System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.26P

Quenching is the process of immersing a hot metal object in a bath for a specified time to improve properties such as hardness. A copper sphere 25 mm in diameter, initially at 300°C, is immersed in a bath at 0°C. Measurements of the sphere’s temperature versus time are shown here. Plot the data and find a functional description of the data.

Times s 0 0.1 0.2 0.3 0.4 0.5 0.6 Temperature  °C 300 150 75 35 12 5 0

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Three cables are pulling on a ring located at the origin, as shown in the diagram below.  FA is 200 N in magnitude with a transverse angle of 30° and an azimuth angle of 140°.  FB is 240 N in magnitude with coordinate direction angles α = 135° and β = 45°.  Determine the magnitude and direction of FC so that the resultant of all 3 force vectors lies on the z-axis and has a magnitude of 300 N.  Specify the direction of FC using its coordinate direction angles.
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