Four identical 80-kg sections are each firmly attached to a central axle, formin

Question

Four identical 80-kg sections are each firmly attached to a central axle, forming a rigid door that revolves freely about a central vertical axis as shown in the figure. A force of magnitude, F = 56 N, is applied perpendicular to the face on the free end of one section as shown. Use the following for symbolic input: m = mass of door section, w = width of door section, H = height of door section, F = magnitude of applied force. (a) Write a symbolic expression for the net torque on the revolving door. net = (b) Write a symbolic expression for the rotational inertia of the rigid revolving door. Rotational Inertia of a Door I = Incorrect: Your answer is incorrect. How do you combine the rotational inertia of different objects to find the rotational inertia of a system? (c) Apply Newton's 2nd law for Rotational Motion and then use the torque equation to determine the tangential acceleration, atan, on the outer edge of the door. Write a symbolic expression for the tangential acceleration: atan = Determine its numerical value: atan = (d) How wide is each door section if the angular acceleration of door is = 0.440 rad/s2? w = m

Explanation / Answer

Here ,

F= 56 N

a) net torque on the door

Tnet = F * w

Tnet =F*w

b)

total inertia of the door = 4 * inertia of each section

total inertia of the door = 4 * m * w^2/3

total inertia of the door = 4*m*w^2/3

c) let the angular acceleration is alpha

using second law of motio

alpha * Inertia = Tnet

(atan/w) * 4*m*w^2/3 = F * w

atan = 3F/(4*m*w^2)

tangential acceleration is 3F/(4*m*w^2)

d)

for angular acceleration = 0.44 rad/s^2

0.44 * 4 * 80 * w^2/3 = 56 * w

solving for w

w = 1.193 m

the width of the door is 1.193 m

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