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Homework Help: Picture of sinusoidal curve with 5 points

  1. Feb 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Sorry I can't provide a visual for this problem, but I'll try my best to explain it
    Given: picture of sinusoidal curve with 5 points from left to right, H C D B A
    H is on downward slope
    C is a min
    D is a max
    B is on upward slope
    A is on upward slope to the right of B

    The bead slides starting from rest at position H on the frictionless wire. The direction of the gravitational field is in the -y direction (toward the bottom of the page).
    (Select T-True, F-False, G-Greater than, L-Less than, E-Equal to. If the first is T, the second G, and the rest F, enter

    A) The acceleration in the y-direction at C is ... zero.
    B) The acceleration at D is zero.
    C) The velocity at B equals the velocity at D.
    D) The speed at D is ... the speed at B.
    E) The acceleration in the x-direction at C is ... zero.
    F) The speed at C is ... the speed at D.

    3. The attempt at a solution

    A) Greater than -- down direction is positive and acceleration is gravity
    B) True -- velocity is slope=0, therefore acceleration=0
    C) False -- not sure,
    D) Less than -- but not sure, speed is magnitude of velocity components, and there is no vertical component of velocity at D, so it should be less than the speed at B
    E) Equal to -- no acceleration in x-direction, unless there's not constant speed..
    F) Equal to -- not sure, there is no vertical component of velocity here
  2. jcsd
  3. Feb 17, 2008 #2
    Your answer is correct, but not your reasoning. The up direction is positive, and
    gravity is not the only source of acceleration.

    If the velocity in the y direction is 0, it doesn't follow that the acceleration in the y direction is 0.

    There is however the problem that the bead never arrives at D. The bead starts out with 0 velocity in a position lower than D. So it has to gain potential energy to get to D, but it starts out with no kinetic energy, so there's no way it can gain this potential energy.
    This means I can't answer B, C, D and F

    E is correct
  4. Feb 17, 2008 #3
    it's actually not a perfect sinusoidal curve; D is a relative max I should have said -- H is above it
  5. Feb 18, 2008 #4
    In that case B is False. The acceleration has 2 components, one along the wire and one perpendicular. The perpendicular component is only 0 for a straight piece of wire.

    For C both the magnitude and direction of the velocity must be the same. the direction of the bead is in the direction of the wire

    D and F: use conservation of energy. If the bead is lower it has less potential energy ...
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