CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies
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Click on the Part 2 Experiments link. On this page you can manipulate the times that cream is added as well as the insulating power of the cups. By experimenting with these inputs you will be able to answer the following questions: What happens to the temperature difference at the end of each run as the time difference between when each person adds their cream increases? Why does this happen?
What happens to the temperature difference as the insulating power increases and decreases? Why?
Answer Key for Coffee with the President and Prime Minister
Whose coffee do you think will be hotter? Why do you think so?
Answers will vary.
President’s coffee temperature:
Prime Minister’s coffee temperature:
What assumptions are being made about the temperature of the cream added to the President and Prime Minister’s coffee?
The temperature of the cream added by the President and the Prime Minister is the same.
The change in temperature caused by the addition of the cream is independent of the temperature of the coffee when the cream is added.
What happens to the temperature difference at the end of each run as the time difference between when each person adds their cream increases? Why does this happen?
As the time difference between when the cream is added increases, the temperature difference at the end of the 20 minute run increases. After the cream is added to one cup of coffee, both cups cool and the temperature difference between the two decreases. When the cream is added to the second cup of coffee, the temperature difference is again immediately increased.
What happens to the temperature difference at the end of each run as the insulating power increases and decreases? Why?
The better the insulation, the less temperature change there is over time for the individual cups of coffee. This means that once the cream has been added to both, the two cups of coffee are closer to being at the same temperature. This is observed because increasing the insulating power reduces the amount of heat exchange between the coffee and the surroundings.
Virtual Bungee Jumping
This model explores the physics of a mass-spring system using a bungee jumping analogy. In the Simple experiments section, students manipulate mass and spring constant (number of bungee cords). They are provided with graphs of position vs. time, position vs. velocity, and restoring force vs. position. In the Extended experiments section, students can manipulate initial displacement and the force of gravity as well as mass and spring constant. Graphs of displacement vs. time and velocity vs. time are displayed for each trial.
Directions and Questions for Virtual Bungee Jumping
To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Virtual Bungee Jumping model.
Open the model with the isee Player and click on Background and Context to read about the problem you will be investigating.
Click on Simple experiments and follow the directions. When you have determined the number of bungee cords that will give you the “best ride” (largest displacement without hitting the ground), click on the Review results link.
On this page, three graphs are displayed: position vs. time, position vs. velocity, and restoring force vs. position. Click on each graph to read a description of the graph.
Now press the Run button and watch the graphs plot as the experiment proceeds and answer the following questions. Note that you may run the simulation multiple times without exiting this page if you need to see a replay of the simulation. When is the velocity of the bungee jumper zero? What is happening to the bungee jumper when the velocity is zero?
When is the velocity of the bungee jumper at a maximum? Where is the bungee jumper at this point?
Does the restoring force increase or decrease when the bungee jumper first jumps? When is the restoring force at a maximum and a minimum?
Go back to the Experiment screen and run several different trials with different masses and numbers of bungee cords. After each run, go to the Review Results page and look at the graphs. What effect does changing the mass seem to have on the total displacement (amplitude), velocity, and restoring force?
What happens to the number of bounces (period) as the mass changes?
What effect does changing the number of bungee cords seem to have on the total displacement, velocity, and restoring force?
What happens to the number of bounces (period) as the number of bungee cords changes?
The bungee jumper represents a mass-spring system, with the jumper acting as the mass and the bungee cords acting as the spring. Do more bungee cords correspond to a stiffer spring or a looser spring? Explain.
Return to the home page and click on Extended Experiments. You will now be able to control the platform height (initial displacement) and force of gravity as well as the mass and number of bungee cords. Experiment to determine how gravity affects the total displacement, velocity, restoring force, and period of the system. Write a paragraph to describe these effects.
Answer Key for Virtual Bungee Jump
When is the velocity of the bungee jumper zero? What is happening to the bungee jumper when the velocity is zero?
When the bungee jumper is at the highest of lowest point of travel. At these points the bungee jumper is changing direction.
When is the velocity of the bungee jumper at a maximum? Where is the bungee jumper at this point?
Velocity is at a maximum halfway between the highest and lowest point. The bungee jumper is in the middle of the jump.
Does the restoring force increase or decrease when the bungee jumper first jumps? When is the restoring force at a maximum and a minimum?
Initially, the restoring force decreases as the bungee jumper is moving away from the platform. Restoring force is at a minimum when the jumper is as far away from the platform as he/she is going to get (maximum displacement). The restoring force is at a maximum when the bungee jumper is at platform (maximum) height.
What effect does changing the mass seem to have on the total displacement (amplitude) and restoring force?
As the mass increases, the amplitude increases.
