Physics I Workbook For Dummies with Online Practice E-Book
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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Nail your next physics exam and prepare yourself for the next level of physics education Physics isn't the easiest part of high school, but it doesn't have to be pull-your-hair-out hard. In Physics I Workbook For Dummies, you get practical guidance to reinforce what you already know and master new physics concepts. You'll gain confidence in critical subject areas like motion, thermodynamics, and electromagnetism while setting yourself up for success in college- and university-level physics courses. This book offers hands-on practice exercises in the book and on an online test bank that come with plain-English answers and step-by-step explanations so you can see what you did right and where you need practice. The perfect combination of instruction and application, Physics I Workbook For Dummies also provides: * Understandable explanations of central physics concepts and the techniques you need to solve common problems * Practice questions with complete answer explanations to test your knowledge as you progress * Highlights of the ten most common pitfalls and traps that students encounter in physics assignments and exams and how to avoid them * A collection of the ten most useful online physics resources, along with free, 1-year access to online chapter quizzes Whether you're planning to tackle the MCAT one day or just want to improve your performance on your next physics test, Physics I Workbook For Dummies offers you an opportunity to master a rewarding and challenging subject that unlocks countless educational and career opportunities.
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Physics I Workbook For Dummies®, 3rd Edition with Online Practice
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Physics I Workbook For Dummies®
To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Physics I Workbook For Dummies Cheat Sheet” in the Search box.
Table of Contents
Cover
Title Page
Copyright
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part 1: Getting Started with Physics
Chapter 1: Reviewing Physics Basics
Measuring the Universe
Putting Scientific Notation to Work
Converting between Units
Converting through Multiple Units
Converting Times
Counting Significant Figures
Coming Prepared with Some Algebra
Being Prepared with Trigonometry
Answers to Problems about Physics Basics
Chapter 2: The Big Three: Displacement, Velocity, and Acceleration
From Point A to B: Displacement
Reading That Speedometer
Putting Pedal to Metal: Acceleration
Connecting Acceleration, Time, and Displacement
Connecting Velocity, Acceleration, and Displacement
Answers to Problems about Displacement, Velocity, and Acceleration
Chapter 3: Vectors: Knowing Where You’re Headed
Creating a Vector
Understanding Vector Components
Finding a Vector’s Components
Finding a Vector’s Magnitude and Direction
Adding Vectors Together
Handling Velocity as a Vector
Answers to Problems about Vectors
Part 2: May the Forces Be with You
Chapter 4: Applying Force
Newton’s First Law of Motion
Newton’s Second Law of Motion
Force Is a Vector
Calculating Net Force and Acceleration
Sorting Out Weight and Mass
The Balancing Act of Equilibrium
Newton’s Third Law of Motion
Answers to Problems about Force
Chapter 5: Working with Inclined Planes
Breaking Ramps Up into Vectors
Acceleration and Inclined Planes
Running Down Ramps: Speed
Friction on Inclined Planes
Static Friction along Ramps
Kinetic Friction along Ramps
Acceleration along Ramps Including Friction
Answers to Problems about Inclined Planes
Chapter 6: Round and Round: Circular Motion
Converting between Angles
Period and Frequency
Getting into Angular Velocity
Whipping Around with Angular Acceleration
Connecting Angular Velocity and Angular Acceleration to Angles
Connecting Angular Acceleration and Angle to Angular Velocity
Handling Centripetal Acceleration
Getting Forceful: Centripetal Force
Answers to Problems about Circular Motion
