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2 coplanar

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2 coplanar

1. 1. Introduction: This unit seeks to introduce to you the different systems of forces. The prerequisite for this is the concept of a force and the various forms of forces occurring in nature. In addition to this, you should have the basic knowledge of algebra, co-ordinate geometry, trigonometry and a little bit of calculus.
2. 2. Introduction: This unit seeks to introduce to you the different systems of forces. The prerequisite for this is the concept of a force and the various forms of forces occurring in nature. In addition to this, you should have the basic knowledge of algebra, co-ordinate geometry, trigonometry and a little bit of calculus. Objectives: After studying this unit, * you should be able to identify the different systems of forces, * concurrent forces vector ally, resolve forces into components, * forces by components, find the moment of a force, * find the resultant of non-concurrent forces.
3. 3. System of Forces: The action of one body on any other body can be called a force. These actions may be of various forms: gravitational force known as weight of a body, force exerted by an elastic spring, force exerted by a locomotive on the train by the track. To specify a force, you need to know its magnitude, direction and the point of application. The magnitude is in Newton in SI unit. By drawing a line to scale showing the magnitude, the arrowhead indicating direction. Such a straight line is called a vector. A combination of several forces acting on a body is called a system of forces or a force system.
4. 4. Consider a sphere of mass m suspended by means of a string resting against a smooth wall, as shown in Figure 1. What are the forces acting on it? Solution: Let us identify the forces acting on the sphere. These are as follows: 1) Weight of the sphere W = mg acting vertically downwards from the centre of gravity of the sphere. 2) Tension in the string Reaction offered by the wall. Thus, the sphere is subjected to a system of three forces as shown in Figure 2. Figure 1 Figure 2
5. 5. * If coplanar forces is acting on a body ===> its total effect is usually expressed in terms of its resultant. * Force being a vector quantity the resultant ===> by using vector algebra e.g.) if the resultant of two forces is to be found out then the law of parallelogram of forces is used.
6. 6. * If coplanar forces is acting on a body ===> its total effect is usually expressed in terms of its resultant. * Force being a vector quantity the resultant ===> by using vector algebra e.g.) if the resultant of two forces is to be found out then the law of parallelogram of forces is used. Law of Parallelogram of Forces : If two forces acting at a point are such that they can be represented in magnitude and direction by the two adjacent sides of parallelogram, the diagonal of the parallelogram passing through their point of inter section gives the resultant in magnitude and direction.
7. 7. Law of Parallelogram of Forces : Consider two forces P and Q acting at point 0 in the body as shown in Figure (a). Their combined effect can be found out by constructing a parallelogram using vector P and vector Q as two adjacent sides of the parallelogram as shown in Figure (b). The diagonal passing through 0 represents their resultant in magnitude and direction. Figure (a) Figure (b)
8. 8. Law of Polygon of Forces : If more than two forces are acting on a body, then the resultant can be found by repeated applications of parallelogram law or the triangle law. Consider five forces each of 80 N acting at o in a body. Draw forces of polygon and show the resultant of all the forces. Let us construct a polygon such that the forces A, B, C, D and E represent the sides of a polygon taken in order, each force being drawn from the end of earlier force then their resultant is represented by the line joining the starting point of the first force A to the end of the last force E.
9. 9. Resolution and Composition: Splitting the force into components ===> Resolution of a force - for determining the resultant Finding the resultant of any number of forces ===> Composition of forces A force making an angle 0 with respect to x axis as shown in Figure, can be resolved into two components FX, and FY, acting along x and y axes respectively.
10. 10. A force of 120N is exerted on a book in the ceiling as shown in Figure 1. Determine the horizontal and vertical components of the force. Solution: Figure 1