The structure of a football goal is shown in the figure below. The bending motion of the structure canbe represented by a flexible cantilever beam with tip mass MT as shown in the figure. The tip massMfrepresents the mass of the horizontal crossbar which is assumed to be rigid in this motion. A singlevertical straight beam having mass of MH, shown in the figure below, is the equivalent model for thetwo symmetrical vertical posts. A soccer ball of mass M, hits the horizontal crossbar with the velocityof Vp.x (t)м,UYINGLI SOLARNGL LAF The response of the horizontal crossbar, mass M, is shown by x(t) in the figure. The vertical beam has acircular cross section of radius r, Young's modulus E and length L. For numerical calculations, use M7 =%3D7.9108 kg, MH = 22.0542 kg, M, = 0.9909 kg, V½ = 5.9645 m/s, L = 2.4468 m, E = 77.7443 GPa and r =0.0749 m. For circular cross-section / = n/4.Considering zero damping and the numerical data given= TTabove, obtain the maximum amplitude of response x(t) after it was hit by soccer ball Mp.3.8491 mm4.7691 mm0.7225 mm2.5990 mm1.5282 mm

Write the expression of conservation of energy. Write the expression of conservation of momentum.…

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 uniform beam of length, L, and mass, M, is freely pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall, so that the beam makes an angle phi with the horizontal as shown below. To answer the questions below, find algebraic expressions for the tension in the cable, the angular acceleration of the beam, should the cable break, and the resulting angular velocity as the beam falls through the vertical position. A. If L = 2.4 m, M = 5 kg, and phi = 45o, then what is the tension in the cable? B. If the cable snaps, what is the angular acceleration about the pivot point? C. What is the angular velocity of the falling beam, just as it hits the wall?
The figure below shows a cable supporting a beam. In addition there is a vertical force acting on the right end of the beam. L Calculate the normal force N(x), the shear force V (x), the moment M(x) as a function of the parameters L and f. (Partial Answer: N(x) = 2f for 0
Please complete the following question and parts with full work thanks :)
For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3
For the loaded beam shown in Figure below : 2.1.Determine the reaction forces at the points of support of the beam in Figure Q2 above by applying the principle of equilibrium of moments and start your solution by drawing free body diagram of the beam. 2.2. Develop the equations for shear force and bending moment for the spans AB, BC and CD of the loaded beam shown above and for each equation developed, determine the values of shear forces and bending moment at the points A, B, C and D 2.3. Draw the shear force and bending moment diagrams for the loaded beam shown above.
For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3
For two existing torques, what third force at a given distance from the pivot will balance them? Imagine a meter stick set up as in the figure. It hangs from a central bracket, and two hanging masses can hang from it from each of their brackets. At a third location, a force probe can either pull up or pull down on the stick, depending on what is needed to balance the stick. The mass of the meter stick is 120 g. sketch the situation (drawing r1, r2, r3, F1, F2, and F3) and determine the magnitude (value) and direction (+ or -) of each torque. Don't include the mass of a bracket that would hold the hanging mass in place; assume the mass listed is the entire mass hanging at that point. For each trial, use the principle of equilibrium (where the sum of torques is zero) to calculate the third, unknown force acting at x3
Note: The solution should not be hand written.
ANSER FAST
Find the shear force at point A, (VA) in kN. Find the bending moment at point A,(MA) and point B,(MB) in kNm. Find the shear force at point B,(VB) in kN.
An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 2.6 m is made of steel with Young's modulus, E = 202.4 x 10⁹ N/m². The second moment of area of the beam 1 = 3.7 x 10-4 m4. The stiffness of the spring, k₁ = 6.2 x 10³ N/m. The mass due to the load being lifted, m₁ = 3.4 x 10² kg. The beam mass is negligible compared with the load. You are required to find the equivalent stiffness of the beam, and then as your answer, to find the natural frequency of the system in Hz. Fill this answer in the box below. (Express your answer to 2dp) Flg. Q3 Answer: m₁ k₁

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