Part 3: Being Energetic: Work
Chapter 7: Working the Physics Way
A Different Kind of Work
Dealing with the Net Force
Getting Energetic: Kinetic Energy
Getting Kinetic Energy from Work
Storing Your Energy: Potential Energy
Powering It Up
Answers to Problems about Work
Chapter 8: Getting Things to Move: Momentum and Kinetic Energy
Acting on Impulse
Getting Some Momentum
Relating Impulse and Momentum
Conserving Momentum
Conserving Kinetic Energy — or Not
Collisions in Two Dimensions
Answers to Problems about Momentum and Kinetic Energy
Chapter 9: Winding It Up: Rotational Motion and Torque
Finding Tangential Speed
Targeting Tangential Acceleration
Angular Velocity as a Vector
Angular Acceleration as a Vector
Doing the Twist: Torque
The Balancing Act: Rotational Equilibrium
Answers to Problems about Rotational Motion and Torque
Chapter 10: Getting Dizzy with Rotational Dynamics
Putting Newton on Wheels
Moments of Inertia for Everyone
Doing Some Rotational Work
Round and Round: Rotational Kinetic Energy
Working with Ramps Again
Can’t Stop This: Angular Momentum
Answers to Problems about Rotational Dynamics
Chapter 11: Simple Harmonic Motion
Hooking into Hooke’s Law
Simply Simple Harmonic Motion
Getting Periodic
Considering Velocity
Figuring the Acceleration
Bouncing Around with Springs
Talking about Energy
Following the Ticktock of Pendulums
Answers to Problems about Simple Harmonic Motion
Part 4: Obeying the Laws of Thermodynamics
Chapter 12: You’re Getting Warm: Thermodynamics
Converting between Temperature Scales
Getting Bigger: Linear Expansion
Plumping It Up: Volume Expansion
Getting Specific with Heat Capacity
Changes of Phase: Latent Heat
Answers to Problems about Thermodynamics
Chapter 13: Under Pressure: From Solid to Liquid to Gas
How Heat Flows: Convection
How Heat Is Produced: Conduction
How Heat Is Produced: Radiation
A Biggie: Avogadro’s Number
Ideally Speaking: The Ideal Gas Law
Molecules in Motion
Answers to Problems about Pressure
Chapter 14: All about Heat and Work
The First Law of Thermodynamics
Constant Pressure: Isobaric Processes
Constant Volume: Isochoric Processes
Constant Temperature: Isothermal Processes
At Constant Heat: Adiabatic
The Direction of Heat: The Second Law of Thermodynamics
Making Heat Work: Heat Engines
Maximum Efficiency: Carnot Heat Engines
The Third Law of Thermodynamics
Answers to Problems about Heat and Work
Part 5: Zap: Electricity
Chapter 15: Static Electricity: Electrons at Rest
Talking about Electric Charges
Getting Forceful with Charges
Electrical Forces Are Vectors
Force at a Distance: Electric Fields
Easy Electric Field: Parallel Plate Capacitors
Ramping Up Some Voltage
Electric Potential from Point Charges
Answers to Problems about Static Electricity
Chapter 16: Electrons in Motion: Circuits
Electrons in a Whirl: Current
Giving You Some Resistance: Ohm's Law
Powering It Up
One after the Other: Series Circuits
All for One: Parallel Circuits
The Whole Story: Kirchhoff's Rules
Answers to Problems about Circuits
Part 6: The Part of Tens
Chapter 17: Ten Common Mistakes People Make When Solving Problems
Mixing Units
Expressing the Answer in the Wrong Units
Swapping Radians and Degrees
Getting Sines and Cosines Mixed Up
Failing to Treat Vectors as Vectors
Neglecting Latent Heat
Getting the Direction of Forces Wrong
Getting the Signs Wrong in Kirchhoff Loops
Adding Resistors Incorrectly
Using the Wrong Temperature in the Ideal Gas Law
Chapter 18: Ten Wild Physics Theories
The Universal Speed Limit
Through the Looking Glass, and What Chien-Shiung Found There
Wanted: Dead and Alive
Quantum Objects Can Tunnel
Mass Is a Kind of Energy
Vacuum Is Not Just Empty Space
“Constants” in Physics Change
Stuck in the Middle of a Proton
The Expansion of the Universe Is Accelerating
Some Things Never Change
Index
Connect with Dummies
End User License Agreement
List of Tables
Chapter 1
Table 1-1 MKS Units of Measurement
Table 1-2 CGS Units of Measurement
Chapter 4
Table 4-1 Units of Force
List of Illustrations
Chapter 1
FIGURE 1-1: A triangle.
