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19 December, 15:01

A bin is given a push across a horizontal surface. The bin has a mass m, the push gives it an initial speed of 1.60 m/s, and the coefficient of kinetic friction between the bin and the surface is 0.150. (a) Use energy considerations to find the distance (in m) the bin moves before it stops. m (b) What If

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  1. 19 December, 15:30
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    The bin moves 0.87 m before it stops.

    Explanation:

    If we analyze the situation and apply the law of conservation of energy to this case, we get:

    Energy Dissipated through Friction = Change in Kinetic Energy of Bin (Loss)

    F d = (0.5) (m) (Vi² - Vf²)

    where,

    F = Frictional Force = μR

    but, R = Normal Reaction = Weight of Bin = mg

    Therefore, F = μmg

    Hence, the equation becomes:

    μmg d = (0.5) (m) (Vi² - Vf²)

    μg d = (0.5) (Vi² - Vf²)

    d = (0.5) (Vi² - Vf²) / μg

    where,

    Vf = Final Velocity = 0 m/s (Since, bin finally stops)

    Vi = Initial Velocity = 1.6 m/s

    μ = coefficient of kinetic friction = 0.15

    g = 9.8 m/s²

    d = distance moved by bin before coming to stop = ?

    Therefore,

    d = (0.5) [ (1.6 m/s) ² - (0 m/s) ²] / (0.15) (9.8 m/s²)

    d = 0.87 m
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