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146 Chapter 4 | Dynamics: Force and Newton's Laws of Motion
of change of position with time.
Essential Knowledge 4.A.3 Forces that systems exert on each other are due to interactions between objects in the systems. If the interacting objects are parts of the same system, there will be no change in the center-of-mass velocity of that system.
Big Idea 5 Changes that occur as a result of interactions are constrained by conservation laws.
Enduring Understanding 5.A Certain quantities are conserved, in the sense that the changes of those quantities in a given
system are always equal to the transfer of that quantity to or from the system by all possible interactions with other systems.
Essential Knowledge 5.A.1 A system is an object or a collection of objects. The objects are treated as having no internal structure.
4.1 Development of Force Concept
Learning Objectives
By the end of this section, you will be able to: • Understand the definition of force.
The information presented in this section supports the following AP® learning objectives and science practices:
• 3.A.2.1 The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with magnitude, direction, and units during the analysis of a situation. (S.P. 1.1)
• 3.A.3.2 The student is able to challenge a claim that an object can exert a force on itself. (S.P. 6.1)
• 3.A.3.3 The student is able to describe a force as an interaction between two objects and identify both objects for any
force. (S.P. 1.4)
• 3.B.2.1 The student is able to create and use free-body diagrams to analyze physical situations to solve problems with
motion qualitatively and quantitatively. (S.P. 1.1, 1.4, 2.2)
Dynamics is the study of the forces that cause objects and systems to move. To understand this, we need a working definition of force. Our intuitive definition of force—that is, a push or a pull—is a good place to start. We know that a push or pull has both magnitude and direction (therefore, it is a vector quantity) and can vary considerably in each regard. For example, a cannon exerts a strong force on a cannonball that is launched into the air. In contrast, Earth exerts only a tiny downward pull on a flea. Our everyday experiences also give us a good idea of how multiple forces add. If two people push in different directions on a third person, as illustrated in Figure 4.3, we might expect the total force to be in the direction shown. Since force is a vector, it adds just like other vectors, as illustrated in Figure 4.3(a) for two ice skaters. Forces, like other vectors, are represented by arrows and can be added using the familiar head-to-tail method or by trigonometric methods. These ideas were developed in Two-Dimensional Kinematics.
By definition, force is always the result of an interaction of two or more objects. No object possesses force on its own. For example, a cannon does not possess force, but it can exert force on a cannonball. Earth does not possess force on its own, but exerts force on a football or on any other massive object. The skaters in Figure 4.3 exert force on one another as they interact.
No object can exert force on itself. When you clap your hands, one hand exerts force on the other. When a train accelerates, it exerts force on the track and vice versa. A bowling ball is accelerated by the hand throwing it; once the hand is no longer in contact with the bowling ball, it is no longer accelerating the bowling ball or exerting force on it. The ball continues moving forward due to inertia.
Figure 4.3 Part (a) shows an overhead view of two ice skaters pushing on a third. Forces are vectors and add like other vectors, so the total force on the third skater is in the direction shown. In part (b), we see a free-body diagram representing the forces acting on the third skater.
Figure 4.3(b) is our first example of a free-body diagram, which is a technique used to illustrate all the external forces acting on a body. The body is represented by a single isolated point (or free body), and only those forces acting on the body from the outside (external forces) are shown. (These forces are the only ones shown, because only external forces acting on the body
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