Chapter 2
FIGURE 2-1: A moving ball.
Chapter 3
FIGURE 3-1: A vector.
FIGURE 3-2: Two vectors.
FIGURE 3-3: Vector coordinate system.
FIGURE 3-4: Resolving a vector.
FIGURE 3-5: Finding a vector’s components.
FIGURE 3-6: Adding two vectors.
FIGURE 3-7: Two vectors being added.
Chapter 4
FIGURE 4-1: Two forces.
FIGURE 4-2: Two forces acting on a hockey puck.
FIGURE 4-3: Three forces balancing out.
Chapter 5
FIGURE 5-1: A cart on an inclined plane.
FIGURE 5-2: An object on a ramp.
Chapter 6
FIGURE 6-1: An angle in a circle.
FIGURE 6-2: Angular velocity in a circle.
FIGURE 6-3: Centripetal acceleration.
Chapter 7
FIGURE 7-1: Dragging a mass.
FIGURE 7-2: Dragging a mass up an incline.
FIGURE 7-3: The safe slides down.
Chapter 8
FIGURE 8-1: Colliding objects.
FIGURE 8-2: A collision between tennis balls.
Chapter 9
FIGURE 9-1: A rotating ball.
FIGURE 9-2: Angular velocity as a vector.
FIGURE 9-3: Angular acceleration as a vector.
FIGURE 9-4: Torque at work.
FIGURE 9-5: Lever arms at work.
FIGURE 9-6: Checking a ladder.
Chapter 10
FIGURE 10-1: A ball moving in a circle.
FIGURE 10-2: A hollow cylinder and a solid cylinder on a ramp.
Chapter 11
FIGURE 11-1: A weight on a spring.
FIGURE 11-2: A pendulum.
Chapter 12
FIGURE 12-1: Linear expansion.
Chapter 13
FIGURE 13-1: Convection causes all of the water in the pot to warm.
FIGURE 13-2: Conduction heats the pot that holds the boiling water.
Chapter 14
FIGURE 14-1: An isobaric system.
FIGURE 14-2: An isobaric graph.
FIGURE 14-3: An isochoric graph.
FIGURE 14-4: An isothermal graph.
FIGURE 14-5: An adiabatic system.
FIGURE 14-6: An adiabatic graph.
FIGURE 14-7: A heat engine.
Chapter 15
FIGURE 15-1: Three charges.
FIGURE 15-2: Electric fields from point charges.
FIGURE 15-3: A parallel plate capacitor.
Chapter 16
FIGURE 16-1: A resistor and a battery in a circuit.
FIGURE 16-2: Resistors in series.
FIGURE 16-3: Resistors in parallel.
FIGURE 16-4: A circuit.
Chapter 17
FIGURE 17-1: A triangle.
FIGURE 17-2: A circuit.
Guide
Cover
Title Page
Copyright
Table of Contents
Begin Reading
Index
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Introduction
Physics is about the world and everything in it. Physics describes that world and the kinds of things that take place in it. Sometimes, however, physics seems like an imposition from outside — a requirement you have to get through.
That’s a shame, because it’s your world that physics describes. Under the burden of physics problems, though, things can get tough. That’s where this book comes in, because it's designed to let you tackle those problems with ease.
Kirchhoff’s laws? No problem. Carnot engines? No worries. This book addresses these topics and more. After you’re done reading, you’ll be a problem-solving pro.
About This Book
This book is crammed with physics example problems and practice questions that are designed to show you solutions for the kinds of problems you may encounter in physics classes. And when you see how the solutions to problems are done step by step, solving similar problems should be a breeze.
Many books have endless conventions that you have to learn before you can start reading. Not this one. In fact, all you need to know is that new terms are given in italics, like this, when they’re introduced. You should also know that vectors, which are those items that have both a magnitude and a direction, are given in bold, like this: B.
