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pairs When identifying interaction pairs, keep in mind that they always will occur in two different free-body diagrams, and they always will have the symmetry of subscripts noted on the previous page In this case, there is one interaction pair, Fbook on hand and Fhand on book Notice also that each object has a weight If the weight force is due to an interaction between the object and Earth s mass, then shouldn t each of these objects also exert a force on Earth If this is the case, shouldn t Earth be accelerating Consider a soccer ball sitting on a table The table, in turn, is sitting on Earth, as shown in Figure 4-12 First, analyze the forces acting on the ball The table exerts an upward force on the ball, and the mass of Earth exerts a downward gravitational force on the ball Even though these forces are in the opposite direction on the same object, they are not an interaction pair They are simply two forces acting on the same object, not the interaction between two objects Consider the ball and the table together In addition to the upward force exerted by the table on the ball, the ball exerts a downward force on the table This is one pair of forces The ball and Earth also have an interaction pair Thus, the interaction pairs related to the soccer ball are Fball on table Ftable on ball and Fball on Earth FEarth on ball It is important to keep in mind that an interaction pair must consist of two forces of equal magnitude pointing in opposite directions These opposing forces must act on two different objects that can exert a force against each other The acceleration caused by the force of an object interacting with Earth is usually a very small number Under most circumstances, the number is so small that for problems involving falling or stationary objects, Earth can be treated as part of the external world rather than as a second system Consider Example Problem 3 using the following problem-solving strategies.

Figure 4-12 A soccer ball on a table on Earth is part of two interaction pairs the interaction between the ball and table and the interaction between the ball and Earth (Not to scale)

test=> fetch backward 2 from all_customers; CustomerID | LastName | FirstName + + WIL001 | Williams | Frank BLU002 | Blum | Barbara (2 rows)

In a tug-of-war, predict how the force you exert on your end of the rope compares to the force your opponent exerts if you pull and your opponent just holds the rope

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Use these strategies to solve problems in which there is an interaction between objects in two different systems 1 Separate the system or systems from the external world 2 Draw a pictorial model with coordinate systems for each system and a physical model that includes free-body diagrams for each system 3 Connect interaction pairs by dashed lines 4 To calculate your answer, use Newton s second law to relate the net force and acceleration for each system 5 Use Newton s third law to equate the magnitudes of the interaction pairs and give the relative direction of each force 6 Solve the problem and check the units, signs, and magnitudes for reasonableness

1 Predict how the forces compare if the rope moves in your direction 2 Test your prediction CAUTION: Do not suddenly let go of the rope Analyze and Conclude 3 Compare the force on your end of the rope to the force on your opponent s end of the rope What happened when you started to move your opponent s direction

Earth s Acceleration When a softball with a mass of 018 kg is dropped, its acceleration toward Earth is equal to g, the acceleration due to gravity What is the force on Earth due to the ball, and what is Earth s resulting acceleration Earth s mass is 60 1024 kg

Draw free-body diagrams for the two systems: the ball and Earth Connect the interaction pair by a dashed line Known:

Unknown:

Use Newton s second law to find the weight of the ball FEarth on ball mballa mball( g) Substitute a g 2) (018 kg)(980 m/s Substitute m ball 18 N Use Newton s third law to find Fball on Earth Fball on Earth FEarth on ball ( 18 N) Substitute FEarth on ball 18 N Use Newton s second law to find aEarth aEarth

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Are the units correct Dimensional analysis verifies force in N and acceleration in m/s2 Do the signs make sense Force and acceleration should be positive Is the magnitude realistic Because of Earth s large mass, the acceleration should be small

28 You lift a relatively light bowling ball with your hand, accelerating it upward What are the forces on the ball What forces does the ball exert What objects are these forces exerted on 29 A brick falls from a construction scaffold Identify any forces acting on the brick Also identify any forces that the brick exerts and the objects on which these forces are exerted (Air resistance may be ignored) 30 You toss a ball up in the air Draw a free-body diagram for the ball while it is still moving upward Identify any forces acting on the ball Figure 4-13 Also identify any forces that the ball exerts and the objects on which these forces are exerted 31 A suitcase sits on a stationary airport luggage cart, as in Figure 4-13 Draw a free-body diagram for each object and specifically indicate any interaction pairs between the two

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