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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A light rod of length 2L is free to rotate in a vertical plane about a frictionless pivot through its center. A particle of mass m1 is attached at one end of the rod, and a mass m2 is at the opposite end, where m1 > m2. The system is released from rest in the vertical position shown in Figure P8.84a, and at some later time, the system is rotating in the Position shown in Figure P8.84b. Take the reference point of the gravitational potential energy to be at the pivot, (a) Find an expression for the system's total mechanical energy in the vertical position. (b) Find an expression for the total mechanical energy in the rotated position shown in Figure P8.84b. (c) Using the fact that the mechanical energy of the system is conserved, how would you determine the angular speed co of the system in the rotated position? (d) Find the magnitude of the torque on the system in the vertical position and in the routed position. Is the torque constant? Explain what these results imply regarding the angular momentum of the system, (c) Find an expression for the magnitude of the angular acceleration of the system in the rotated position. Does your result make sense when the rod is horizontal? When it is vertical? Explain.

images

Figure P8.84

(a)

To determine
The total mechanical energy of the system about vertical position.

Explanation

Given Info:

The mass of the particles are m1 and m2 and light rod of length 2L . Mass m1 is attached at one end and m2 attached at other end.

In Figure P8.84 (a) the system has only potential energy and at centre the potential energy is zero since the reference point of the gravitational potential energy is at the pivot that is at the midpoint

(b)

To determine
Total mechanical energy in the rotated position.

(c)

To determine
The angular speed of the rotated system

(d)

To determine
The magnitude of torque in the vertical and rotated position

(e)

To determine
The magnitude of angular acceleration of the system in the rotated position.

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