You can learn about physics, and you can learn to do physics. This institute is for the science students who want to become scientists/engineers/doctors. Learning about physics will help you appreciate the role of this fundamental science in explaining both natural and technological phenomena. Learning to do physics will make you adept at solving quantitative problems—finding answers to questions about how the natural world works and about how we forge the technologies at the heart of modern society.
Physics problems can be challenging, calling for clever insight and mathematical agility. That challenge is what gives physics a reputation as a difficult subject. But underlying all of physics is only a handful of basic principles. Because physics is so fundamental, it’s also inherently simple. There are only a few basic ideas to learn; if you really understand those, you can apply them in a wide variety of situations. These ideas and their applications are all connected, and we’ll emphasize those connections and the underlying simplicity of physics by reminding you how the many examples, applications, and problems are manifestations of the same few basic principles. If you approach physics as a hodgepodge of unrelated laws and equations, you’ll miss the point and make things difficult. But if you look for the basic principles, for connections among seemingly unrelated phenomena and problems, then you’ll discover the underlying simplicity that reflects the scope and power of physics—the fundamental science.
Problem Solving: The IDEA Strategy
Solving a quantitative physics problem always starts with basic principles or concepts and ends with a precise answer expressed as either a numerical quantity or an algebraic expression. Whatever the principle, whatever the realm of physics, and whatever the specific situation, the path from principle to answer follows four simple steps, steps that make up a comprehensive strategy for approaching all problems in physics. Their acronym, IDEA, will help you remember these steps, and they’ll be reinforced as we apply them over and over again in classroom examples throughout the course at IMPACT ACADEMY. We’ll generally write all four steps separately, And in some chapters we’ll introduce versions of this strategy tailored to specific material. The IDEA strategy isn’t a “cookbook” formula for working physics problems. Rather, it’s a tool for organizing your thoughts, clarifying your conceptual understanding, developing and executing plans for solving problems, and assessing your answers.
PROBLEM-SOLVING STRATEGY
1. INTERPRET: The first step is to interpret the problem to be sure you know what it’s asking. Then identify the applicable concepts and principles—Newton’s laws of motion, conservation of energy, the first law of thermodynamics, Gauss’s law, and so forth. Also identify the players in the situation—the object whose motion you’re asked to describe, the forces acting, the thermodynamic system you’re to analyse, the charges that produce an electric field, the components in an electric circuit, the light rays that will help you locate an image, and so on.
2. DEVELOP: The second step is to develop a plan for solving the problem. It’s always helpful and often essential to draw a diagram showing the situation. Your drawing should indicate objects, forces, and other physical entities. Labelling masses, positions, forces, velocities, heat flows, electric or magnetic fields, and other quantities will be a big help. Next, determine the relevant mathematical formulas—namely, those that contain the quantities you’re given in the problem as well as the unknown(s) you’re solving for. Don’t just grab equations—rather, think about how each reflects the underlying concepts and principles that you’ve identified as applying to this problem. The plan you develop might include calculating intermediate quantities, finding values in a table, or even solving a preliminary problem whose answer you need in order to get your final result.
3. EVALUATE: Physics problems have numerical or symbolic answers, and you need to evaluate your answer. In this step you execute your plan, going in sequence through the steps you’ve outlined. Here’s where your math skills come in. Use algebra, trig, or calculus, as needed, to solve your equations. It’s a good idea to keep all numerical quantities, whether known or not, in symbolic form as you work through the solution of your problem. At the end you can plug in numbers and work the arithmetic to evaluate the numerical answer, if the problem calls for one.
4. ASSESS: Don’t be satisfied with your answer until you assess whether it makes sense! Are the units correct? Do the numbers sound reasonable? Does the algebraic form of your answer work in obvious special cases, like perhaps “turning off” gravity or making an object’s mass zero or infinite? Checking special cases not only helps you decide whether your answer makes sense but also can give you insights into the underlying physics. In classroom examples, we’ll often use this step to enhance your knowledge of physics by relating the example to other applications of physics.
Don’t memorize the IDEA problem-solving strategy. Instead, grow to understand it as you see it applied in examples and as you apply it yourself in working assignment problems.
