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28 August, 23:36

What is the mass of a brick that falls off a cliff and is moving at 20 m/s just before hitting the ground?

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  1. 29 August, 00:05
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    the mass of the brick is approximately m ≈ 173 gr

    Step-by-step explanation:

    If the brick if thrown from a cliff, is likely that it had reached its terminal velocity by the moment it is near the ground. Then by Newton's first law

    m*g - 1/2*ρ*C*v²*A = 0

    m = 1/2*ρ*C*v²*A/g

    where

    ρ = density of air. We assume a density of 1.225 kg/m³

    v = terminal velocity = 20 m/s

    C = drag coefficient = 0.82 for a brick shape

    g = gravity = 9.8 m/s²

    A = area perpendicular to the ground. We assume that it the smaller area, since is the more stable alignment. Then for a standard brick of 225 mm x 112.5 mm x 75 mm → A = 112.5 mm * 75 mm = 8.43*10⁻³ m²

    replacing values

    m = 1/2*ρ*C*v²*A/g = 1/2*1.225 kg/m³*0.82 * (20 m/s) ²*8.43*10⁻³ m²/9.8 m/s² = 0.1728 Kg ≈ 173 gr

    m ≈ 173 gr
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