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Math Help - kinetic energy integral

  1. #1
    Junior Member winterwyrm's Avatar
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    kinetic energy integral

    A 2.1 kg block is initially at rest on a horizontal frictionless surface when a horizontal force in the positive direction of an x axis is applied to the block. The force is given by (x) = (4.2 - x2) N, where x is in meters and the initial position of the block is x = 0. (a) What is the kinetic energy of the block as it passes through x = 3.3 m? (b) What is the maximum kinetic energy of the block between x = 0 and x = 3.3 m?
    Thanks a ton.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    I'm assuming that the force you posted is (4.2 - x^2)\vec{i}


    (a) ... \Delta KE = W = \int_0^{3.3} (4.2 - x^2)\, dx

    (b) ...  \frac{dW}{dx} = \frac{d}{dx} \int_0^x (4.2 - t^2) \, dt

    once you find it, set \frac{dW}{dx} = 0 and determine the x-value that minimizes W.
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  3. #3
    Junior Member winterwyrm's Avatar
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    you must be a physics type, great job. But shouldn't it be the maximum W?
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  4. #4
    MHF Contributor
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    yea ... was thinking max-min and the min stuck in my head.
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