Forces_Notes

 2013 Yeow Kok Han Page 1 FFoorrcceess 11 IInnttrroodduuccttiioonn This chapter is about recognising the different kinds of forces a t work in different situations and knowing the characteristics of the forces. This is important whenever one is interested in explaining the motion of objects, which is the focus of the chapter on Dynamics. Understanding the forces at work is also important in calculating work done for a given situation. 22 EEllaassttiicc FFoorrccee Most objects, e.g. a spring or a rubber block, when stretched or compressed, will exert a force op posite in direction to that applied on the object. The force exerted by the object on the external agent is an elastic force. In Fig. 2.1, the elastic force is also sometimes called tensile force or tension. When the elastic fo rce is proportional to the distance extended or compressed, the object is said to obey Hooke’s law. Hooke’s law states that where k is a positive constant and the negative sign indicates that the elast ic force is opposite to the direction of displacement. Though called a ‘law’, Hooke’s law is not universal or always obeyed. There are many objects or materials which do not obey Hooke’s law at all or may obey it for a limited range of x only. k is known as the constant of proportionality or in the case of a spring, also called the spring constant. Note that k is constant only as long as the dimensions and material of the object are not changed. For a given x, the larger the value of k, the larger the elastic force and hence the larger the external force needed to cause the displacement x. Therefore k is also called the stiffness. NNeewwttoonn’’ss TThhiirrdd LLaaww Note that in Fig. 2.1 the force exerted by hand on spring is equal in magnitude but opposite in direction to the force exerted by spring on hand . This is reflected by the arrows of equal length but opposite directions. In fact, Newton’s third law states: All forces exist in such equal and opposite pairs or action-reaction pairs. An elastic body is one which can return to its original size and shape after being deformed. In response to an external applied force, an elastic body will exert an elastic force on the external body. When the elastic force varies linearly with the extension or compression, the elastic body is said to obey Hooke’s law. Newton’s third law implies that forces always occur in pairs When body A exerts a force on body B, body B must exert an equal but opposite force on body A. Pulling forces exerted by hands on spring Elastic forces exerted by spring on hands Pushing forces exerted by hands on block Elastic forces exerted by block on hands Fig. 2.1 Fig. 2.2 xkF   or F = kx (magnitudes) Springs identical except for different lengths have different k values Fig. 2.3 Springs identical except for different materials have