Kinematics-torque Question! As a younger sister many moons ago, you were being c
ID: 1391775 • Letter: K
Question
Kinematics-torque Question!
As a younger sister many moons ago, you were being chased by your older brother who was seeing red because you accidentally put a hole in his brand new soccer ball. You ran into the bathroom to escape his vengeance and tried to shut the door before he followed you in. The 2.50 m-tall, 1.10 m-wide door was initially open by 90 degree. The door weighed 625 N and at the time you could apply a 160 N force at the edge of the door and perpendicular to it throughout its motion. How much of a head start (in time) did you need in order to shut the door before your angry sibling came charging into the bathroom?Explanation / Answer
Mass of the door, M = W/g = 625/9.8 = 63.8 kg
Moment of inertia of the door about pivot, I = M*L^2/3
= 63.8*1.1^2/3
= 25.72 kg.m^2
let alfa is the angular accelartion.
now Apply, Torque, T = I*alfa
alfa = T/I
= 160*1.1*sin(90)/25.72
= 6.84 rad/s^2
let t is the time taken to shut the door.
Now use kinematic equation.
theta = 0.5*alfa*t^2
t = sqrt(2*theta/alfa)
= sqrt(2*(pi/2)/6.84)
= 0.68 s <<<<<<<<<<<<<--------------------Answer
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