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 1.40 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?

Answer 1

the time needed for her to close the door is 1.36 s.

Step-by-step 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