13.
You don’t have to look far to find your next piece of physics. (You never do.) As you exit your house in the morning, for example, you may hear a crash up the street. Two cars have collided at a high speed, and locked together, they’re sliding your way. Thanks to physics (and more specifically, Part III of this book), you can make the necessary measurements and predictions to know exactly how far you have to move to get out of the way.
Having mastered the ideas of energy and momentum helps at such a time. You use these ideas to describe the motion of objects with mass. The energy of motion is called kinetic energy, and when you accelerate a car from 0 to 60 miles per hour in 10 seconds, the car ends up with plenty of kinetic energy.
Where does the kinetic energy come from? It comes from work, which is what happens when a force moves an object through a distance. The energy can also come from potential energy, the energy stored in the object, which comes from the work done by a particular kind of force, such as gravity or electrical forces. Using gasoline, for example, an engine does work on the car to get it up to speed. But you need a force to accelerate something, and the way the engine does work on the car, surprisingly, is to use the force of friction with the road. Without friction, the wheels would simply spin, but because of a frictional force, the tires impart a force on the road. For every force between two objects, there is a reactive force of equal size but in the opposite direction. So the road also exerts a force on the car, which causes it to accelerate.
Or say that you’re moving a piano up the stairs of your new place. After you move up the stairs, your piano has potential energy, simply because you put in a lot of work against gravity to get the piano up those six floors. Unfortunately, your roommate hates pianos and drops yours out the window. What happens next? The potential energy of the piano due to its height in a gravitational field is converted into kinetic energy, the energy of motion. You decide to calculate the final speed of the piano as it hits the street. (Next, you calculate the bill for the piano, hand it to your roommate, and go back downstairs to get your drum set.)
Ever notice that when you’re 5,000 feet down in the ocean, the pressure is different from at the surface? Never been 5,000 feet beneath the ocean waves? Then you may have noticed the difference in pressure when you dive into a swimming pool. The deeper you go, the higher the pressure is because of the weight of the water above you exerting a force downward. Pressure is just force per area.
Got a swimming pool? Any physicists worth their salt can tell you the approximate pressure at the bottom if you tell them how deep the pool is. When working with fluids, you have all kinds of other quantities to measure, such as the velocity of fluids through small holes, a fluid’s density, and so on. Once again, physics responds with grace under pressure. You can read about forces in fluids in Chapter 8.
Feeling Hot but Not Bothered: Thermodynamics
Heat and cold are parts of your everyday life. Ever take a look at the beads of condensation on a cold glass of water in a warm room? Water vapor in the air is being cooled when it touches the glass, and it condenses into liquid water. The condensing water vapor passes thermal energy to the glass, which passes thermal energy to the cold drink, which ends up getting warmer as a result.
Thermodynamics can tell you how much heat you’re radiating away on a cold day, how many bags of ice you need to cool a lava pit, and anything else that deals with heat energy. You can also take the study of thermodynamics beyond planet Earth. Why is space cold? In a normal environment, you radiate heat to everything around you, and everything around you radiates heat back to you. But in space, your heat just radiates away, so you can freeze.
Radiating heat is just one of the three ways heat can be transferred. You can discover plenty more about heat, whether created by a heat source like the sun or by friction, through the topics in Part IV.
Chapter 2
Reviewing Physics Measurement and Math Fundamentals
▶ Mastering measurements (and keeping them straight as you solve equations)
▶ Accounting for significant digits and possible error
▶ Brushing up on basic algebra and trig concepts
Physics uses observations and measurements to make mental and mathematical models that explain how the world (and everything in it) works. This process is unfamiliar to most people, which is where this chapter comes in.
This chapter covers some basic skills you need for the coming chapters. We cover measurements and scientific notation, give you a refresher on basic algebra and trigonometry, and show you which digits in a number to pay attention to – and which ones to ignore. Continue on to build a physics foundation, solid and unshakable, that you can rely on throughout this book.
Measuring the World around You and Making Predictions
Physics excels at measuring and predicting the physical world – after all, that’s why physics exists. Measuring is the starting point – part of observing the world so you can then model and predict it. You have several different measuring sticks at your disposal: some for length, some for mass or weight, some for time, and so on. Mastering those measurements is part of mastering physics.
To keep like measurements together, physicists and mathematicians have grouped them into measurement systems. The most common measurement system you see in introductory physics is the meter-kilogram-second (MKS) system, referred to as SI (short for Système International d’Unités, the International System of Units), but you may also come across the foot-pound-second (FPS) system. Table 2-1 lists the primary units of measurement in the MKS system, along with their abbreviations.
Table 2-1 MKS Units of Measurement
These are the measuring sticks that will become familiar to you as you solve problems and triumph over the math in this book. Also for reference, Table 2-2 shows the primary units of measurement (and their abbreviations) in the CGS system. (Don’t bother memorizing the ones you’re not familiar with now; you can come back to them later as needed.)
Table 2-2 CGS Units of Measurement
Warning: Because different measurement systems use different standard lengths, you can get several different numbers for one part of a problem, depending on the measurement you use. For example, if you’re measuring the depth of the water in a swimming pool, you can use the MKS measurement system, which gives you an answer in meters, or the less common FPS system, in which case you determine the depth of the water in feet. The point? When working with equations, stick with the same measurement system all the way through the problem. If you don’t, your answer will be a meaningless hodgepodge, because you’re switching measuring sticks for multiple items as you try to arrive at a single answer. Mixing up the measurements causes problems – imagine baking a cake where the recipe calls for 2 cups of flour, but you use 2 liters instead.
Examples
Q. You’re told to measure the length of a racecar track using the MKS system. What unit(s) will your measurement be in?
A. The correct answer is meters. The unit of length in the MKS system is the meter.
Q. You’re told to measure the mass of a marble using the CGS system. What unit(s) will your measurement be in?
A. The correct answer is grams. The unit of mass in the CGS system is the gram.
Practice Questions
1. You’re