Section 1 Objectives Describe how force affects the motion of an object. Interpret and construct free-body diagrams. force an action exerted on an object that may change the object s state of rest or motion Changes in Motion Key Term force Force You exert a force on a ball when you throw or kick the ball, and you exert a force on a chair when you sit in the chair. Forces describe the interactions between an object and its environment. Forces can cause accelerations. In many situations, a force exerted on an object can change the object s velocity with respect to time. Some examples of these situations are shown in Figure 1.1. A force can cause a stationary object to move, as when you throw a ball. Force also causes moving objects to stop, as when you catch a ball. A force can also cause a moving object to change direction, such as when a baseball collides with a bat and flies off in another direction. Notice that in each of these cases, the force is responsible for a change in velocity with respect to time an acceleration. Figure 1.1 Three Ways That Forces Change Motion Force can cause objects to start moving, stop moving, and/or (c) change direction. (c) The SI unit of force is the newton. The SI unit of force is the newton, named after Sir Isaac Newton (1642 1727), whose work contributed much to the modern understanding of force and motion. The newton (N) is defined as the amount of force that, when acting on a 1 kg mass, produces an acceleration of 1 m/s 2. Therefore, 1 N = 1 kg 1 m/s 2. The weight of an object is a measure of the magnitude of the gravitational force exerted on the object. It is the result of the interaction of an 118
Figure 1.2 Units of Mass, Acceleration, and Force System Mass Acceleration Force SI kg m/s 2 N = kg m/s 2 Did YOU Know? The symbol for the pound, lb, comes from libra, the Latin word for pound, a unit of measure that has been used since medieval times to measure weight. cgs g cm/s 2 dyne = g cm/s 2 Avoirdupois slug ft/s 2 lb = slug ft/s 2 object s mass with the gravitational field of another object, such as Earth. As shown in Figure 1.2, many of the terms and units you use every day to talk about weight are really units of force that can be converted to newtons. For example, a _ 1 lb stick of margarine has a weight equivalent to a 4 force of about 1 N, as shown in the following conversions: 1 lb = 4.448 N 1 N = 0.225 lb Forces can act through contact or at a distance. If you pull on a spring, the spring stretches. If you pull on a wagon, the wagon moves. When a football is caught, its motion is stopped. These pushes and pulls are examples of contact forces, which are so named because they result from physical contact between two objects. Contact forces are usually easy to identify when you analyze a situation. Another class of forces called field forces does not involve physical contact between two objects. One example of this kind of force is gravitational force. Whenever an object falls to Earth, the object is accelerated by Earth s gravity. In other words, Earth exerts a force on the object even when Earth is not in immediate physical contact with the object. Another common example of a field force is the attraction or repulsion between electric charges. You can observe this force by rubbing a balloon against your hair and then observing how little pieces of paper appear to jump up and cling to the balloon s surface, as shown in Figure 1.3. The paper is pulled by the balloon s electric field. The theory of fields was developed as a tool to explain how objects could exert force on each other without touching. According to this theory, masses create gravitational fields in the space around them. An object falls to Earth because of the interaction between the object s mass and Earth s gravitational field. Similarly, charged objects create electromagnetic fields. The distinction between contact forces and field forces is useful when dealing with forces that we observe at the macroscopic level. (Macroscopic refers to the realm of phenomena that are visible to the naked eye.) As we will see later, all macroscopic contact forces are actually due to microscopic field forces. For instance, contact forces in a collision are due to electric fields between atoms and molecules. In fact, every force can be categorized as one of four fundamental field forces. Figure 1.3 Electric Force The electric field around the rubbed balloon exerts an attractive electric force on the pieces of paper. Forces and the Laws of Motion 119
Materials 1 toy car 1 book Force and Changes in Motion Use a toy car and a book to model a car colliding with a brick wall. Observe the motion of the car before and after the crash. Identify as many changes in its motion as you can, such as changes in speed or direction. Make a list of all of the changes, and try to identify the forces that caused them. Make a force diagram of the collision. Force Diagrams When you push a toy car, it accelerates. If you push the car harder, the acceleration will be greater. In other words, the acceleration of the car depends on the force s magnitude. The direction in which the car moves depends on the direction of the force. For example, if you push the toy car from the front, the car will move in a different direction than if you push it from behind. Force is a vector. Because the effect of a force depends on both magnitude and direction, force is a vector quantity. Diagrams that show force vectors as arrows, such as Figure 1.4, are called force diagrams. In this book, the arrows used to represent forces are blue. The tail of an arrow is attached to the object