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While exploring a castle, Xena the Exterminator is spotted by a dragon who chases her down a hallway. Xena 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 3.10 m and a width of 1.20 m , and its weight is 730 N . You can ignore the friction at the hinges.

If Xena applies a force of 220 N at the edge of the door and perpendicular to it, how much time does it take her to close the door?

Respuesta :

Answer:

.65 s

Explanation:

Torque will create angular acceleration in the door .

Torque = force x perpendicular distance from the hinge

= 220 x 1.2 = 264 Nm

Moment of inertia of the door about hinge

I = 1 /3 x m l²

m is mass of the door and l is its width

=  [tex]\frac{730\times1.2\times1.2}{3\times9.8}[/tex]

= 35.755 kg m²

Angular acceleration α = Torque / moment of inertia

= [tex]\frac{264}{35.755}[/tex]

= 7.38 rad s²

Angle to be rotated θ = π/2

π/2 = .5 α t²

1.56 = .5 x 7.38 t²

t = 0.65 s

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