Homework Statement

Question :
two masses MA = 1 kg and MB = 2 kg are connected by a massless spring as shown in figure. A force of 4 N acts on the 2 kg mass.
http://www.vidyamandir.com//displayImageServlet?appletImgId=8a7b221f1fcc7894011ff9cccfe412f0 [Broken]


Is it necessary that the acceleration of A always be less or equal to the acceleration of B?
If yes,then prove it...If no then also prove it,please.



2. The attempt at a solution
I thought this way..Working in centre of mass's frame,both blocks seem to oscillate about it.So,at some instant both will have same accelerations w.r.t. Centre of mass then, using pseudo force concept the net acc. of the block be will get greater than that of block A..
Correct me if i am wrong...

 

[Doc Al]

What forces act on A? On B?

 

[rohitarura]

Only one force acts and that on B only.

 

[Doc Al]

Only one force acts and that on B only.

There's only one external force acting on the two-block system, but to find the acceleration of each block consider each block separately.

What forces act on each? Compare the expressions for the net force on each, then see if you can draw any conclusions.

 

[rohitarura]

But, the forces on each keep varying??

We can have the equations,
4-kx=2a_B
kx=a_A

k being the unknown spring constant,and x is extension in it..

If we can prove,
a(B)-a(A)=2-kx/3 can be negative then its done...

 

[minger]

If you are considering block B alone, why do you have twice the mass of B?

 

[Doc Al]

But, the forces on each keep varying??

Right, the spring force can be almost anything. That's the key.

We can have the equations,
4-kx=2a_B
kx=a_A

OK. So then:
a_B = 2 -kx/2
a_A = kx

Can you think of a value of kx that makes a_A > a_B ?

 

[rohitarura]

Ya, kx=1N?

So, what does this imply?

 

[Doc Al]

Ya, kx=1N?

No, that value makes a_B = 3/2 & a_A = 1. Choose another. (What value would make a_B = 0?)

 

[rohitarura]

Earlier i accidentally took its opposite

Taking,kx=4N,will make it..

 

[Doc Al]

Taking,kx=4N,will make it..

OK. So what does that tell you?

 

[rohitarura]

It tells that it is not necessary that the acceleration of A always be less or equal to the acceleration of B...But my fellows says the opposite?He says if 1 force is pulling such a system then acc. of the block A can't be greater than that of the block on which the force is applied i.e.,block B??

 

[Doc Al]

It tells that it is not necessary that the acceleration of A always be less or equal to the acceleration of B...

OK.

But my fellows says the opposite?He says if 1 force is pulling such a system then acc. of the block A can't be greater than that of the block on which the force is applied i.e.,block B??

Ask him why he thinks that.

No information is given about how much the spring is stretched, so nothing stops us from imagining a situation where the stretch is as much as we like.

 

[rohitarura]

Thank you very very much Sir.I'm very satisfied with your valuable views...Thanks