STATICSCHAPTER 3

EXTERNAL AND INTERNAL FORCES

• The forces acting on the body of the rigid can be divided into two groups 1) and 2 external forces ) internal forces.

• 1 - . External forces exerted represent action other bodies on the rigid body into consideration.

• 2 - . Internal forces are those that keep the particles that make up units to the rigid body .

• 2 - .las internal forces are those units that maintains the particles that form the rigid body .

PRINCIPLE OF TRANSMISSIBILITY. EQUIVALENT FORCES

• Transmitting the principle states that the equilibrium conditions or movement of a rigid body remain unchanged if a force F which acts at a given point of that body is replaced by a force F which has the same magnitude and direction but which acts on a different point as long as both have the same action forces .

VECTOR PRODUCT OF TWO VECTORS

• To better understand the effect of a force on a rigid body , then introduce a new concept : the moment of a force about a point.

• Products vector expressed in rectangular component term

• The following will occur to determine the vector product of any of the unit vectors i , j, k were defined in chapter two considering the product ix j . as both vectors have a magnitude equal to 1 and given that they are angled straight with each other , their product vetores i , j, k are mutually perpendicular and form a right hand triad .

MOMENTS OF FORCE ABOUT A POINT

VARIGON THEOREM

• A force F acting on a rigid body . As is known, the force F is represented by a vector that defines the magnitude and direction. However, the effect of the force on the rigid body also depends on its application point .

• The distributive property vector products can be used to determine the moment when the various forces resulting from concurrent . If the forces F1 F2 ... forces applied at the same point A , and if the vector r represents the position A, from the equation in section 3.4 it can be concluded that

• r X ( F1 + F2 + ... ) = r X r X F1 + F2 + ...

• The rectangular components of the moment of a force

PRODUCT OF TWO VECTORS

• The dot product of two vectors P and Q is defined as the product of the magnitudes of P and Q and the cosine of the angle 0 formed by PYQ (Figure 3.19).

• The escales product of P and Q is denoted by PQ Then , we write

• PQ = cos P.Q

• Triple mixed product of three vectors

• Triple defines a triple scalar product or product mixed three vectors S , P and Q as the scalar expression .

• S. ( P x Q )

• Formed which is obtained by the dot product of vector S with the product of P and Q

MOMENT OF FORCE WITH RESPECT TO A GIVEN AXIS

• Now that has increased knowledge of vector algebra , we can introduce a new concept : moment of a force about an axis.

• Consider again the force F acting on the rigid body and the moment MO of this force with respect to O.

MOMENTS OF A PAIR / EQUIVALENT PAIRS

• It is said that two forces Fy- F having the same magnitude and line of action opposite parallel form a pair . Obviously, the sum of the components of the two forces in any direction is equal to zero.

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• Before establishing two power systems produce the same effect on a rigid body , it must be demonstrated based on experimental evidence that has been presented so far.

EQUIPOTENT VECTOR SYSTEMS

• In general, when two vector systems satisfy the equations (3.57 ) O ( 3.58) , that is, when its output and respectively resulting moments about an arbitrary point O are equal, it is said that the two systems are equipotent . Therefore, the result of setting is finished in the previous section can be stated as follows .