A force F = (cx – 3.00x^2)i^ acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant.

Question

A force F = (cx – 3.00x^2)i^ acts on a virus as the virus moves along an x axis, with F measured in Newtons, x in meters, and c a constant. At x = 0, the virus’s kinetic energy is 20.0 J, while at x = 3.00 m, it is 11.0 J. Find c.

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Trúc Chi 4 years 2021-08-09T11:33:54+00:00 1 Answers 10 views 0

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  1. trucchi
    0
    2021-08-09T11:35:18+00:00
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    Answer:

    c = 4

    Explanation:

    From work-energy theorem KE = workdone.

    Given F = (cx – 3.00x²)i

    W = ∫Fdx = ∫(cx – 3.00x²)dx = cx²/2 –3.00x³/3 + A

    W = cx²/2 –x³ + A

    Where A is a constant

    At x = 0, KE = 20J

    So W = 20J at x = 0

    20 = c×0 – 0 +A

    A = 20

    So W = cx²/2 –x³ + 20

    Also when x = 3.00m, W = KE = 11J

    So

    11 = c×3²/2 – 3³ + 20

    11 = 4.5c – 7

    4.5c = 11 + 7

    4.5c = 18

    c = 18/4.5 = 4

    c = 4

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