Lesson 1: Force as an Interaction

Transcription

1 1.1 Observe and Represent Lesson 1: Force as an Interaction a) Pick up a tennis ball and hold it in your hand. Now pick up a medicine 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. 4 PUM Dynamics Lesson 1: Force as an Interaction

2 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 on the website or CD if your class does not have the equipment. Before watching the video or performing the experiment, write a prediction of what should happen to the bottle based on your hypothesis. d) Watch the video or perform the experiment: (Or on the CD it is on the List of Videos, Bottle in a vacuum). e) 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 heavy 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). PUM Dynamics Lesson 1: Force as an Interaction 5

3 1.4 Represent and Reason a) Think of a word to describe the force arrows 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 medicine 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 medicine 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 medicine ball. Is the tennis ball in equilibrium? Explain. 1.5 Observe and Explain a) Perform the experiments described in the first column. Then record your data and fill in the empty cells. Remember that the scale, as a measuring instrument, has an uncertainty of measurement associated with it. 6 PUM Dynamics Lesson 1: Force as an Interaction

4 Experiment Draw a picture of the apparatus. List objects interactin g with the object of interest. Draw a force diagram for the object. Discuss what objects exert forces balancing the force that Earth exerts on the object. What is/are the direction of the balancing force/forces? Write a mathematical expression for the forces exerted on the object. Specify your axis. (a) Hang an object from a spring scale. Record reading of the scale here (b) Lower the object onto a platform scale so it touches the scale. Record new reading of the spring scale Record the reading platform scale (c) Remove the spring scale and leave the object on the platform scale. Record new reading platform scale (d) You place the object on a horizontal meter stick whose ends rest on two blocks. Record what happens (e) You place the object on a thick, foam cushion. Record what happens (f) You place the object on a tabletop. Record what happens (g) You place the block on the platform scale and then tilt the scale at a small angle. Record what happens PUM Dynamics Lesson 1: Force as an Interaction 7

5 a) Some people think that only alive (animate) objects can exert forces. The table is not alive. How can a table push on an object? b) 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? 1.6 Reason a) Summarize in what direction the force is exerted on an object of interest by the supporting object. b) Is this force always equal in magnitude and direction to the force that Earth exerts on the object? Provide experimental evidence and reasoning to support your opinion. c) Look at the force diagram shown in the below. How would the force diagram change if instead of dragging the box on a smooth floor, you dragged it on the carpet? 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. 1. Sketch the situation SKETCH FORCE DIAGRAM y 2. Circle the object of interest 3. Draw a dot representing the box F Floor on Box 6. Label the forces F Rope on Box 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 8 PUM Dynamics Lesson 1: Force as an Interaction

6 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. The force causes some effect or influence of the one object on the second object. Forces are represented by a symbol with an arrow above it to show that the force has direction 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. The arrow above force indicates that force is the physical quantity that both has magnitude and direction. The symbol also indicated 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 will write it as F Ball on Earth. 1.7 Reason Describe a situation in which a surface exerts ONLY a horizontal force on the object. Draw a picture of the situation. Then draw a force diagram. 1.8 Represent and Reason A person pushes a box across a very smooth floor. a) Examine the force diagram to the right. Do the forces in the vertical direction balance? Do the forces in the horizontal direction balance? b) Draw an arrow to indicate the direction of the unbalanced force, if there is one. Discuss whether the result is reasonable. 1.9 Represent and Reason PUM Dynamics Lesson 1: Force as an Interaction 9

7 Read each of the scenarios and then draw a force diagram for the selected object of interest. 1. You are throwing a tennis ball upward. Consider the moment right before the ball leaves your hand. The ball is the object of interest. 3. The ball is at the top of the flight. The ball is the object of interest 2. The ball is flying up. The ball is the object of interest. 4. The ball is being caught by you. Consider the moment when your hands are stopping the ball. The ball is the object of interest. Now use the rubric below to self-assess your force diagrams. Do not worry about the length of force arrows yet. Missing An attempt Needs improvement Acceptable No force diagram is constructed. Force diagram is constructed but contains major errors: missing or extra forces (not matching with the interacting objects), incorrect directions of arrows, or incorrect relative length of force arrows. Force diagram contains no errors in force arrows but lacks a key feature such as labels of forces with two subscripts or forces are not drawn from single point. The diagram contains forces for each interaction and each force is labeled so that one can clearly understand what each force represents. Relative lengths of force arrows are correct. 10 PUM Dynamics Lesson 1: Force as an Interaction

8 Homework 1.10 Represent and Reason a) Draw force diagrams and use them to determine the direction of the unbalanced force exerted on the following objects of interest: i. A hockey puck moving on ice slows to a stop. The puck is the object of interest. ii. A box is sliding down an inclined plane. The box is the object of interest. iii. You start lifting up a heavy suitcase; the suitcase is the object of interest. iv. A boat floats in the ocean; the boat is the object of interest. v. You are pulling a sled on fresh snow at constant speed; the sled is the object of interest. vi. You are pushing a lawnmower; the lawnmower is the object of interest. b) Examine the unlabeled force diagrams and come up with a real life situation that they might describe. Then label each force with the appropriate subscripts Reason You are sitting on a chair reading this problem. What are the objects that exert forces on the chair? Choose the right answer: (a) no forces are exerted on the chair; (b) you are exerting a force; (c) you, Earth and gravity; (d) Earth, floor, and you; (e) floor, you and gravity Represent and reason You are holding a medicine ball steady. Choose the force diagram that represents the forces exerted on the ball best: a) b) c) d) e) F H on B F H on B F E on B F E on B F E on B F E on B F H on B 1.13 Estimate uncertainty F gravity Rob and Tina collected data using a scale that had divisions every newton (N): 0 N, 1 N, 2 N, 3 N, etc. When Tina hung her bag on the spring scale, she wrote the reading of the scale as 2.2 N. Rob repeated the experiment and wrote the reading as 2.3 N. They used the same bag. Why are their numbers different? Who do you think is correct? Based on your answer, decide how precisely you can measure the force with this scale Estimate uncertainty Find three measuring devices in your house (each one needs to show the quantity that it is measuring, the units of measurement, and a scale). a) Write down the experimental uncertainty for each instrument. You may need to recall how we determined experimental uncertainty in the kinematics module. PUM Dynamics Lesson 1: Force as an Interaction 11

9 b) Now take a measurement with each instrument and write the result so that it incorporates the experimental uncertainty Estimate Uncertainty You drop a tennis ball from the second floor window three times. Your friend Tina is using a stopwatch to record the time of flight. Here are the results of her measurements: 1.11 s; 1.14 s; and 1.12 s. What is the average time Tina measured? What is the random uncertainty of the measurement? Write the result in the form of t = t average ± t Significant Figures Two friends are discussing their cash allowance. Jake says that he gets $15month. Robin says that she gets $15.00 a month. Who is more likely to get more per month? 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. 12 PUM Dynamics Lesson 1: Force as an Interaction