# Solving Physics Problems

At some point in their studies, almost all physics students find themselves thinking, “I understand the concepts, but I just can’t solve the problems.” But in physics, truly understanding a concept means being able to apply it to a variety of problems. Learning how to solve problems is absolutely essential; you don’t know physics unless you can do physics.

How do you learn to solve physics problems? In every chapter of this book you will find Problem-Solving Strategies that offer techniques for setting up and solving problems efficiently and accurately. Following each Problem-Solving Strategy are one or more worked Examples that show these techniques in action. (The Problem-Solving Strategies will also steer you away from some incorrect techniques that you may be tempted to use.) You’ll also find additional examples that aren’t associated with a particular Problem-Solving Strategy. In addition, at the end of each chapter you’ll find a Bridging Problem that uses more than one of the key ideas from the chapter. Study these strategies and problems carefully, and work through each example for yourself on a piece of paper.

Different techniques are useful for solving different kinds of physics problems, which is why this book offers dozens of Problem-Solving Strategies. No matter what kind of problem you’re dealing with, however, there are certain key steps that you’ll always follow. (These same steps are equally useful for problems in math, engineering, chemistry, and many other fields.) In this book we’ve organized these steps into four stages of solving a problem.

All of the Problem-Solving Strategies and Examples in this book will follow these four steps. (In some cases we will combine the first two or three steps.) We encourage you to follow these same steps when you solve problems yourself. You may find it useful to remember the acronym I SEE—short for Identify, Set up, Execute, and Evaluate.

Topics You May Be Interested In
Nature Of Physics Buoyancy
Solving Physics Problems The Gravitational Force Between Spherical Mass Distributions
Solved Examples On Equilibrium Black Holes, The Schwarzschild Radius, And The Event Horizon
Fluid Mechanics Summary
Absolute Pressure And Gauge Pressure Simple Harmonic Motion

Idealized Models

In everyday conversation we use the word “model” to mean either a small-scale replica, such as a model railroad, or a person who displays articles of clothing (or the absence thereof). In physics a model is a simplified version of a physical system that would be too complicated to analyze in full detail.

For example, suppose we want to analyze the motion of a thrown baseball (Fig. 1.2a). How complicated is this problem? The ball is not a perfect sphere (it has raised seams), and it spins as it moves through the air. Air resistance and wind influence its motion, the ball’s weight varies a little as its altitude changes, and so on. If we try to include all these things, the analysis gets hopelessly complicated. Instead, we invent a simplified version of the problem. We ignore the size and shape of the ball by representing it as a point object, or particle. We ignore air resistance by making the ball move in a vacuum, and we make the weight constant. Now we have a problem that is simple enough to deal with (Fig. 1.2b). We will analyze this model in detail in Chapter 3.

We have to overlook quite a few minor effects to make an idealized model, but we must be careful not to neglect too much. If we ignore the effects of gravity completely, then our model predicts that when we throw the ball up, it will go in a straight line and disappear into space. A useful model simplifies a problem enough to make it manageable, yet keeps its essential features.

Topics You May Be Interested In
Vectors And Vector Addition Kepler's Third Law
Summary Of Equilibrium And Elasticity Black Holes
Pressure Gauges The Escape Speed From A Star
Deriving Bernoullis Equation A Visit To A Black Hole
Turbulence Periodic Motion

The validity of the predictions we make using a model is limited by the validity of the model. For example, Galileo’s prediction about falling objects (see Section 1.1) corresponds to an idealized model that does not include the effects of air resistance. This model works fairly well for a dropped cannonball, but not so well for a feather.

Idealized models play a crucial role throughout this book. Watch for them in discussions of physical theories and their applications to specific problems.

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Ans: Introduce the systems of units used to describe physical quantities and discuss ways to describe the accuracy of a number. view more..
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Ans: Different techniques are useful for solving different kinds of physics problems, which is why this book offers dozens of Problem-Solving Strategies view more..
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Ans: Experiments require measurements, and we generally use numbers to describe the results of measurements. Any number that is used to describe a physical phenomenon quantitatively is called a physical quantity. view more..
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Ans: An equation must always be dimensional consistent. You can’t add apples and automobiles; two terms may be added or equated only if they have the same units. view more..
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Ans: Measurements always have uncertainties. If you measure the thickness of the cover of a hardbound version of this book using an ordinary ruler, your measurement is reliable to only the nearest millimeter, and your result will be 3 mm. It would be wrong to state this result as 3.00 mm; given the limitations of the measuring device, you can’t tell whether the actual thickness is 3.00 mm, 2.85 mm, or 3.11 mm. view more..
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Ans: We have stressed the importance of knowing the accuracy of numbers that represent physical quantities. But even a very crude estimate of a quantity often gives us useful information. Sometimes we know how to calculate a certain quantity, but we have to guess at the data we need for the calculation. Or the calculation might be too complicated to carry out exactly, so we make rough approximations. view more..
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Ans: Some physical quantities, such as time, temperature, mass, and density, can be described completely by a single number with a unit. But many other important quantities in physics have a direction associated with them and cannot be described by a single number. view more..
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Ans: A body that can be modeled as a particle is in equilibrium whenever the vector sum of the forces acting on it is zero. But for the situations we’ve just described, that condition isn’t enough. If forces act at different points on an extended body, an additional requirement must be satisfied to ensure that the body has no tendency to rotate: The sum of the torques about any point must be zero. This requirement is based on the principles of rotational dynamics view more..
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Ans: In this chapter we’ll apply the first and second conditions for equilibrium to situations in which a rigid body is at rest (no translation or rotation). Such a body is said to be in static equilibrium view more..
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Ans: In most equilibrium problems, one of the forces acting on the body is its weight. We need to be able to calculate the torque of this force. The weight doesn’t act at a single point; it is distributed over the entire body. But we can always calculate the torque due to the body’s weight by assuming that the entire force of gravity (weight) is concentrated at a point called the center of gravity view more..
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Ans: We can often use symmetry considerations to locate the center of gravity of a body, just as we did for the center of mass. The center of gravity of a homoge-neous sphere, cube, or rectangular plate is at its geometric center. The center of gravity of a right circular cylinder or cone is on its axis of symmetry. view more..
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Ans: There are just two key conditions for rigid-body equilibrium: The vector sum of the forces on the body must be zero, and the sum of the torques about any point must be zero. To keep things simple, we’ll restrict our attention to situations in which we can treat all forces as acting in a single plane, which we’ll call the xy-plane view more..
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Ans: The rigid body is a useful idealized model, but the stretching, squeezing, and twisting of real bodies when forces are applied are often too important to ignore. view more..
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Ans: The simplest elastic behavior to understand is the stretching of a bar, rod, or wire when its ends are pulled (Fig. 11.12a). Figure 11.14 shows an object that initially has uniform cross-sectional area A and length l0. We then apply forces of equal magnitude F# but opposite directions at the ends (this ensures that the object has no tendency to move left or right). We say that the object is in tension. view more..
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Ans: When a scuba diver plunges deep into the ocean, the water exerts nearly uniform pressure everywhere on his surface and squeezes him to a slightly smaller volume. This is a different situation from the tensile and compressive stresses and strains we have discussed. view more..

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