Three packing crates of masses, M1 = 6 kg, M2 = 2 kg and M3 = 8 kg are connected by a light string of negligible mass that pas

Question

Three packing crates of masses, M1 = 6 kg, M2 = 2 kg
and M3 = 8 kg are connected by a light string of
negligible mass that passes over the pulley as shown.
Masses M1 and M3 lies on a 30o
incline plane which
slides down the plane. The coefficient of kinetic friction
on the incline plane is 0.28.
Determine the acceleration of the system.

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Eirian 5 years 2021-09-05T04:56:54+00:00 1 Answers 33 views 0

Answers ( )

  1. Nick
    0
    2021-09-05T04:58:23+00:00
    Reply

    Answer:

     a = 2.5 m / s²

    Explanation:

    This is an exercise of Newton’s second law, in this case we fix a coordinate system with the x axis parallel to the plane with positive direction

    Let’s write the second law for bodies in the inclined plane

        W₁ₓ + W₃ₓ – fr = (m₁ + m₃) a

        N₁ – W_{1y} + N₃- W_{3y} = 0

        N₁ + N₃ = W_{1y} + W_{3y}

    let’s use trigonometry to find the weight components

        sin 30 = Wₓ/ W

        Wₓ = W sin 30

        cos 30 = W_{y} / W

        W_{y} = W cos 30

    we substitute

        N₁+ N₃ = W₁ cos 30 + W₃ cos 30

        W₁ₓ + W₃ₓ – μ (m₁ + m₃) g cos30 = (m₁ + m₃) a

         a = (m₁g sin 30 + m₃g sin 30 – μ (m₁ + m₃) g cos 30) / (m₁ + m₃)

         a = g sin 30 – μ g cos30

    let’s calculate

         a = 9.8 sin 30 – 0.28 9.8 cos 30

         a = 4.9 – 2,376

         a = 2.5 m / s²

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