A 5 kg block is sliding on a horizontal surface while being pulled by a child using a rope attached to the center of the block. The rope exe

Question

A 5 kg block is sliding on a horizontal surface while being pulled by a child using a rope attached to the center of the block. The rope exerts a constant force of 28.2 N at an angle of \theta=θ = 30 degrees above the horizontal on the block. Friction exists between the block and supporting surface (with \mu_s=\:μ s = 0.25 and \mu_k=\:μ k = 0.12 ). What is the horizontal acceleration of the block?

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Nguyệt Ánh 4 years 2021-08-13T04:14:55+00:00 1 Answers 6 views 0

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    2021-08-13T04:16:18+00:00

    Answer:

    The horizontal acceleration of the block is 4.05 m/s².

    Explanation:

    The horizontal acceleration can be found as follows:

     F = m \cdot a

     Fcos(\theta) - \mu_{k}N = m\cdot a

     Fcos(\theta) - \mu_{k}[mg - Fsen(\theta)] = m\cdot a  

     a = \frac{Fcos(\theta) - \mu_{k}[mg - Fsen(\theta)]}{m}

    Where:

    a: is the acceleration

    F: is the force exerted by the rope = 28.2 N

    θ: is the angle = 30°

    \mu_{k}: is the kinetic coefficient = 0.12

    m: is the mass = 5 kg

    g: is the gravity = 9.81 m/s²

     a = \frac{28.2 N*cos(30) - 0.12[5 kg*9.81 m/s^{2} - 28.2 N*sen(30)]}{5 kg} = 4.05 m/s^{2}

    Therefore, the horizontal acceleration of the block is 4.05 m/s².

    I hope it helps you!

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