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27 April, 22:42

A box of books weighing 305 N is shoved

across the floor by a force of 516 N exerted

downward at an angle of 32° below the hori-

zontal.

The acceleration of gravity is 9.81 m/s.

If her between the box and the floor is 0.59,

how long does it take to move the box 5.82 m,

starting from rest?

+2
Answers (1)
  1. 28 April, 00:22
    0
    3.1 s

    Explanation:

    from the question we are given the the following:

    Weight of books (Fb) = 305 N

    Push force (Fp) = 516 N

    distance (s) = 5.82 m

    Angle of force exerted = 32 degrees

    acceleration due to gravity (g) = 9.81 m/s^{2}

    coefficient of friction Uk = 0.59

    time (t) = ?

    mass of the book (m) = weight / (g) = 305 / 9.8 = 31 kg

    lets first get the net force from the summation of vertical forces

    Fnet = Fpush + Fgravity

    F net = 516 + 305sin32

    F net = 677.6 N

    now lets get the acceleration from the summation of the horizontal forces

    Fpcos32 - friction force = m x a

    Fpcos32 - (Uk x F net) = m x a

    516cos32 - (0.59 x 677.6) = 31 x a

    37.8 = 31a

    a = 1.22m/s^{2}

    now that we have our acceleration we can get the time from the equation of motion

    s = ut + o. 5at^{2}

    u (initial velocity) = 0 because the box was initially at rest

    5.82 = (0 x t) + (0.5 x 1.22 x t^{2})

    5.82 = 0.61t^{2}

    t = 3.1 s
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