{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw5 - Homework 5 DueTuesday October 27 http...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 5 DueTuesday October 27 http: nsgsun.aae.uiuc.edu AAE250 1. Problem 4-4 from Greenwood: Particles m1 = m and m2 = 2m are connected by a massless string and undergo free planar motion. Initially they rotate about each other with a constant separation l0 and an angular velocity !0: Then a device in m1 reels in the connecting string until its length is 1 l0 and is again constant. At 2 this later time, nd a the angular velocity ! b the tension in the string 2. Consider the following system of particles ^ m1 = 2 kg; r1 = ^ + j + k m; v1 = 7^ m=s; i i m2 = 1 kg; r2 = 4^ + 3k m; v2 = ,6^ m=s j ^ j m3 = 1:5 kg; r3 = 2^ + 2k m; v3 = ,3^ m=s i ^ i ^ m4 = :5 kg; r4 = 4k m; v4 = 12^ + 5k m=s i ^ a Find the mass center of the system of particles at the instant shown. b Find the linear momentum of the system of particles at the instant shown. c Find the angular momentum of the system of particles about point O at the instant shown. d Find the angular momentum of the system of particles about the center of mass at the instant shown. e If the only forces acting are the internal forces of attraction between the particles, what can be said about the subsequent motion of the system? What quantities will be conserved? 3. A mass particle m is launched in a uniform gravitational eld with launch speed v0 and launch angle 0 as shown. The value of m is constant. AAE 250 1 y 1 0 1 0g 1 0 1 0 1 0 v0 11 00m 0 x a Determine the Lagrangian function L for the system and obtain the equations of motion1 b Find all available constants of the motion and evaluate them in terms of initial launch conditions. c Solve the equations of motion for the given initial conditions. 4. Problem 6-7 from Greenwood: A double pendulum consists of two massless rods of length l and two particles of mass m which can move in a given vertical plane as shown see gure in text. a Assuming frictionless joints, and using and as coordinates, obtain the di erential equations of motion. b What are the linearized equations2 for small and ? Note: and v0 are initial conditions on the solutions to the equations of motion, but do not appear in the equations of motion themselves 2To linearize, approximate sin by and cos by 1 why?, and neglect terms containing products of coordinates and or velocities for example, neglect 2 or _: 1 2 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern