System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 1, Problem 1.15P
The distance a spring stretches from its “free length” is a function of how much tension is applied to it. The following table gives the spring length y that was produced in a particular spring by the given applied force f. The spring’s free length is 4.7 in. Find a functional relation between f and x, the extension from the free length (y = y − 4.7).
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1: A weight of 12 Newtons in hung from a spring. The spring deflects 8 cm. What is the spring constant for this spring? Use Hooke’s Law. How far will the spring deflect if a weight of 20 Newtons is hung from the spring instead? Draw a schematic or diagram. Show all calculations.
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When a beam section is subjected to a shear load, a
shear stress distribution is developed on the section. The
distribution of the shear stress is not linear. Elasticity
theory can be used to calculate the shear stress at any
point.
However, a simpler method can be used to calculate the
average shear stress across the width of the section, a
distance y above or below the neutral axis. The average
VQ
shear stress is given by T =
Here V is the shear
It
force on the section, I is the moment of inertia of the
entire section about the neutral axis, and t is the width of
the section at the distance y where the shear stress is
being calculated. Q is the product of the area of the
section above (or below) y and the distance from the
neutral axis to the centroid of that area (Figure 1). In
short, Q is the moment of the area about the neutral axis.
I
Figure
1 of 1
An I-beam has a flange width b = 250 mm, height h = 250 mm, web thickness tw = 9 mm, and flange thickness tf = 14 mm. Use the…
Chapter 1 Solutions
System Dynamics
Ch. 1 - Prob. 1.1PCh. 1 - Folklore has it that Sir Isaac Newton formulated...Ch. 1 - A ball is thrown a distance of 50 feet. 5 inches....Ch. 1 - An American football field is 100 yards long. How...Ch. 1 - How long is a 100-meter dash in feet?Ch. 1 - Convert 50 feet per second to miles per hour.Ch. 1 - The speed limit in some countries is 100...Ch. 1 - How many 60 watt lightbulbs are equivalent to one...Ch. 1 - Convert the temperature of 70°F to °C.Ch. 1 - Convert 30°C to °F.
Ch. 1 - A particular motor rotates at 3000 revolutions per...Ch. 1 - The displacement of a certain object is described...Ch. 1 - Prob. 1.13PCh. 1 - The displacement in meters of a certain vibrating...Ch. 1 - The distance a spring stretches from its “free...Ch. 1 - The following “small angle” approximation for the...Ch. 1 - Prob. 1.17PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Prob. 1.19PCh. 1 - Obtain two linear approximations of the function...Ch. 1 - Obtain a linear approximation of the function fh=h...Ch. 1 - The flow rate f in m3/s of water through a...Ch. 1 - Prob. 1.23PCh. 1 - The population data for a certain country are...Ch. 1 - Prob. 1.25PCh. 1 - Quenching is the process of immersing a hot metal...Ch. 1 - The useful life of a machine bearing depends on...Ch. 1 - 1.28 A certain electric circuit has a resistor and...Ch. 1 - 1.29 Water (of volume 425 ml) in a glass measuring...Ch. 1 - Consider the milk container of Example 1.4.2...Ch. 1 - Consider the milk container of Example 1.4.2...
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