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Math Help - Forces Question

  1. #1
    Member looi76's Avatar
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    Forces Question

    Question:
    A steel ball of mass 73g is held above a horizontal steel plate, as illustrated in the figure below.



    The ball is dropped from rest and it bounces on the plate, reaching a height h.

    (a) Calculate the speed of ball as it reaches the plate.

    (b) As the ball loses contact with the plate after bouncing, the kinetic energy of the ball is 90\% of that just before bouncing. Calculate
    (i) the height h to which the ball bounces.
    (ii) the speed of the ball as it leaves the plate after bouncing.

    (c) Using your answers to (a) and (b), determine the change in momentum of the ball during the bounce.

    Attempt:
    (a) h = 1.6m \ , \ g = 9.81 ms^{-2}

    \frac{1}{2}\not{m}v^2 = \not{m}gh

    v = \sqrt{2gh}
    v = \sqrt{2 \times 9.81 \times 1.6}
    v = 5.6 ms^{-1}

    (b)(i) Don't know how to solve this this question... need help!
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  2. #2
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    Quote Originally Posted by looi76 View Post
    (b)(i) Don't know how to solve this this question... need help!
    Since when the ball just loses contact it has 90% of the kinetic energy, the ball will go up until all of this kinetic energy is converted to potential energy.

    So

    0.9 \left(\frac12 mv^2 \right) = mgh

    h = \frac{0.9v^2}{2g}

    Here v is the velocity when the ball just loses contact with the plank
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  3. #3
    Member looi76's Avatar
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    Thnx Isomorphism,

    (b)(i) 1.4m
    (ii) 5.3ms^{-1}

    Part C

    Change \ in \ Momentum = Final Momentum - Initial Momentum
    Change \ in \ Momentum = mv - mu
    Change \ in \ Momentum = (73 \times 10^{-3} \times 5.3) - (73 \times 10^{-3} \times 5.6)
    Change \ in \ Momentum = -2.19 \times 10^{-3}Ns

    Where did I go wrong?
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  4. #4
    Lord of certain Rings
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    Quote Originally Posted by looi76 View Post
    Thnx Isomorphism,

    (b)(i) 1.4m
    (ii) 5.3ms^{-1}





    Quote Originally Posted by looi76 View Post
    Part C

    Change \ in \ Momentum = Final Momentum - Initial Momentum
    Change \ in \ Momentum = mv - mu
    Change \ in \ Momentum = (73 \times 10^{-3} \times 5.3) - (73 \times 10^{-3} \times 5.6)
    Change \ in \ Momentum = -2.19 \times 10^{-3}Ns

    Where did I go wrong?
    I think its right.Why do you think its wrong?
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  5. #5
    Member looi76's Avatar
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    I think its right.Why do you think its wrong?
    The answer in the book is 0.80Ns
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  6. #6
    Member looi76's Avatar
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    Here is the answer, I scanned it:



    Can you help me now?
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  7. #7
    Lord of certain Rings
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    Quote Originally Posted by looi76 View Post
    Thnx Isomorphism,

    (b)(i) 1.4m
    (ii) 5.3ms^{-1}

    Part C

    Change \ in \ Momentum = Final Momentum - Initial Momentum
    Change \ in \ Momentum = mv - mu
    Change \ in \ Momentum = (73 \times 10^{-3} \times 5.3) - (73 \times 10^{-3} \times 5.6)
    Change \ in \ Momentum = -2.19 \times 10^{-3}Ns

    Where did I go wrong?
    Oh yes , silly me...

    The velocity of the ball is directed towards the plank. While it leaves the plank, it is directed away. So if you assume one is positive, the other is negative...

    Now this means
    Change \ in \ Momentum = mv - mu
    Change \ in \ Momentum = (73 \times 10^{-3} \times 5.3) - (73 \times 10^{-3} \times (-5.6))
    (That is because v = 5.3 and u = -5.6.)
    Change \ in \ Momentum = (73 \times 10^{-3} \times 5.3) + (73 \times 10^{-3} \times (5.6))
    Change \ in \ Momentum = 0.8 Ns
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