In This Chapter

Handling common mistakes

Knowing how to spot potential problems

This chapter discusses the most common errors people make when working out physics problems. In our many years of teaching physics, certain types of problems stand out, and you see them here.

Mixing Units

The most common error made in solving physics problems involves mixing the units from one system with another system. If the problem is given to you in inches, kilograms, and seconds, convert it into a consistent system of units before proceeding to work out the answer. For example, if you want to use the MKS system, convert everything into MKS before working out the problem.

Expressing the Answer in the Wrong Units

If the problem asks for the answer in the MKS system, don’t give it in CGS units. You’d be surprised at how common these errors are; people are so relieved that they’ve solved the problem that they goof it up in the last step. Also, don’t forget your units on your final answer.

Swapping Radians and Degrees

Degrees are commonly used in physics problems — except when it comes to angular velocity and acceleration. That’s when you have to make sure you’re working with radians. Use the 180°π conversion factor to convert from radians to degrees when needed.

Tip: If you are using a graphing calculator, make sure that it is set to the correct mode (degrees or radians) for the type of problem that you are solving.

Getting Sines and Cosines Mixed Up

Physics students often make the mistake of interchanging sines and cosines. Take a look at Figure 18-1 and keep the following relationships in mind:

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Figure 18-1: A triangle.

Not Treating Vectors as Vectors

When you add vectors, use vector addition. That means resolving vectors into components. Too many people just add the magnitudes of the vectors without realizing that they should be adding components instead.

Mixing Up the Signs of the Components of Vectors

Before you write down equations involving components of vectors, you should choose a coordinate system by deciding which directions are the positive x and positive y directions. Most of the time, you choose up or north to be the positive y direction and right or east to be the positive x direction. If you’re not sure about the direction, you should guess — if you guess wrong, you’ll end up with a minus sign.

Getting the Direction of Forces Wrong

When you are solving a force problem, you can keep track of the directions of the forces by drawing a free-body diagram. The gravitational force exerted by the Earth always points toward the center of the Earth. The normal force is always perpendicular to the surface (not necessarily up!). The frictional force opposes the relative motion of surfaces in contact.

Neglecting Latent Heat

When you’re faced with a problem that involves a phase change, such as from ice to water, don’t forget to take the latent heat into account. When ice changes into water, it absorbs latent heat that you have to account for in your solution.

Using the Wrong Temperature in the Ideal Gas Law

When you use the ideal gas law, always convert the temperature to kelvins. Often you are given the temperature in Celsius. To convert from degrees Celsius to kelvins, just add 273.15.

Getting the Signs Wrong in the First Law of Thermodynamics

You can figure out the signs in the first law of thermodynamics by thinking about the conservation of energy. The internal energy of the system increases if the system absorbs heat or if the surroundings do work on the system.

Ten Common Mistakes People Make When Solving Problems