Force as an Interaction 1.1 Observe and Represent a) Pick up a tennis ball and hold it in your hand. Now pick up a bowling ball and hold it. Do you feel the difference? How can you describe what you feel in simple words? b) Think of how we represented the motion of objects in the last module. What are some possible ways of representing the interaction between your hand and the tennis ball? c) Let s choose the ball as our object of interest. Represent the medicine ball with a dot and label the dot with Ball. Draw an arrow to show how your hand pushes the ball. Connect the tail of the arrow to the dot. This arrow represents the force that your hand exerts on the ball. The word force is used in physics for a physical quantity that characterizes the interaction of two objects. A single object does not have a force by default, as the force is defined through the interaction of two objects. Remember that all physical quantities are measured in units. The unit of force is called the newton (N), where 1 N = (1 kg)(1 m/s 2 ). d) How could you label this force arrow to show that it is the force your hand exerts on the ball? Add this label to your representation. Here s An Idea! To show that the force arrow represents the push that the hand exerts on the ball, we can use a symbol F with two little words at the bottom on the right. These are called subscripts. For example: If we look at the interaction of a golf ball and a golf club while the club is hitting the ball. Then if we choose the golf ball as the object of interest, the golf club exerts a force on the golf ball. As a label for an arrow on a force diagram, this would be written as F club on ball. e) What do you think would happen to the ball if your hand were the only object interacting with it? What does this tell you about other objects interacting with the ball? f) What other objects are interacting with the ball? List each object and the direction of the push or pull.
1.2 Test Your Reasoning a) In the previous activity, did you say that air interacts with the ball for part f? How do you think air interacts with the ball? b) What experiment can you perform to test your idea about whether the air pushes up or down on the ball? c) Use the video experiment at http://paer.rutgers.edu/pt3/movies/bottle_in_vacuum.mov. Before watching the video, write a prediction of what should happen to the bottle based on your hypothesis of how air interacts with the ball. d) Watch the video and summarize what effect the air has on the ball. 1.3 Represent and Reason a) In activity 1.1, did you say that gravity interacts with the ball? Gravity is not an object; you cannot hold or touch it. So when we use the word gravity to note the pull down on all objects on Earth, what is the object that exerts this downward pull? b) Add another arrow on your diagram in 1.1 (c). Label the arrow with the appropriate subscripts. c) What do you notice about the length of the arrows in your diagram? What do you think would happen if the arrow representing the interaction with your hand were longer than the arrow due to the interaction with Earth? If it were the other way around? d) Now draw a diagram for the bowling ball. How are the force arrows different from the arrows on the diagram for the tennis ball? The diagrams you created in activity 1.1 through 1.3 are called force diagrams. Force diagrams are used to represent the forces exerted on an object of interest (system) by other objects. A system is an object or group of objects that we are interested in analyzing. Everything outside the system is called the environment and consists of objects that might interact with and affect the system object s motion. These are external interactions. When we draw force diagrams, we only consider the forces exerted on the system object(s). 1.4 Represent and Reason a) Think of a word to describe how the lengths of the force arrows compare to each other in each force diagram.
When the forces exerted on an object of interest are balanced, we say that the object is in EQUILIBRIUM (equilibrium does not necessarily mean rest). b) How might we represent our force diagrams with a mathematical representation or math statement? Write a math statement for the total force exerted on the bowling ball. Need Some Help? Imagine putting an axis next to the force diagram with the origin at the dot. You can use + for the up direction and for the downward direction. For example: Let s take the situation of a puppy curled up in your lap. Then we can write the total force exerted on the puppy by your legs and Earth as: F legs on dog + F Earth on dog = 0. c) For your math statement, does it matter whether you chose up as positive or down as positive? How would this affect the math statement you wrote? What happens to the total force exerted on the ball if we switched the axis? Notice that depending on the orientation of the axis, either F Hand on Ball or F Earth on Ball has a negative value, thus the sum of a positive and a negative number can be zero. How do we know which force is positive and which one is negative? If the force arrow points in the positive direction of the chosen axis, we consider the force positive. If the +y axis points down, for example, then F Earth on Ball > 0 and F Hand on Ball < 0. d) Look at your force diagrams for the tennis ball and bowling ball? What is the same about the diagrams? What is different? e) Write an expression for the forces exerted on the tennis ball similar to the expression you wrote for the bowling ball. Is the tennis ball in equilibrium? Explain.
1.5 Observe and Explain a) You place an object on a table. Draw a force diagram of the object. b) What is exerting a force that balances the force that Earth exerts on the object? What is the direction of the balancing force? c) Write a mathematical expression for the forces exerted on the object. Specify your axis. d) Some people think that only alive (animate) objects can exert forces. The table is not alive. How can a table push on an object? e) A book rests on top of a table. Jim says that the force exerted by the table on the book is always the same in magnitude as the force exerted by Earth on the book. Why would Jim say this? Do you agree or disagree with Jim? If you disagree, how can you argue your case? The diagrams we constructed above are force diagrams. A force diagram is a physical representation used to analyze and evaluate processes involving forces. In order to create a force diagram, follow the 6 steps below. SKETCH 1. Sketch the situation FORCE DIAGRAM + 2. Circle the object of interest 3. Draw a dot representing the box r F S on B F Floor on S Box on BF 6. Label the forces 4. Identify interactions between the system and other objects. Here: Earth, floor, rope and surface F Earth on Box Check for understanding: What does the length of an arrow on the diagram mean? 5. Draw forces to represent interactions, watch the length of arrows
System: A system is the object of interest that we choose to analyze. Make a sketch of the process that you are analyzing. Then circle the object of interest your system. Everything outside that system is called the environment and consists of objects that might interact with and affect the system object s motion. These are external interactions. Force: A force that one object exerts on another characterizes an interaction between the two objects. Forces are represented by the symbol F and with two subscripts indicating the two objects. For example, if Earth pulls on a ball, we note the force exerted by Earth on the ball as: F Earth on ball. Force is a physical quantity that has both magnitude and direction. The symbol also indicates that in this case our system is the ball and Earth is the external object. If we are interested in the force that the ball exerts on Earth, we write it as F ball on Earth. Reflect: What did you learn about forces in this lesson? You heard the expression May the force be with you. Explain why it is not a possible thing for a force in physics.