(i) Draw the Free Body Diagram (FBD)(ii) Use Lagrange's method to derive the equations of the motion(iii) Use Newton's approach to derive the equations of the motion A mass m is hanging from a cord attached to the circular homogeneous disk (at point A) ofmass M and radius R, as shown in Figure 1. The disk is restrained from rotating by a springattached at point B at radius r from the center (point O). There is no friction at the pivot.MDisk Mass Moment of Inertia:Figure 1

Answered: Image /qna-images/answer/91ccd1f0-b382-4a2d-83e7-c0b32c11018f.jpg

Answered: A mass m is hanging from a cord…

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

See similar textbooks

Similar questions

A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (2) ) the work done by the couple moment. __________(J) (two decimal places)
It is common to hang objects on doorknobs and over-the-door hooks. There is a limit to the amount of weight that a door can hold because of the forces exerted on the hinges. A door of height h = 2.5 m and width h/2 has a mass of M = 36 kg. The mass is distributed uniformly, so the center of mass is located at the geometric center of the door. One hinge is located a distance h/4 from the top of the door. The second hinge is a distance h/4 from the bottom of the door. Refer to (a) in the figure. The door’s weight is supported entirely by the two hinges and each hinge supports half of the weight. In other words, the vertical force exerted by each hinge is exactly one half of the total weight, including any additional load. For this problem, take the positive y-direction to be directly upward and the positive x-direction pointing from the hinge side of the door to the knob side. 1.) calculate the force, with its sign in Newtons that the upper hinge exerts on the door in the x axis.…
The structure of a football goal is shown in the figure below. The bending motion of the structure can be represented by a flexible cantilever beam with tip mass M¡ as shown in the figure. The tip mass M, represents the mass of the horizontal crossbar which is assumed 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 vertical posts. A soccer ball of mass M, hits the horizontal crossbar with the velocity of Vp. x(t) м, VINGLI SOLAR The response of the horizontal crossbar, mass M, is shown by x(t) in the figure. The vertical 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)…
Calculate the internal forces at the section (1) for the loaded 3-D system given in the figure.
A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position (state 1) to the vertical position (state 2), determine the following. 5) when use T to represent kinetic energy, V potential energy, U work done and if the bar is at rest at state 1, the principle of work-energy in this case could be expressed as____________ . V1+∑U(1-2)=T2+V2 T1+V1=T2+V2…
The thin rod in the figure has a mass of 15kg and is attached to a spring of constant k = 50 N / m at one end, which has an unstretched length of 1.5 m. If the rod is released from rest in horizontal position (e = 0 °) and only conservative forces act on it, determine: a) What is the moment of inertia of the thin rod around the axis of rotation at A? b) What is the angle at which the rod is momentarily at rest again? c) What is the maximum angular velocity of the path? 2 m 2 m ww. 60
A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (1) if datum is set as when θ=90°, the gravational potential energy of the bar when AB is horizontal will be ____________(J) (two decimal places)
4. Three uniform masses (each mass: m) are connected by three massless arms whose lengths are all 2 as shown a figure. All mases are in x-y plane. (1) Find the inertia tensor at O. (2) Find the principle axes and the principle components. 2 √3 1 -2 0 -1 -1 -2
2m dz - m. None of them اپن For the robot above, please determine Uo (the potential energy of Link #0) OU 9.8 OU = 5.6 OUo = 4,9 OU=19.6 * d₁, d₂ and ₂ are the joint variables m₂ = m₁ = m₂ = m₂ = 1 kg The moment of inertia of the last link is 3 kg.m². The mass centers are located on the middle point of each link.
A thin circular disc is fitted to a shaft as shown in figure. Weight of the disc is 500 N and diameter is 1.2 m. Shaft rotates at 300 r.p.m in anticlockwise direction when seen from the right side. Find the effect of the gyroscopic couple on the shaft and the bearing reactions at A and B taking the effect of the weight of the disc. 1 m. 1.5 m Figure
Find the mode shapes of the systems in the figure?
A bar is attached to the spring at the point C. The left end of the bar is pin supported and can rotates about the pin at Point A. The mass of the bar is m=20kg. The total length of the bar is LAB=3m and LAC=2m. Point A is 0.6 m below the ceiling. A clockwise constant couple moment M= 30Nm is applied on the bar so that the bar rotates from the horizontal position with θ=0° to the vertical position with θ=90°. The spring always maintains at the vertical position. The spring’s stiffness coefficient is k=30N/m and its unstretched length is 0.5 m. The acceleration due to gravity g=9.81 m/s2. During the process that the bar rotates from the horizontal position to the vertical position, determine the following. (4) the work done by the reaction force of the pin.____________ (J)

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS