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27 May, 15:49

While exploring a castle, Exena the Exterminator is spotted by a dragon who chases her down a hallway. Exena runs into a room and attempts to swing the heavy door shut before the dragon gets her. The door is initially perpendicular to the wall, so it must be turned through 90∘ to close. The door has a height of 3.00 m and a width of 1.40 m, and its weight is 790 N. You can ignore the friction at the hinges. If Exena applies a force of220 N at the edge of the door and perpendicular to it, how muchtime does it take her to close the door?

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  1. 27 May, 16:19
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    the time needed for her to close the door is 1.36 s.

    Explanation:

    given information:

    Force, F = 220 N

    width, r = 1.40 m

    weight, W = 790 N

    height, h = 3.00 m

    angle, θ = 90° = π/2

    to find the times needed to close the door we can use the following equation

    θ = ω₀t + 1/2 αt²

    where

    θ = angle

    ω = angular velocity

    α = angular acceleration

    t = time

    in this case, the angular velocity is zero. thus,

    θ = 1/2 αt²

    now, we can find the angular speed by using the torque formula

    τ = I α

    where

    τ = torque

    I = Inertia

    we know that

    τ = F r

    and

    I = 1/3 mr²

    so,

    τ = I α

    F r = 1/3 mr² α

    α = 3 F/mr

    = 3 F / (w/g) r

    = 3 (220) / (790/9.8) 1.4

    = 5.85 rad/s²

    θ = 1/2 αt²

    π/2 = 1/2 5.85 t²

    t = 1.36 s
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