1 / 5

EGR 280 Mechanics 17 – Work and Energy of Rigid Bodies

EGR 280 Mechanics 17 – Work and Energy of Rigid Bodies. Kinetics of rigid bodies in plane motion – Work and Energy Principle of Work and Energy for a Rigid Body Our basic principle still applies: T 1 + U 12 = T 2 where T 1 = total kinetic energy in position 1

bruis
Télécharger la présentation

EGR 280 Mechanics 17 – Work and Energy of Rigid Bodies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. EGR 280 Mechanics 17 – Work and Energy of Rigid Bodies

  2. Kinetics of rigid bodies in plane motion – Work and Energy Principle of Work and Energy for a Rigid Body Our basic principle still applies: T1 + U12 = T2 where T1 = total kinetic energy in position 1 U12 = total external work done from position 1 to position 2 T2 = total kinetic energy in position 2

  3. Recall: • A system of forces can be reduced to a resultant force and a resultant moment at some point. • Any general motion can be reduced to a translation and a rotation about some point. The total work done by the resultant force and the resultant moment is U12 = ∫F·dr+ ∫M·dθ Some forces never do work, such as the reaction forces at non-moving supports. Also, the friction force at the point of contact of a rolling body does no work. 2 1 θ2 F M r θ1

  4. Kinetic Energy of a Rigid Body in Plane Motion T = ½mvG2 + ∫½ (v´)·(v´)dm = ½mvG2 + ½∫(ω × r´)·(ω × r´)dm = ½mvG2 + ½ ω2 ∫(r´)2dm T = ½mvG2 + ½ IGω2 Where IG is the mass moment of inertia of the body with respect to the centroidal axis perpendicular to the plane of motion. Special case: Non-centroidal rotation vG = ωd T = ½mvG2 + ½ IGω2 T = ½m(ωd)2 + ½ IGω2 T = ½ IOω2 where IO = IG + md2 is the mass moment of inertia about the fixed point O. v´ dm r´ G ω O ω d vG G

  5. Conservation of Mechanical Energy If all of the forces that act on the rigid body are independent of the path of the body, then the total mechanical energy of the body is conserved: T1 + V1 = T2 + V2 Power P = dU/dt = d(F·dr + M·dθ)/dt P = F·v + M·ω

More Related