Summer School 2007B. Rossetto1 4. Forces  Definition A force is defined by a vector and an application point: 1 - the modulus F = is the strength (newton) 2 - the support D must be attached to the point to which the force is applied 3 - the arrow gives the direction of action D P D’ Consequence: do not have the same effect if they are not applied to the same point P of a rigid body. They differ by their torque. P’ The moment/P characterizes the ability to make the body turn around P Definition of the torque of with respect to P:

Summer School 2007B. Rossetto2 4. Forces  Torque of a couple D P D’ P’ O H H’ 1 – Definition. A couple is a set of two equal and opposite forces 2 – Torque of a couple/0: (O between P and P’ ) Proof : from the definition

Summer School 2007B. Rossetto3 4. Kinematics  First law of Newton (inertia principle) Define a system (particle, set of particles, solid)

Summer School 2007B. Rossetto4 4. Statics  Point or particle equilibrium 1 - Identify all the applied forces to the point 2 - Use the fundamental theorem derived from Newyon 1 st law No translation: Exemple : equilibrium of some point P : x y T1T1 T2T2 P  Knowing P,  and , we deduce T 1 and T 2 (other way : triangle relationship)

Summer School 2007B. Rossetto5 4. Statics  Solid Equilibrium 1 - Define a system and identify all the applied forces 2 - Apply the fundamental theorems : No translation: No rotation with respect to O: Note that these topics requires some knowledge about solid concepts, like center of mass (cf. chap. 8)

Summer School 2007B. Rossetto6 4. Statics  Solid Equilibrium r1r1 To the center of the first wheel: In this example, it is necessary to define the system to apply the theorems The same equations can be written for the second wheel. Finally, we find: T=W/2 r2r2

Summer School 2007B. Rossetto7 4. Statics  Solid Equilibrium Example: ladder equilibrium. W:weight, supposed applied in G L: length, : angle : sliding friction characterization   G B A ( static >  dynamic ) Finally: