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Energy conservation of ice problem

  1. Apr 1, 2017 #1
    1. The problem statement, all variables and given/known data
    A block of ice (that we shall treat as a particle) slides with negligible friction or air resistance on the curved tpath sketched (black line). The mass of the block is m = 44 kg. Its initial speed is v0 = 1.3 m.s–1. The height h= 4.1 m. At the bottom, the path has a radius of curvature (fine circle) R = 3.4 m. At the bottom of the path, what is the force exerted on the ice by the path?

    2. Relevant equations
    K + V = constant

    3. The attempt at a solution
    Energy before it slides = after it slides:
    mgh + 1/2 * m*v0^2 = 1/2 * m*v_final^2 (at the bottom h = 0 -> mgh=0)
    44*9.8*4.1 + 1/2*44*1.3^2 = 1/2*44*v_final^2 -> v_final=9.06m/s

    Circular motion:
    Fc=ma=m*v_f^2/R=44*9.06^2/3.4=1062N upwards
    W=mg=44*9.8=431.2N downwards
    F_path=1062-431.2=630.8N upwards

    Could someone suggest where I did wrong?
  2. jcsd
  3. Apr 1, 2017 #2
    The pic is here Snip20170401_5.png
  4. Apr 1, 2017 #3


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    If W and F_path are in opposite directions, the magnitude of the net force is 680.8 N - 431.2 N, no?
  5. Apr 1, 2017 #4


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    This is a very common error.
    Centripetal force is not an applied force. It is that component of the resultant which is perpendicular to the velocity.
    So in ΣF=ma, the centripetal force is the ma on the right, and the perpendicular component of each applied force appears in the sum on the left.
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