Answered: A uniform drawbridge must be held at a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 32P

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Question

A uniform drawbridge must be held at a 37.5 ∘∘ angle above the horizontal to allow ships to pass underneath. The drawbridge weighs 45000 NN, is 16.5 mm long, and pivots about a hinge at its lower end. A cable is connected 3.00 mm from the hinge, as measured along the bridge, and pulls horizontally on the bridge to hold it in place.

1)What is the tension in the cable?

2)Find the magnitude of the force the hinge exerts on the bridge.

3)Find the direction of the force the hinge exerts on the bridge.

4)If the cable suddenly breaks, what is the initial angular acceleration of the bridge?

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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