While exploring a castle, Exena the Exterminator is spotted by a dragon who chas

Question

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 1.20 m , and its weight is 730 N . You can ignore the friction at the hinges.

A) If Exena applies a force of 250 N at the edge of the door and perpendicular to it, how much time does it take her to close the door?

Use 9.80 m/s2 for the acceleration due to gravity.

Explanation / Answer

let,

width ofnte door l=1.2 m

height of the door h=3 m

weight of the ddor W=730 N

force applied F=250 N

angular dispalcement, theta=90 degrees=pi/2 rad

use,

Torque=r*F

I*alpa=l*F

1/3*(m*l^2)*alpa=l*F

1/3*(w/g)*l)*alpa=*F

===> alpa=3*F*g/(W*l)

alpa=3*250*9.8/(730*1.2)

angular acceleration alpa=8.39 rad/sec^2

and

theta=wo*t+1/2*alpa*t^2

pi/2=0+1/2*8.39*t^2

===> t=0.612 sec

time taken to close the door ( or rotate 90 degrees) is t=0.612 sec

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