If the motor exerts a constant force of 300 N on the cable, determine the speed of the 26-kg crate when it travels s = 10 m up the plane, st

Question

If the motor exerts a constant force of 300 N on the cable, determine the speed of the 26-kg crate when it travels s = 10 m up the plane, starting from rest. The coefficient of kinetic friction between the crate and the plane is μk = 0.3.

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Thanh Thu 5 months 2021-08-05T01:03:04+00:00 1 Answers 98 views 0

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    2021-08-05T01:04:27+00:00

    Answer:

    10.32m/s

    Explanation:

    F = ma

    T -mg sinθ-f =ma

    We can conclude that T = 300 newtons by taking a freebody of the cable. So we need to determine only the frictional force.

    f(n) = 0

    mgcosθ = N = 0

    N = mgcosθ

    T – mg sinθ – u mgcosθ = ma

    a = T – mg (sinθ + u cosθ) / m

    a = \frac{300 - 26(9.8)(\sin 30^0 + 0.3 \cos 30^0)}{20}

    a = 5.32m/s^2

    Use constant acceleration kinematics:

    v_f^2=V_i^2+2ad\\V_f^2 = \sqrt{2ad}

    = = \sqrt{2\times 5.32\times10} \\\\=10.32m/s

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