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Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,always

  1. May 15, 2009 #1
    1. The problem statement, all variables and given/known data
    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...
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 15, 2009 #2

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    What forces act on A? On B?
     
  4. May 15, 2009 #3
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    Only one force acts and that on B only.
     
  5. May 15, 2009 #4

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    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.
     
  6. May 15, 2009 #5
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    But, the forces on each keep varying??

    We can have the equations,
    4-kx=2aB
    kx=aA

    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...
     
  7. May 15, 2009 #6

    minger

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    If you are considering block B alone, why do you have twice the mass of B?
     
  8. May 15, 2009 #7

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

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

    OK. So then:
    aB = 2 -kx/2
    aA = kx

    Can you think of a value of kx that makes aA > aB ?
     
  9. May 15, 2009 #8
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    Ya, kx=1N???

    So, what does this imply???
     
  10. May 15, 2009 #9

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    No, that value makes aB = 3/2 & aA = 1. Choose another. (What value would make aB = 0?)
     
  11. May 15, 2009 #10
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    Earlier i accidentally took its opposite

    Taking,kx=4N,will make it..
     
  12. May 15, 2009 #11

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    OK. So what does that tell you?
     
  13. May 15, 2009 #12
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    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??
     
  14. May 15, 2009 #13

    Doc Al

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    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

    OK.
    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.
     
  15. May 15, 2009 #14
    Re: Newton's Laws-Is it necessary that 1 block has lesser acceleration than other,al

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