Example: Use Lagrangian dynamics to determine the equation of motion for the shown RR manipulator. Each link has length /, and total mass m;. (X2,y2
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Obtain the dynamic equations of the RR manipulator in the figure using the Lagrangian method. write in standard form.(by using formulas in photo)
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- Part F Calculate the direction of the net force on particle 3 due to the other two. Express your answer as positive angle using two significant figures. ? Submit Request AnswerHanging from the ceiling over a baby bed, well out of baby's reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m, and they are equally spaced by a distance d, as shown. The angles labeled ? describe the angle formed by the end of the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal, labeled ?. Let T1 be the tension in the leftmost section of the string, T2 be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment. a). Find an equation for the tension in each section of the string in terms of the variables m, g, and theta. b). Find the angle phi in terms of the angle theta. c). If theta = 6.27°, what is the value of phi (in degrees)? d). Find the distance x between the endpoints in terms of d and ?.4. A particle of mass m moves in a central field of attractive force that has a magnitude () eat, where kand a are constants, t is the time, and ris the distance of m from the force's center. Find the Lagrangian and Hamiltonian functions. Compare the Hamiltonian and the total energy of the system and discuss the conservation of energy for the system.
- Obtain the Lagrangian equations of the PR(prismatic+rotarary) manipulator in the figure. write in vector form. (use the kinetic and potential energy,angular and lineer velecoties-h-m1-m2-I1-I2-w for finding lagrange equations) I want to see how the kinetic and potential energies obtained for each link are found. (do not copy the answer from another answered question)make it clear and bold answerFor the problem described below, please fully sketch the scenario described in the problem statement, characterize the mass balance (conservative vs non- conservative and steady-state vs not at steady-state) giving reasons for your characterization of the system, and locate the mass balance in both space and time. Please DO NOT solve the problem. Coming home after the end of the winter semester, you find that your family's swimming pool has not be maintained well. In particular, it has no chlorine residual at all, and it is full of tree leaves. You buy a concentrated chlorine solution (1% as Cl₂) and begin to meter it into the pool at a rate of 100 mL/hour. The pool has a volume of 200 m³. You also add new water, and remove in-pool water, at a rate of 3.785 L/minute. The chlorine reacts with the organic matter in the with a rate of 0.5/hour. How long will it take to get the Cl2 residual up to 1 mg/L if you add Cl2 continously.
- 1. 2. The figure shows multiple solid disks with uniform mass distribution that are spinning about its center. The mass of the disks are the same, but they have different radii, as shown. Rank the disks by the amount of energy needed to spin the disk so that the outer edge of the disk has linear velocity v, from greatest to least. Explain your reasoning. A B C Two students are discussing their previous answer. Student 1: I ranked the largest disk as the greatest amount of energy needed because it has the greatest moment of inertia. Student 2: But, I think we need to also include the angular velocity. Since w=v/r, the angular velocity is smaller for the larger disk and I think all three require the same amount of energy. Do you agree or disagree with either or both of these students? Briefly explain your reasoning.Please find the answer using [ijk] notation and matrices. At the very least find the inertia about C. Please use parallel axis theorem. 1. Calculate the moments of inertia of the system consisting of a slender, ho- mogeneous straight rod of length I and mass m with a thin disk of radius r and mass m about a) A and b) C, respectively. Use xyz - frame as the system - xed frame. Thin disk is rigidly attached to the rod perpendicularly and C is the center of the disk. Assume the constant density for the rod and disk system. In the gure, the rod is on the zy - plane and has an angle \theta relative to the y-axis Z Rod A 日 Thin disk +- y Figure 1: Rod with disk attachedNeglecting the latitudinal variation in the radius of the earth, derive a formula for the angle a between the gravitational acceleration vector go and the effective gravity Jeff at the surface of the earth as a function of latitude . [Draw a labelled diagram showing the Earth with go, Jeff and the centrifugal acceleration at latitude p. Be careful to identify all dependence on o.] At what latitude is the angle a a maximum and what is its maximum value? Next, derive a formula relating Jeff ² to go and 6, and use it to prove that Jeff go for any o. Find the ratio of the maximum centrifugal acceleration to go. [~ Holton 1.1]
- An experimental device imparts a force of magnitude F-34 lb to the front edge of the rim at A to simulate the effect of a slam dunk. Compute the moment of the force F about point O and about point B. The moments are positive if counterclockwise, negative if clockwise. Finally, locate a point Ċ from the base at O to the location on the ground where the force imparts zero moment. The distance d from point o to point C is positive if C is to the right of O, and negative if to the left. Assume a - 36 in., b - 28 in., h -12 in., H-10 ft, c-5, and d-9. b F Answers: Mo- MB- d= i i H lb-ft lb-ft ftShow all working explaining detailly each step.Next, imagine that a bullet impacts the block that you see and embeds itself. Let's say that you know the speed of the bullet just before it hits and also the mass of the bullet. Explain, with words and equations, how you would determine the angle theta. eed to know i L-h L Center of Pendulum catch