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Newton's Cradle help please. Exam study

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Imagine a regular Newtons cradle (google it). The problem gives a the following information.
    All the spherical ball have the same mass. Ball 1, m_1 is initially raised at height H_i.

    A) Consider a stack consisting of just two balls. Let the speed of the first ball just before the collision be V_o. Solve V_f in terms of H. Solve for V_0 in terms of H.

    ANS : Using the conservation of energy equation I got H = 0.5V_f^2 / g.


    B) Just after the collision , the first ball bounces back at speed V_1, and the second ball moves forward at speed V_2. State the law of conservation of momentum for the general cases of masses m_1 and m_2 in terms of speed V_1 , V_2, and V_f ?

    not sure what this is asking. Is is just m_1*V_1 + m_2*V_2 = m_1*V_1f + m_1 * V_1f


    C) State the law of conservation of energy for elastic collision for the general case of masses m_1 and m_2 in terms of speed V_1, V_2, and V_f?

    Is it just 1/2(m_1*V_1 + m_2*V_2) = (m_1*V_1f + m_1 * V_1f) 1/2

    D) Solve for the speeds V_1 and V_2 for the special case that m = m, and m_2 = 2 M using the equations from part b and c above. Show that your solution satisfies the conservation of momentum and energy during the collision.
    NEED HELP ON THIS PART!!!

    E) To What height,H_1 will the first mass rebound after the elastic collision? To what maximum height, H_2, will the second mass rise before falling back.

    Intuitively , H_1 rebounds to height 0.
    And not sure about the next part.
     
  2. jcsd
  3. Mar 26, 2009 #2

    tiny-tim

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    Hi tnutty! :smile:

    That's correct … except shouldn't you have put one of them = 0? :wink:
    hmmm … what's in your brain may be correct, but what you've written is the same as for momentum :redface:
    Find either V1 or V2 from the first equation, and substitute that value into the second equation :smile:
     
  4. Mar 26, 2009 #3
    Part C is 1/mv^2 for each with initial and final.

    pard D) How do you find v_!1?

    And how would you find at what H_1, and H_2 the ball reaches, if the mass
    ratio of m1/m2 = 1/3, or 4/2 ?
     
  5. Mar 26, 2009 #4

    tiny-tim

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    Do you mean 1/2 mv2 ?
    As I said before: Find either V1 or V2 from the first equation, and substitute that value into the second equation :smile:
     
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