As the mass increases, the range of values of restoring force increases.
What happens to the number of bounces (period) as the mass changes?
The higher the mass, the fewer the bounces and longer the period.
What effect does changing the number of bungee cords seem to have on the total displacement and restoring force?
As the number of cords increases, the amplitude decreases.
As the number of cords increases, the slope of the line for restoring force vs. position becomes steeper.
What happens to the number of bounces (period) as the number of bungee cords changes?
The number of bounces increase and the period decreases.
The bungee jumper represents a mass-spring system, with the jumper acting as the mass and the bungee cords acting as the spring. Do more bungee cords correspond to a stiffer spring or a looser spring? Explain.
More bungee cords are the same as a stiffer spring. The stiffer the spring, the less displacement there is. When the number of bungee cords is at a minimum, the jumper never bounces back.
What is the effect of gravity on the total displacement, velocity, and period of the system? Write a paragraph to describe the effect.
Gravity increases the displacement and velocity of the jumper, but has no effect on the period.
Virginia Physics Standards of Learning
This chapter fulfills sections PH.2, PH.3, PH.5, and PH.6 of the Virginia Physics Curriculum.
Chapter 13: Modeling and Simulating NASA's Launch Abort System
Introduction
Complex systems abound in our world and it is valuable to model and simulate them to better understand how they work and improve their design. In our case, the model will be a set of physical laws and assumptions that can be applied using a computer program to simulate (
or imitate) the motion of NASA’s Launch Abort System (LAS) system for the Orion Crew Exploration Vehicle (CEV). As stated in the abstract of a paper by Davidson, et al [1] “Aborts during the critical ascent flight phase require the design and operation of Orion Crew Exploration Vehicle (CEV) systems to escape from the Crew Launch Vehicle (CLV) and return the crew safely to the Earth. To accomplish this requirement of continuous abort coverage, CEV ascent abort modes are being designed and analyzed to accommodate the velocity, altitude, atmospheric, and vehicle configuration changes that occur during ascent. Aborts from the launch pad to early in the flight of the CLV second stage are performed using the Launch Abort System (LAS). During this type of abort, the LAS Abort Motor is used to pull the Crew Module (CM) safely away from the CLV and Service Module (SM). LAS abort guidance and control studies and design trades are being conducted so that more informed decisions can be made regarding the vehicle abort requirements, design, and operation.”
The LAS has been tested and according to the NASA web site [2], “NASA's Pad Abort 1 flight test, a launch of the abort system designed for the Orion crew vehicle, lifted off at 9 a.m. EDT May 6 at the U.S. Army's White Sands Missile Range (WSMR) near Las Cruces, N.M. The flight lasted about 135 seconds from launch until the crew module touchdown about a mile north of the launch pad. The flight was the first fully-integrated test of this launch abort system design. The information gathered from the test will help refine design and analysis for future launch abort systems, resulting in safer and more reliable crew escape capability during rocket launch emergencies. Refer to NASA’s myexploration web site for a video of the test flight and more details about the LAS and the Pad Abort 1 flight test.
From the description of the LAS, it is clear that systems can be very complex and you can have systems within systems. The LAS is a subsystem of the CEV system, just as Earth’s atmosphere is a subsystem of the Earth system and the atmosphere plays a very important role in the LAS. It is clear that systems and subsystems can interact to further complicate the modeling.
Physics and Engineering
Physics attempts to understand the physical world through theories and models and engineering applies the models to design and understand real-world objects like the LAS. However, physicists and engineers may both do either physics or engineering, which represent two extremes of a continuum of activities. Osborne Reynolds (1842 –1912), one of the first professors of engineering in the UK, did research in fluid dynamics and developed turbulence principles that allowed data on small models (such as ships) to be applied to larger full-scale objects. Richard Feynman (1918-1988), who won the Nobel Prize for fundamental work in quantum electrodynamics, helped determine the cause of the failure in the Challenger disaster of 1986. In the processes of doing physics or engineering, practitioners use modeling and simulation to help understand theories/laws and to design/understand real-world products.
Theory/Law, Prediction and Observation/Experiment
One way of looking at how science and engineering work is pictured in the diagram below. Scientists and engineers create theories and laws to explain what they observe and then try to predict new things from their theory/law (A law is a statement that is true given a set of assumptions and a theory attempts to offer explanations for basic observed truths. See the chapter, "Toward Understanding Gravitation" in this book for more detail). Then they go back and observe to see if their prediction holds. When their prediction doesn’t hold, they modify their theory/law or maybe even have to build a new theory/law. There is no set order in the theory/law, observe/experiment, predict cycle, and depending on the circumstances, scientists and engineers will jump around between the three complementary processes.
