Work done by a force dW=f·du=fu2=|f‖ldu‖cos(fu) dw f. du · Work done by a moment: dW=M. de= M: 0 dw Extend definition to material bodies: total work is the addition of the work done on all particles by forces distributed over the volume W by forces distributed over the surface t·udS by concentrated forces W=∑f·u(x) nother classification Work done by external forces: we will assume that external forces dont change during the motion or deformation, i. e, they are independent of the displacements. This will lead to the potential character of the external work and to the definition of the potential of the erternal force as the negative of the work done by the external forces Work done by internal forces: the internal forces do depend on the deformation In general, the work done by external forces and the work done by nternal forces don't match(we saw that part of the work changes the kinetic energy of the material)� � � • Work done by a force: dW = f · du = fiui = �f� �du� cos(fu� ) (1) � B � B WAB = dW = f · du (2) A A • Work done by a moment: dW = M · dθ = Miθi (3) � B � B WAB = dW = M · dθ (4) A A • Extend definition to material bodies: total work is the addition of the work done on all particles: – by forces distributed over the volume: W = f · udV V – by forces distributed over the surface: W = t · udS S – by concentrated forces: n W = fi · u(xi) i=1 Another classification: • Work done by external forces: we will assume that external forces don’t change during the motion or deformation, i.e., they are independent of the displacements. This will lead to the potential character of the external work and to the definition of the potential of the external forces as the negative of the work done by the external forces. • Work done by internal forces: the internal forces do depend on the deformation. In general, the work done by external forces and the work done by internal forces don’t match (we saw that part of the work changes the kinetic energy of the material). 2