physics

A box of books weighing 314 N is shoved across the floor by a force of 475 N exerted downward at an angle of 35° below the horizontal.
(a) If μk between the box and the floor is 0.53, how long does it take to move the box 5.00 m starting from rest?
What is the maximum coefficient of kinetic friction between the box and the floor that allows the box to move from this applied force.

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  1. Wb = 314 N.
    m*g = 314
    m = 314/g = 314/9.8=32 kg.=mass of box.

    Fb = 314N[0o].
    Fp = 314*sin(0) = 0 = Force parallel to floor.
    Fv = 314*cos(0)+475*sin35 = 586 N. =
    Force perpendicular to floor.

    Fk = u*Fv = 0.53 * 586 = 310.6 N. = Force of kinetic friction.

    a. Fap*cos35-Fp-Fk = m*a
    475*cos35-0-310.6 = 32*a
    389-310.6 = 32a
    78.4 = 32a
    a = 2.45m/s^2.

    d = 0.5a*t^2 = 5 m.
    0.5*2.45t^2 = 5
    1.225t^2 = 5
    t^2 = 4.082
    t = 2.02 s.

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