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19 March, 23:03

The motor exerts a force of F = (20t2) N on the cable, where t is in seconds. Determine the speed of the 25-kg crate when t = 4 s. The coefficients of static and kinetic friction between the crate and the plane are ms = 0.3 and mk = 0.25, respectively.

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  1. 20 March, 01:59
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    Force F = 20 t² N so force is variable.

    friction on the crate = mgμ, μ is coefficient of kinetic friction, m is mass

    Net force

    = F - mgμ

    = 20 t² - mgμ = m dv / dt (Newton's 2 nd law)

    m dv = (20 t² - mgμ) dt

    Integrating on both sides,

    m v = 20 (t³ / 3) - mgμ t

    Putting the values,

    25 x v = 20 x 4³/3 - 25 x 9.8 x. 25 x 4

    25 v = 426.67 - 245

    25 v = 181.67

    v = 7.27

    v = 7.27 m / s
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