Answered: A heavy swing door has a mass of m =…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A heavy swing door has a mass of

m = 8,000 kg,

a width

w = 1.0 m,

and a height

H = 3.9 m.

The door swings about a vertical axis passing through its center. The moment of inertia of this door about the vertical axis of rotation is given by

I =

mw².

(a) You stand on one side and push at the outer edge of the door and perpendicular to the face of the door with a force of

F = 12.0 N.

Your friend pushes on the other outer edge of the door from the opposite side with the same force. What is the net torque, in N · m, applied to the door?

(b)What is the angular acceleration of the door in rad/s?

(c) Now consider a heavy door, with the same mass and dimensions as the one in part (a), that swings about a vertical axis passing through one long edge as shown in the diagram below. The moment of inertia of the door about this new axis of rotation is given by

I =

mw²,

where m is the mass and w is the width of the door.

How much force, in Newtons, must you and your friend each apply to the free end of the door on the same side and perpendicular to the plane of the door in order to produce the same torque as that produced by both of you in part (a) above?

(d) What is the angular acceleration of the door in rad/s?

Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .

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