To practice Problem-Solving Strategy 10.1 Rotationa Dynamics for Rigid Bodies. W

Question

To practice Problem-Solving Strategy 10.1 Rotationa Dynamics for Rigid Bodies. 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 to her (Figure The door is initially perpendicular to the wall, so it must be turned through 90 to close it. The door is 3.00 m tall and 1.25 m wide, and it weighs 750 N You can ignore the friction at the hinges. If Exena 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? Figure 1 of 1

Explanation / Answer

Moment of inertia of rectangular plate about its side of length l and width w and thickness t
I = rho*t*l*w^3/3
FOrce = F = 220 N
Torque T = F*w = 220*1.25 = 275 Nm
now from newton's second law
T = I*alpha
alpha is the angular acceleration
now, rho*l*w*t*g = 750 N
l = 3 m
w = 1.25 m
I = 750*1.25^2/g*3 = 39.819 kg m^2

275 = I*alpha
alpha = 6.9062 rad/s/s
for theta = pi/2 rotation
and initial angular velocity wo = 0
thtea = 0.5*alpha*t^2
t = 0.674 s

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