1.1 System, Environment, Process Constant vs Conserved From time to time, we will find it useful to focus our attention on a certain part of the universe and consider it separately from everything else. We select a number of physical objects and call them the system. Everything else in the universe is called the environment. As time goes by, the system may change. We can pick two clock readings, and call what happens in between a process. Before the process, the system is in its initial state and at the end of the process the system is in its final state. In a sketch, we outline the system objects carefully. If the earth is in the system we show this clearly. Consider the following sketches of a system which includes two carts on a track: a. In the sketch above, what objects are in the system? b. What objects are NOT in the system? c. Describe the process that occurred d. External interactions are between a system object and an object in the environment. Describe at least two external interactions in this process e. Internal interactions are between two system objects. Describe one above. f. Describe a "process" that might occur in a playground. Select system objects and sketch initial and final states. The concept of "system" is similar to "object of interest" except that a system can contain many objects. The choice of system objects is up to the investigator and depends on the problem being addressed. Learning to choose useful systems is part of the skill that makes you a good scientist. Like any other skill, it is developed by trial and error at first, then improved by practice. Constant and Conserved Constant describes a quantity that does not change over a time interval. For example, the amount of money in my pocket is constant from 6am when I get up to 11am when I go to lunch. The amount does not change. Conserved describes a quantity that may change during a period of time, but does NOT appear from nowhere or disappear without trace. You can always find a system within which a conserved quantity is constant. For example: At 11am I spend $2.75 on lunch in the cafeteria. The amount of money in my pocket changes, but my money does not disappear. The cafeteria lady has it now. a. In the "buying lunch" situation, within what choice of system is the quantity of money NOT constant? b. Within what choice of system is the quantity of money constant?
1.2 Observe and Find a Pattern a) Observe the following experiments with two frictionless carts moving on a smooth track. Then use the data in the table below to complete a quantitative analysis for each experiment. Consider your system of analysis to be both carts. 1. Cart A (500 g) is moving left at a constant speed (1.0 m/s) and hits identical cart B (500 g) that is stationary. Cart A stops, and cart B starts moving at a constant speed (1.0 m/s) to the left. 2. Cart A, loaded with blocks (total mass 800 g) and moving left at 2 m/s hits Cart B (mass 400 g) which is stationary. After the collision, both carts move to the left, cart B at 2.0 m/s and cart A at 1.0 m/s.
3. Cart A (500 g) has a piece of front and moves left at 1.0 m/s. Identical cart B (500 g) moves right at constant speed 1.0 m/s. The carts collide, stick together, and stop. 4. Cart A, loaded with blocks (total mass 800 g) has a piece of front and moves left at 1.0 m/s. Cart B (400 g) moves right at constant speed 1.0 m/s. The carts collide, stick together, and move left at 0.33 m/s.
5. Cart A, loaded with blocks (total mass 800 g) has a piece of front and moves left at 2.0 m/s. Cart B (400 g) moves right at constant speed 1.0 m/s. The carts collide, stick together, and move left at 1.0 m/s. b) After you come up with a physical quantity that is conserved in each experiment, decide if a quantity, or a combination of quantities is conserved in all experiments. 1.3 Observe and Explain The table below provides more data about the collisions of two different carts, including the initial velocities of the carts before the collision (v i ), the final velocities after the collision (v f ), and the masses of the carts. (hint: pay attention to the vector signs for the velocities) Before Collision After Collision Cart 1 v i1 (m/s) Cart 2 v i2 (m/s) Cart 1 v f1 (m/s) Cart 2 v f2 (m/s) 1 m + 2.0 m 0 m + 1.0 m + 1.0 2 m + 2.0 m -2.0 m - 1.0 m + 1.0 3 2m + 2.0 m -1.5 2m + 0.5 m + 1.5 4 2m + 2.0 m -2.0 2m 0 m + 2.0 a) Determine if the same quantity is conserved in these experiments as was conserved in the previous activity. b) Based on the experiments above, make a judgment about the quantity you identified in 1.2. c) Why is mass x speed not appropriate for the constant quantity? Give an example from the experiments above where mass x speed is not constant. d) What are the units for this new physical quantity?
1.4 Regular Problem A 1998 910-kg Toyota Tercel travels at a speed of 32 m/s. (a) At what speed must a 2002 1950-kg Toyota 4Runner travel to have the same momentum? (b) At what speed must a 7.3-kg bowling ball travel to have the same momentum? 1.5 Regular Problem Your 0.0567-kg tennis ball traveling at 25 m/s hits a practice wall and rebounds in the opposite direction with the same speed. Sketch the before and after situations. What is the ball s change in momentum (both magnitude and direction)? 1.6 Regular Problem An 85-kg defensive tackle runs down the football field at 7 m/s when he collides with a 70 kg tight-end who is standing still to receive the football. The defensive tackle grabs the tight-end as they collide. Draw a sketch of the initial and final state. Identify your system. How fast and in what direction are the two football players moving after they collide? 1.7 Multiple-choice Question Which of the following objects has the greatest momentum? a) A 3000 kg truck stopped in traffic. b) A 950 kg Chevrolet minivan moving at 18 m/s. c) A 40 g bullet traveling at a speed of 120 m/s. d) A 52 kg figure skater gliding across the ice at 3 m/s. Reflect: How do you understand the concept of momentum? How can you represent momentum? How is momentum different from velocity? How is momentum different from the product of mass and speed?