When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium. Consider these objects: (1) a book resting on a table, (2) a hockey puck sliding with constant velocity across a frictionless surface, (3) the rotating blades of a ceiling fan, and (4) the wheel of a bicycle that is traveling along a straight path at constant speed. For each of these four objects;

From equations 12-3 and 12-5 When forces are acting on the body in xy plane For static equilibrium

Summery An object at equilibrium has no net influences to cause it to move, either in translation (linear motion) or rotation. The basic conditions for equilibrium are:

c, e, f

Figure 12-25 shows an array of six particles, each with mass m, fixed to the edge of a rigid structure of negligible mass. The distance between adjacent particles along the edge is 2.00 m. The following table gives the value of g (m/s2) at each particle’s location. Using the coordinate system shown, find (a) the x coordinate xcom and (b) the y coordinate ycom of the center of mass of the six-particle system. Then find (c) the x coordinate xcog and (d) the y coordinate ycog of the center of gravity of the six-particle system.

Balancing torque equations: -6d(20)+2d(10)+0(F1)-d(30)+2d(F2)=0 F2=65 N To find F1, balance the forces along y-axis -F1+20-10+65-30=0 F1=45 N (a) no; (b) at site of F1, perpendicular to plane of figure; (c) 45 N

Since the sphere is in static equilibrium, the vector sum of all external forces acting on it must be zero.

In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure. d

In physics, elasticity is the tendency of solid materials to return to their original shape after being deformed. Solid objects will deform when forces are applied on them. Three Ways. Figure 12-11 shows three ways in which a solid might change its dimensions when forces act on it. hydraulic stress in (c). Tensile stress (a) shearing stress in (b)

the stress The strain, or unit deformation Young’s modulus shear modulus The strain the stress bulk modulus The strain the stress

a) Structural steel (ASTM-A36). b) In compression. c) High strength d) Douglas fir.

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(b) Since the cable is at 30º from horizontal, then horizontal equilibrium of forces requires that the horizontal hinge force be α β (c) And vertical equilibrium of forces gives the vertical hinge force component: α