In a test to determine the crushing characteristics of a packing material, a steel cone...

In a test to determine the crushing characteristics of a packing material, a steel cone of mass m is released, falls a distance h, 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 = d, determine the constant k in terms of the test conditions and results. Utilize a single application of the workenergy equation.