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9 May, 15:23

A block with mass m1 = 9.4 kg is on an incline with an angle θ = 25° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.22 and μs = 0.242. 1) When there is no friction, what is the magnitude of the acceleration of the block?

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  1. 9 May, 15:30
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    a = 4.14 m/s²

    Explanation:

    We calculate the weight component parallel to the displacement of the block:

    We define the x-axis in the direction of the inclined plane, 25° to the horizontal.

    W = m*g : Total block weight

    Wx = W*sen25° = m*g * sen25°

    We apply Newton's second law:

    ∑F = m*a (Formula 1)

    ∑F : algebraic sum of the forces in Newton (N)

    m : mass in kilograms (kg)

    a : acceleration in meters over second square (m/s²)

    Problem development

    We apply the formula (1) to calculate the acceleration of the block:

    ∑Fx = m*a

    Wx = m*a

    m*g * sen25° = m*a : We divide by m on both sides of the equation

    g * sen25° = a

    a = g * sen25° = 9.8 * sen25° = 4.14 m/s²
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