(30 pts) Problem 1A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. Amoment Mmgr4is applied to the rod. Assume that the bowl is fixed and its rim is in thehorizontal plane.HINT: It will help you to find the length l of that portion of the rod that remains outside thebowl.M2ra) How many degrees of freedom does this system have?b) Write an equation for the virtual work in terms of the angle 0 and the motion of thecenter of mass (TF)c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)a. HINT: Use the center of the bowl as the coordinate system origin for the problem.d) In the case of no applied moment (i.e., M 0), derive an equation that can be used tosolve for the equilibrium angle of the rod. DO NOT solve the equatione) In the case of an applied moment (i.e., M=mgr= -) derive an equation that can be used to4solve for the equilibrium angle of the rod. DO NOT solve the equation.f) Can the angle 0 and the motion of the center of mass (77) be used as generalizedcoordinates? Why or why not?

Answered: (30 pts) Problem 1 A thin uniform rod…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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igure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y 0, and the springs are in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. DE only 225 Your tasks: X k 0 3k a F a M y A Derive an equation of motion for the system in terms of the angular displacement 0, and its derivatives (you should not have y or its derivatives in this equation.) B Derive an equation of motion for the system in terms of the displacement y, and its derivatives (you should not have or its derivatives in this equation. C Assuming there is no external actuator force F acting on the system, write down the total energy H of the system in terms of 0,0 and element constants. Derive an expression for the time derivative H of the total energy. D Transform the equation from part B, which is in y, to another…
3Skype O Launch MX A Meet - pcX + 2020 SEC x Zohdy -D x Course: 2 x M Inbox (97 X M Inbox (1) Course H x e.com/course.html?courseld=16544025&OpenVellumHMAC=2edceb9788c2d7ed3b6b62e30e29d5d3#10001 (Up Maps O Web design tutori. W MATH180: HW08-. A Review I Constants Blocks of mass m, and m2 are connected by a massless string that passes over the pulley in the figure (Flgure 1). The pulley turns on frictionless bearings, and mass mi slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest. Part C Suppose the pulley has mass m, and radius R. Find the acceleration of m1. Verify that your answers agree with part A if you set m, = 0. Express your answer in terms of some or all of the variables m1, m2, mp, and constant g. ΑΣφ ? a1 = Submit Request Answer Figure Part D Find the tension in the upper portion of the string. Verify that your answers agree with part B if you set m, = 0. Express your answer terms of some all of the variables m1, m2, mp, and…
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1) In units of newtons, what is the magnitude of the force through the Achilles tendon if he stands on one foot? 2) Calculate the force in units of newtons at the pivot of the simplified lever system shown. That force is representative of forces in the ankle joint.
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Question 2) The figure shows a mechanical model of the Russel fracture traction device and the leg. The leg is held in balance in the position indicated by the two weights attached to the two cables. The combined weight of the leg and the cast is W=210 N. The horizontal distance between points A and B where the cables are attached to the leg is L=100 cm and the vertical distance is d=6 cm. Point C is the center of gravity of the cast and leg at three quarters of the L measured from point A (3L/4= 75 cm). The angle that cable 2 makes with the horizontal is measured as β=33°. Accordingly, in order for the leg to remain in balance in the shown position; a) Find the tensile force T1 in cable 1. (Write your result in N) b) Find the tensile force T2 in cable 2. (Write your result in N) c) Find the angle α of cable 1 with the horizontal. Response
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The plank only turns about the pivot. So, the forces on the plank, the weights of F1 and F2 and of the plank itself W, and the reaction N from the pivot are balanced. F1+F2 + W=N ○ eggs on one side of the seesaw making it tilt being unbalanced : I need a equation and it explained
I need AB,Cx,Cy
Three springs are connected to a mass and to fixed supports. When the coordinate y is equal to zero, there is no spring force. Your tasks: Tw m k3 Fload Ő nly A Draw the free body diagram for the mass m including all 3 spring forces and the load force Fload). ( Figure 1: System schematic for Problem 1. B Draw the free body diagram for the mass m, but combine the springs into one equivalent spring with spring constant keq. Write the equivalent stiffness of the spring keq in terms of the other spring constants. (3 C Given that k₁ = 300 N/m, k₂ = 100 N/mnd k3 = 200 N/mand Fload = 300 N, calculate the loaded deflection Yloaded D Compute the amount of potential energy stored in each spring. E Compute the forces, in Newtons, in each spring and denote them as F₁, F2, and F3 when the load from Part D is applied. Wh

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