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Figure 4-1 The book is the system The table, the hand, and Earth s mass (through gravity) all exert forces on the book
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Again, think about the different ways in which you could move a textbook You could touch it directly and push or pull it, or you could tie a string around it and pull on the string These are examples of contact forces A contact force exists when an object from the external world touches a system and thereby exerts a force on it If you are holding this physics textbook right now, your hands are exerting a contact force on it If you place the book on a table, you are no longer exerting a force on the book The table, however, is exerting a force because the table and the book are in contact There are other ways in which you could change the motion of the textbook You could drop it, and as you learned in 3, it would accelerate as it falls to the ground The gravitational force of Earth acting on the book causes this acceleration This force affects the book whether or not Earth is actually touching it This is an example of a field force Field forces are exerted without contact Can you think of other kinds of field forces If you have ever experimented with magnets, you know that they exert forces without touching You will investigate magnetism and other similar forces in more detail in future chapters For now, the only field force that you need to consider is the gravitational force Forces result from interactions; thus, each force has a specific and identifiable cause called the agent You should be able to name the agent exerting each force, as well as the system upon which the force is exerted For example, when you push your textbook, your hand (the agent) exerts a force on the textbook (the system) If there are not both an agent and a system, a force does not exist What about the gravitational force If you allow your textbook to fall, the agent is the mass of Earth exerting a field force on the book
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4 Forces in One Dimension
Contact with external world Frope on ball
y System
Contact with external world Fhand on ball
Figure 4-2 To make a physical model of the forces acting on an object, apply the particle model and draw an arrow to represent each force Label each force, including its agent
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FEarth s mass
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Free-body diagrams Just as pictorial models and motion diagrams are useful in solving problems about motion, similar representations will help you to analyze how forces affect motion The first step in solving any problem is to create a pictorial model For example, to represent the forces on a ball tied to a string or held in your hand, sketch the situations, as shown in Figures 4-2a and 4-2b Circle the system and identify every place where the system touches the external world It is at these places that contact forces are exerted Identify the contact forces Then identify any field forces on the system This gives you the pictorial model To make a physical representation of the forces acting on the ball in Figures 4-2a and 4-2b, apply the particle model and represent the object with a dot Represent each force with a blue arrow that points in the direction that the force is applied Try to make the length of each arrow proportional to the size of the force Often, you will draw these diagrams before you know the magnitudes of all the forces In such cases, make your best estimate Always draw the force arrows pointing away from the particle, even when the force is a push Make sure that you label each force Use the symbol F with a subscript label to identify both the agent and the object on which the force is exerted Finally, choose a direction to be positive and indicate this off to the side of your diagram Usually, you select the positive direction to be in the direction of the greatest amount of force This typically makes the problem easiest to solve by reducing the number of negative values in your calculations This type of physical model, which represents the forces acting on a system, is called a free-body diagram
For each of the following situations, specify the system and draw a motion diagram and a free-body diagram Label all forces with their agents, and indicate the direction of the acceleration and of the net force Draw vectors of appropriate lengths
1 A flowerpot falls freely from a windowsill (Ignore any forces due to air resistance) 2 A sky diver falls downward through the air at constant velocity (The air exerts an upward force on the person) 3 A cable pulls a crate at a constant speed across a horizontal surface The surface provides a force that resists the crate s motion 4 A rope lifts a bucket at a constant speed (Ignore air resistance) 5 A rope lowers a bucket at a constant speed (Ignore air resistance)
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