on which the force is acting. A force vector points in the direction of the force, and its length is proportional to the magnitude of the force. At this point, we will disregard the size and shape of objects and assume that all forces act at the center of an object. In force diagrams, all forces are drawn as if they act at that point, no matter where the force is applied. A free-body diagram helps analyze a situation. After engineers analyzing a test-car crash have identified all of the forces involved, they isolate the car from the other objects in its environment. One of their goals is to determine which forces affect the car and its passengers. Figure 1.4 is a free-body diagram. This diagram represents the same collision that the force diagram does but shows only the car and the forces acting on the car. The forces exerted by the car on other objects are not included in the free-body diagram because they do not affect the motion of the car. A free-body diagram is used to analyze only the forces affecting the motion of a single object. Free-body diagrams are constructed and analyzed just like other vector diagrams. In Sample Problem A, you will learn to draw free-body diagrams for some situations described in this book. Later, you will learn to use free-body diagrams to find component and resultant forces. Figure 1.4 Force Diagrams Versus Free-body Diagrams In a force diagram, vector arrows represent all the forces acting in a situation. A free-body diagram shows only the forces acting on the object of interest in this case, the car. 120
Drawing Free-Body Diagrams Sample Problem A The photograph at right shows a person pulling a sled. Draw a free-body diagram for this sled. The magnitudes of the forces acting on the sled are 60 N by the string, 130 N by Earth (gravitational force), and 90 N upward by the ground. Analyze Identify the forces acting on the object and the directions of the forces. The string exerts 60 N on the sled in the direction that the string pulls. Earth exerts a downward force of 130 N on the sled. The ground exerts an upward force of 90 N on the sled. Tips and Tricks In a free-body diagram, only include forces acting on the object. Do not include forces that the object exerts on other objects. In this problem, the forces are given, but later in the chapter, you will need to identify the forces when drawing a free-body diagram. Plan Draw a diagram to represent the isolated object. It is often helpful to draw a very simple shape with some distinguishing characteristics that will help you visualize the object, as shown in. Free-body diagrams are often drawn using simple squares, circles, or even points to represent the object. solve Draw and label vector arrows for all external forces acting on the object. A free-body diagram of the sled will show all the forces acting on the sled as if the forces are acting on the center of the sled. First, draw and label an arrow that represents the force exerted by the string attached to the sled. The arrow should point in the same direction as the force that the string exerts on the sled, as in. Tips and Tricks When you draw an arrow representing a force, it is important to label the arrow with either the magnitude of the force or a name that will distinguish it from the other forces acting on the object. Also, be sure that the length of the arrow approximately represents the magnitude of the force. (c) F Earth Birgit Koch/age fotostock Next, draw and label the gravitational force, which is directed toward the center of Earth, as shown in (c). Finally, draw and label the upward force exerted by the ground, as shown in (d). Diagram (d) is the completed free-body diagram of the sled being pulled. (d) F ground F Earth Continued Forces and the Laws of Motion 121
Drawing Free-Body Diagrams (continued) 1. A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are the force due to gravity (250 000 N downward), the force exerted by the road (250 000 N upward), and the force exerted by the cable connecting the trailer to the truck (20 000 N to the right). The forces acting on the truck are the force due to gravity (80 000 N downward), the force exerted by the road (80 000 N upward), the force exerted by the cable (20 000 N to the left), and the force causing the truck to move forward (26 400 N to the right). a. Draw and label a free-body diagram of the trailer. b. Draw and label a free-body diagram of the truck. 2. A physics book is at rest on a desk. Gravitational force pulls the book down. The desk exerts an upward force on the book that is equal in magnitude to the gravitational force. Draw a free-body diagram of the book. Section 1 Formative ASSESSMENT Reviewing Main Ideas 1. List three examples of each of the following: a. a force causing an object to start moving b. a force causing an object to stop moving c. a force causing an object to change its direction of motion 2. Give two examples of field forces described in this section and two examples of contact forces you observe in everyday life. Explain why you think that these are forces. 3. What is the SI unit of force? What is this unit equivalent to in terms of fundamental units? 4. Why is force a vector quantity? 5. Draw a free-body diagram of a football being kicked. Assume that the only forces acting on the ball are the force due to gravity and the force exerted by the kicker. Interpreting Graphics 6. Study the force diagram on the right. Redraw the diagram, and label each vector arrow with a description of the force. In each description, include the object exerting the force and the object on which the force is acting. 122