Figure 1: Modeling and simulation using a computer can play a very important role in the above process. (Attribution: Randall Caton, CC-BY-SA.)
Modeling, Simulation and the LAS
Newton’s laws will play an essential role in the process of simulating the LAS as they are the basic laws that govern the motion of the LAS. In programming the simulation using Etoys, we will make various assumptions that will be part of the model. Etoys is embedded in the Squeak programming environment. Squeak is a free, open-source, object-oriented, multimedia authoring environment that runs on many platforms and can be used to construct active learning environments. Programs can be written in the Squeak environment by novices using Etoys graphical programming tiles or by experts using Smalltalk. Everything in the Etoys world is an object. Each object has properties and can send messages to other objects. The objects are like actors on a stage. Each object can be imbued with actions that create interactive experiences for learners and authoring is always on. Students learning from this chapter will be using Etoys to simulate the LAS. When first learning to program simulations, it is best to start with the simplest case and work towards the more complex actual case by relaxing some of the simplifying assumptions. Students will make a series of modifications to the simulation as they progress towards a more realistic model of the LAS.
Describing One-Dimensional Motion
We will start by describing one-dimensional motion, even though the LAS is embedded in a three-dimensional world. As long ago as the century, Galileo Galilei (1564-1642) made great progress in understanding motion in three-dimensions by breaking the problem into separate one-dimensional problems. From centuries of study, scientists have determined that position, velocity, and acceleration are the important and necessary quantities to describe motion. See Kinematics in this book for more discussion of one-dimensional motion: motion diagrams, observing motion with motion sensors, graphing of motion and understanding graphs of motion. Also see Laboratory Activities in this book for experiments on motion.
Position and Displacement
Position is where you are in space. It is measured with respect to a coordinate origin using MKS units of meters. When simulating the one-dimensional rocket, we will be interested in the up and down position of the rocket. We often call that the direction and the position value . Displacement is defined as the difference in position between two elapsed times. Displacement differs from our concept of distance. If we make a round trip going from Minneapolis to Grand Rapids Minnesota, the displacement is zero while the distance traveled is around 650 kilometers. Displacement, not distance, is the crucial concept in understanding motion.
Velocity
Velocity is how fast you move through space. It is the rate of change of position with time. Average velocity is defined as the displacement divided by the time elapsed. For large elapsed times, average velocity gives us a very rough idea of how rapidly we moved through space and sometimes not even that. For the round trip described above the average velocity is zero even though we may have been moving at a reasonable average rate during the whole trip. The concept of average velocity becomes most useful when we consider its limit as the elapsed time interval approaches zero. Then we get a measure of the rate of motion at the instant in question. We call the limit of the average velocity as the elapsed time approaches zero the instantaneous velocity. If you know calculus, it is the derivative of position with time . Graphically, instantaneous velocity is the slope of the tangent line to the vs. curve at the time in question (see Kinematics for more detail). The concept of instantaneous velocity is essential to a further understanding of motion.
Acceleration
Velocities aren't always steady - they often change with time. Sometimes the magnitude (or absolute value) of the velocity increases, like when you drop a ball, and sometimes velocities decrease or stay steady. It is valuable to realize that we use the same process in defining rates of change of velocity as we did above when defining rates of change of position. Acceleration is the term we use for rate of change of velocity. Average acceleration is the change in velocity divided by the elapsed time. Again it is instantaneous acceleration, or the limit of the average acceleration as the elapsed time approaches zero, that tells the best story about motion. If you know calculus, it is the derivat
ive of velocity with time (, where is the component of the velocity along the direction). Graphically, instantaneous acceleration is the slope of the tangent line to the vs. curve at the time in question. On Earth, freely falling objects accelerate downward at roughly 10 m/s/s. Once the rocket engines cut off, the only force on the rocket is gravity (if we neglect air resistance) and we say the rocket is in freefall accelerating downward at a constant rate – even if its motion continues upward for some time.
Positive and Negative
It is important to assign a positive or negative sign to the values of position, velocity and acceleration. It makes a big difference whether the rocket is going upward or downward. We will choose upward as positive. You could choose downward as positive as long as you are consistent, but every sign would be interpreted oppositely. For position, picking upward positive means that everything above the origin (launch pad) is positive and everything below is negative. For velocity, moving upward is positive and moving downward is negative. Finally, the acceleration of the rocket during the burn is positive because we are increasing its velocity upward. Once the burn stops, the acceleration is negative because gravity pulls the rocket downward. Use the concepts of positive and negative when you analyze and interpret your data and graphs later.
Force: The Cause of Motion
Mass