In a test to determine the crushing characteristics of a packing material, a steel cone of mass m = 2.6 kg is released, falls a distance h = 700 mm, and then penetrates the material. The radius of the cone is proportional to the square of the distance from its tip. The resistance R of the material to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the fourth power of the cone penetration distance x, or R = kx4. If the cone comes to rest at a distance x = 28 mm, determine the constant k in terms of the test conditions and results. Utilize a single application of the work-energy equation.
In a test to determine the crushing characteristics of a packing material, a steel cone of mass m = 2.6 kg is released, falls a distance h = 700 mm, and then penetrates the material. The radius of the cone is proportional to the square of the distance from its tip. The resistance R of the material to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the fourth power of the cone penetration distance x, or R = kx4. If the cone comes to rest at a distance x = 28 mm, determine the constant k in terms of the test conditions and results. Utilize a single application of the work-energy equation.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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In a test to determine the crushing characteristics of a packing material, a steel cone of mass m = 2.6 kg is released, falls a distance h = 700 mm, and then penetrates the material. The radius of the cone is proportional to the square of the distance from its tip. The resistance R of the material to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the fourth power of the cone penetration distance x, or R = kx4. If the cone comes to rest at a distance x = 28 mm, determine the constant k in terms of the test conditions and results. Utilize a single application of the work-energy equation.
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Chapter 3, Practice Problem 3/056
In a test to determine the crushing characteristics of a packing material, a steel cone of mass m = 2.6 kg is released, falls a distance h = 700 mm, and then penetrates the material. The radius of the cone is
proportional to the square of the distance from its tip. The resistance R of the material to penetration depends on the cross-sectional area of the penetrating object and thus is proportional to the fourth power of the
cone penetration distance x, or R = kx4. If the cone comes to rest at a distance x = 28 mm, determine the constantk in terms of the test conditions and results. Utilize a single application of the work-energy
equation.
h
Answer: k =
|(10°) N/m4
the tolerance is +/-2%
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