The structure of a football goal is shown in the figure below. The bending motion of thestructure can be represented by a flexible cantilever beam with tip mass M¡ as shownin the figure. The tip mass M, represents the mass of the horizontal crossbar which isassumed to be rigid in this motion. A single vertical straight beam having mass of MH,shown in the figure below, is the equivalent model for the two symmetrical verticalposts. A soccer ball of mass M, hits the horizontal crossbar with the velocity of Vp.x(t)м,VINGLI SOLARThe response of the horizontal crossbar, mass M, is shown by x(t) in the figure. Thevertical beam has a circular cross section of radius r, Young's modulus E and length L.For numerical calculations, use M, = 23.2130 kg, MH = 28.6617 kg. M, = 0.5497 kg, Vý= 8.8974 m/s, L= 2.7757 m, E = 133.5685 GPa andr= 0.0437 m. For circular cross-section I = Tr/4.Considering zero damping and the numerical data given above,obtain the maximum amplitude of response x(t) after it was hit by soccer ball Mp.

When the soccer ball hits the crossbar then apply the conservation of linear momentum, Here, vo is…

Answered: The structure of a football goal is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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a beam is supported by a pin support at A and a roller support at B. For this question, leave your answer in terms of the variables w and L. (a) Using equilibrium of the full beam, find the support forces at A and B. (b) First section: Make an arbitrary cut between points A and B. Take the distance of the cut to be x along the beam from point A. Draw the free-body diagram for the left section and find functions for the internal shear force, V(x), and bending moment, M(x), in the section of the beam between A and B. (c) Second section: Repeat part (b) for the section of the beam between B and C. Take x to still be the distance from point A. (f) Find the value of x at which V(x) = 0. The internal bending moment reaches a maximum at the same point as V(x) = 0. Find the maximum bending mo- ment. pin Sketch the shear and bending moment diagrams. B L W C roller
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