tutorials in introductory physics homework solutions

tutorials in introductory physics homework solutions

Tutorials in Introductory Physics Homework Solutions

1. Overview of Introductory Physics Concepts

The overview of introductory physics concepts sets the stage for the core concepts covered in the entire book. The first major idea is the concept of a measurement. A measurement is the action of comparing a physical quality with a standard unit of that quality. If a certain number of standard units can be identified or defined as being in a given array, then the multitude of the quantity can be given as the product of that number and the standard unit. Other major concepts include the types of quantities in physics, and the difference between scalars, which are fully described by a magnitude (a number and some units), and vectors, which are fully described by stating both a magnitude and a direction. Such vector quantities form a fundamental part of the analysis in physics. Scalars and vectors are used to give information about the relative magnitude of a quantity, as well as direction. Another important concept discussed is Newton’s Laws, which are a set of principles that help to explain the motion of objects for which the mass is much larger than the mass of individual molecules. These laws help to describe how a force influences the motion or the velocity of an object, and are used to explain the concept of inertia. A force represents the interaction between matter and energy; it is always known by the effect that it produces. Thus, the concept of forces in relation to the physical behaviors of objects is also discussed in this section. Finally, the physics of motion and the formulation and interpretation of the first equation of motion are discussed in detail. These concepts will serve as the foundation for the study of more complex physical theories in the future. By successfully completing this section, students will be able to derive meaning from a wide array of physical settings and relate the arguments of the theory to practical experiences. The material in this section also serves as the building blocks for a more mathematical approach to physical behaviors, introducing students to the power of computational thought and logic. Can they understand the value of using model-based reasoning to produce code and yield numeric or visual outputs, students grow increasingly aware of those constructs which help account for repeatability and accuracy in science. Such model-based thought, code, and visuals will be employed throughout the book, particularly during the discussion of kinematics and other advanced topics. Students will also begin to discuss and interpret the more theoretical concepts introduced in this section, such as the notions of understanding and explanation and the means by which scientific inquiry develops. These conversations begin to emerge naturally from the more concrete mechanical descriptions as the potential energy and its recounting as negative work opens the door for thoughtful debate. By the end of the first section, students will have taken steps through both physical and qualitative arguments so as to find a linear acceleration and identify.

2. Mechanics: Newton’s Laws and Kinematics

The next section of the book is on mechanics, which includes topics such as Newton’s laws and kinematics. Newton’s three laws of motion are collectively known as Newton’s laws. When an object is at rest or moving at a constant speed in a straight path, it will continue to stay that way unless some net force acts on the object. This is known as Newton’s first law of motion. When a net force acts on an object, it will accelerate in the direction of the net force. The acceleration is directly proportional to the magnitude of the net force and inversely proportional to the mass of the object. This relationship is expressed through a = f / m. This is known as Newton’s second law of motion. We have seen that forces cause acceleration. Now we will discuss a concept called kinematics. Kinematics describes the motion of points, bodies (objects), and systems of bodies (group of objects). The various scientists who initially developed the study of kinematics include Galileo, Newton, and Euler. In kinematics, we are more focused on describing the objects on how they move, their various parameters associated with motion. These parameters include displacement, velocity, time, and the various constants associated with the parameters. Also, we are more focused on deriving equations which explain the motion of the object. We are going to look into these equations in the later sections. Galileo was the first to introduce the basic principles of kinematics. Every student taking a class in mechanics must be well grounded in this subject. Calculus will actually aid, but the knowledge of using the basic kinematic equations is very much essential. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. This is known as an inertial frame of reference. When we compare our earth to other objects in space, sometimes our earth can be assumed as an inertial frame of reference. On earth, the drivers are constantly making adjustments to their vehicles. A sudden brake causes a forward jerk, and such a case is known as non-uniform motion. Also, keep in mind that when a net force is zero, the object is said to be in equilibrium. The equilibrium state could either be at rest or moving at a constant velocity.

