DEFINITION AND CLASSIFICATION OF FORCES

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Hortense Jones
6 years ago
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1 DEINITION AND CLASSIICATION O ORCES

2 As defined before, force is an action of one body on another. It is a vector quantity since its effect depends on the direction as well as on the magnitude of the action.

3 The effect of the force applied to the bracket depends on P, the angle q and the location of the point of application. Changing any one of these three specifications will alter the effect on the bracket such as the internal force generated in the wall or deformation of the bracket material at any point. Thus, the complete specification of the action of a force must include its magnitude, direction and point of application.

4 We can separate the action of a force on a body into two effects as external and internal. or the bracket, the effects of P external to the bracket are the reactive forces (not shown) exerted on the bracket by the wall. orces external to a body can be either applied or reactive forces. The effect of internal to the bracket is the resulting internal forces and deformations distributed throughout the material of the bracket. P

5 orces are classified as either contact or body forces. A contact force is produced by direct physical contact; an example is the force exerted on a body by a supporting surface. A body force is generated when a body is located within a force field such as a gravitational, electric or magnetic field. An example of a body force is your weight.

6 orces may be further classified as concentrated or distributed. Every contact force is actually applied over a finite area and is therefore a distributed force. However, when the dimensions of the area are very small compared with the other dimensions of the body, the force may be considered concentrated at a point. orce can be distributed over an area, as in the case of mechanical contact, over a volume when a body force such as weight is acting or over a line, as in the case of the weight of a suspended cable.

7 The weight of a body is the force of gravitational attraction distributed over its volume and may be taken as a concentrated force acting through the center of gravity.

8 Concentrated orce Distributed orce

9 Action and Reaction According to Newton s third law, the action of a force is always accompanied by an equal and opposite reaction. It is essential to distinguish between the action and the reaction in a pair of forces. To do so, we first isolate the body in question and then identify the force exerted on that body (not the force exerted by the body). It is very easy to mistakenly use the wrong force of the pair unless we distinguish carefully between action and reaction.

10 CLASSIICATION O ORCES ACCORDING TO THEIR WAYS O APPLICATION

11 The relationship between a force and its vector components must not be confused with the relationship between a force and its perpendicular (orthogonal) projections onto the same axes.

12 or example, the perpendicular projections of force onto axes a and b are a and b, which are parallel to the vector components of 1 and. It is seen that the components of a vector are not necessarily equal to the projections of the vector onto the same axes. The components and projections of are perpendicular. are equal only when the axes a and b

13 SOME COMMON TYPES O ORCES

14 CONTACT AND RICTION ORCE Let s consider two bodies which are in contact. The force acting on body 1 from body is. can be divided into two components as a N normal force, drawn perpendicular to the tangent line at the point of contact and force, drawn parallel to the tangent line. f tangent

15 N is named as the normal component of the contact force and f is named as the friction component of the contact force. If the contacting surfaces are smooth, then can be neglected ( f =0); but if the contacting surfaces are rough it has to be taken into consideration. f

16 The relationship between and is given by f =mn, where m is a dimensionless coefficient of friction varying between 0 and 1. N f tangent

17 ORCES IN STRINGS, CABLES, WIRES, ROPES, CHAINS AND BELTS orces in strings, cables, etc. are always taken along the string, cable, etc. and their direction always points away from the body in consideration. They exert force only when they are tight. When loose they exert no force. Hence, they always work in tension. Usually their weights are neglected compared to the forces they carry or support. T

18 ORCES IN PULLEY BELT SYSTEMS Pulleys are wheels with grooves that are used to change the directions of belts or ropes and generate a higher output load with a much smaller input force. Unless stated otherwise, or apparent from the problem, the tension forces at both sides of a belt are taken as equal. They are equal as long as the belt does not slide on the pulley, and the pulley rotates freely with a constant velocity.

19 ORCES IN SPRINGS Spring force is always directed along the spring and is in the direction as if to return the spring into its undeformed length. spring =kx (Spring force) (k: spring constant, x: deformation of the spring) spring

21 THREE DIMENSIONAL DESCRIPTION O ORCE

22 * When the direction angles of a force is given; The angles, the line of action of a force makes with the x, y and z axes are named as direction angles. The cosines of these angles are called direction cosines; they specify the line of action of a vector with respect to coordinate axes. In this case, direction angles are q x, q y and q z. Direction cosines are cos q x, cos q y and cos q z. cos q x = l cos q y = m cos q z = n z y x

23 z y x e 1 e nk mj li e 1 n m l k j i z y x z y x

24 When coordinates of two points along the line of action of a force is given; x y z B(x, y,z ) A(x 1, y 1,z 1 ) AB z z y y x x k z z j y y i x x e e e

25 * When two angles describing the line of action of a force is given; z z f y y x q xy x

26 Dot Product The dot product of two vectors P and Q is defined as the product of their magnitudes times the cosine of the angle a between them. The projection of a vector along a given axis or on a directed line: AB is the projection of on AB ( which is a scalar). AB is the projection vector of on AB (which is a vector)

EQUILIBRIUM OF RIGID BODIES IN TWO DIMENSIONS

EQUILIBRIUM OF RIGID BODIES IN TWO DIMENSIONS If the resultant of all external forces acting on a rigid body is zero, then the body is said to be in equilibrium. Therefore, in order for the rigid body