Machinery's Handbook, 31st Edition
160 Force Systems 10 6 pascals) may be more convenient multiples in practice. Thus, note: 1 N/mm 2 = 1 MN/m 2 = 1 MPa. In addition to the pascal, the bar, a non-SI unit, is in use in the field of pressure measure ment in some countries, including England. Thus, in view of existing practice, the Interna tional Committee of Weights and Measures (CIPM) decided in 1969 to retain this unit for a limited time for use with those of SI. 1 bar = 10 5 pascals and 1 hectobar = 10 7 pascals. Force Systems Scalar and Vector Quantities.— The quantities dealt with in mechanics are of two kinds according to whether magnitude alone or direction as well as magnitude must be known in order to completely specify them. Quantities such as time, volume and density are com pletely specified when their magnitude is known. Such quantities are called scalar quanti ties. Quantities such as force, velocity, acceleration, moment, and displacement must, in order to be specified completely, include direction as well as magnitude, are called vector quantities. Graphical Representation of Forces.— A force has three characteristics which, when known, determine it. They are direction, point of application , and magnitude . The direc tion of a force is the direction it tends to move the body upon which it acts. The point of application is the place on the line of action where the force is applied. Forces may con- veniently be represented by straight lines and arrow heads. The arrow head indicates the direction of the force, and the length of the line, its magnitude to any suitable scale. The point of application may be at any point on the line, but it is generally convenient to assume it to be at one end. In Fig. 1, a force is supposed to act along line AB in a direction from left to right. The length of line AB shows the magnitude of the force. If point A is the point of application, the force is exerted as a pull, but if point B be assumed to be the point of ap- plication, it would indicate that the force is exerted as a push.
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Fig. 1. Vector Velocities, moments, displacements, etc. may similarly be represented and manipulated graphically because they are all of the same class of quantities, vectors. (See Scalar and Vector Quantities .) Addition and Subtraction of Forces: The resultant of two forces applied at the same point and acting in the same direction, as in Fig. 2, is equal to the sum of the forces. For example, if forces AB and AC , one equal to 2 lbs the other equal to 3 lbs, are applied at point A , then their resultant AD equals the sum of these forces, or 5 lbs.
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Fig. 2. Fig. 3. If two forces act in opposite directions, as in Fig. 3, then their resultant is equal to their difference, and the direction of the resultant is the same as the direction of the greater of the two forces. For example, AB and AC are both applied at point A ; then, if AB equals 4 N and AC equals 6 N, the resultant force AD equals 2 N and acts in the direction of AC .
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