3. Electricity and Magnetism

Topic 3 in “Tutorials in Introductory Physics Homework Solutions” focuses on electricity and magnetism. This is the scientific study of the electromagnetic forces that occur in nature. The topic started with electric forces: the attraction or repulsion between two charged objects. It was explained that positive charges are created by removing negative charges and negative charges are created by removing positive charges from a neutral object. Also, forces were discussed. When two positively charged things are interacting, it was stated how the force will act but we were informed that these forces may act as non-contact forces but they are still what’s called ‘field force’ – we cannot see them. Also, a hint was given about what these ‘electric fields’ would look like (they would start from a positive charge and go on to a negative charge). The “Tutorials in Introductory Physics Homework Solutions” covers various concepts in introductory physics. The overview provides a general understanding of these concepts. The book then focuses on mechanics, which includes topics such as Newton’s Laws and Kinematics. The next section covers electricity and magnetism. Following that, the book delves into waves and optics. Finally, there is a section on thermodynamics and modern physics. Overall, the book provides comprehensive solutions to homework problems related to these various areas of physics.

4. Waves and Optics

The Waves and Optics section of the Tutorials in Introductory Physics provides a very effective set of exercises on plane mirrors, convex and concave mirrors, and converging lenses, in addition to topics such as Snell’s law and wave interference. These topics can be readily incorporated into a traditional lecture/discussion course in several ways, such as in-class demonstrations followed by instructor-led discussions or student predictions and peer instruction. As an alternative, group activities followed by a class consensus on the results could be performed. These exercises would then serve as a collection of suggestions for forming more extensive homework assignments or even for designing more elaborate laboratory activities. Moreover, with the strong connection between these concepts and their everyday experiences, students typically express a higher level of interest in geometric and wave optics (as demonstrated by the course evaluation). So, the homework problems and solutions offered in this section are very important to the overall student progress and satisfaction in the course. For instance, “Do other animals, like humans, experience total internal reflection?” is one of the questions given in this section after the introduction of Snell’s law. Its meaning and significance for different animals can be discussed in an interactive approach. The Tutorials in Introductory Physics is designed to help students obtain a deep understanding of a variety of topics in introductory physics course, such as kinematics, Newton’s laws, work and energy, oscillatory motion, and waves. By using this peer instruction method not only will students obtain a better understanding of the concepts but also develop the ability of working in a team and cultivating the interest for the subject.

5. Thermodynamics and Modern Physics

The Thermodynamics and Modern Physics section of “Tutorials in Introductory Physics Homework Solutions” starts with an overview of heat and temperature. In the first tutorial of this section, Tutorial 14, we are asked to find the heat required to convert ice at a certain temperature to water vapor at another temperature. We are asked to work out each step of the process, and to explain what physically is going on at each step. We are also reminded of a few key ideas: that heat is not the same as temperature, but that it is rather a form of energy. Different materials require different amounts of heat to change temperature. The next topic we cover is the kinetic theory of gases, discussed in three tutorials (15-17). We already came across the basics of this theory in the foundation section, but here we explore it in more detail. This theory describes gases as being made up of particles – either atoms or molecules – that are constantly moving. We updated our familiar idea that temperature is a measure of the average kinetic energy of particles in a substance, in that we found equations for the average translational and rotational kinetic energies of each particle in a gas. We also tested certain equations against experimental data, and applied the theory to the idea of an “rms” speed – that is, the root mean square average of the speeds of particles in a substance. The final topic we’ve started so far in the third section of the book is the study of thermodynamics, which is about the inter-conversion of different forms of energy. As with other areas of physics, we don’t learn about thermodynamics as a closed set of ideas. Instead, we continuously update and check our understanding of this area in the light of new results or the development of new theories. The first law of thermodynamics, which is also known as the principle of conservation of energy, is discussed in three tutorials (18-20). We started by looking at the energy of a system, and discussing what it means if it changes. We also examined the ways in which the energy of a closed system can change, for example through heating or work done on the system. Finally, we discussed how heating or work done by a system on its surroundings can result in changes in the macroscopic properties – for example, a temperature rise.