Foolish Assumptions
We’re assuming that you’re using this book in conjunction with a physics class or textbook, because this book keeps the derivation of physical formulas to a minimum. The emphasis here is on solving problems, not deriving formulas. So some knowledge of the physics you’re going to be using here is helpful. This book is designed to help you with the nitty-gritty, not to introduce the topics from scratch.
You should also know some algebra. You don’t need to be an algebra pro, but you should know how to move items from one side of an equation to another and how to solve for values. Take a look at the discussion in Chapter 1 if you’re unsure.
You also need a little knowledge of trigonometry, but not much. Again, take a look at the discussion in Chapter 1, where all the trig you need to know — a grasp of sine and cosine — is reviewed in full.
Icons Used in This Book
You find a few icons in this book, and here’s what they mean:
This icon points out helpful hints, ideas, or shortcuts that save you time or that give you alternative ways to think about a particular concept.
This icon marks something to remember, such as a law of physics or a particularly juicy equation.
This icon means that what follows is technical, insider stuff. You don’t have to read it if you don’t want to, but if you want to become a physics pro (and who doesn’t?), take a look.
This icon highlights examples that show you how to work each type of problem.
Beyond the Book
In addition to what you’re reading right now, this book has a free access-anywhere Cheat Sheet for when you need a quick physics refresher. To get this Cheat Sheet, simply go to www.dummies.com and type Physics I Workbook For Dummies Cheat Sheet in the Search box. There you’ll find common mistakes to avoid, the values of important constants, and equations to remember.
This book also comes with over 200 online practice questions that you can use to test your knowledge of different physics topics. To gain access to the online practice, all you have to do is register. Just follow these simple steps:
Register your book or ebook at Dummies.com to get your PIN. Go to
www.dummies.com/go/getaccess
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Select your product from the dropdown list on that page.
Follow the prompts to validate your product, and then check your email for a confirmation message that includes your PIN and instructions for logging in.
If you do not receive this email within two hours, please check your spam folder before contacting us through our Technical Support website at http://support.wiley.com or by phone at 877-762-2974.
Now you’re ready to go! You can come back to the practice material as often as you want — simply log on with the username and password you created during your initial login. No need to enter the access code a second time.
Your registration is good for one year from the day you activate your PIN.
Where to Go from Here
You’re ready to jump into Chapter 1. You don’t have to start there, of course. You can read this book in any order you like instead of reading it from beginning to end. But if you want some important, general, problem-solving background, take a look at Chapter 1 first.
Part 1
Getting Started with Physics
IN THIS PART …
Grasp fundamental physics measurements, scientific notation, and converting among units, distances, and time.
Master the motion of displacement, velocity, and acceleration.
Point yourself in the right direction with vectors.
Chapter 1
Reviewing Physics Basics
IN THIS CHAPTER
Laying down measurements
Simplifying with scientific notation
Practicing conversions
Drawing on algebra and trigonometry
This chapter gets the ball rolling by discussing some fundamental physics measurements. At its root, physics is all about making measurements (and using those measurements as the basis of predictions), so it’s the perfect place to start! As you go through the process of converting measurements from one unit to another, you’ll practice applying math skills to physics problems.
Measuring the Universe
A great deal of physics has to do with making measurements — that’s the way all physics gets started. For that reason, physics uses a number of measurement systems, such as the CGS (centimeter-gram-second) system and the MKS (meter-kilogram-second) system. You also use the standard English system of inches and feet and so on — that’s the FPI (foot-pound-inch) system.
In physics, most measurements have units, such as meters or seconds. For example, when you measure how far and how fast a hockey puck slid, you need to measure both the distance in centimeters and the time in seconds.
For reference, Table 1-1 gives you the primary units of measurement in the MKS system.
Table 1-1 MKS Units of Measurement
Measurement
Unit
Abbreviation
Length
meter
m
Mass
kilogram
kg
Time
second
s or sec
Force
newton
N
Energy
joule
J
Pressure
pascal
P
Electric current
ampere
A
Magnetism
tesla
T
Electric charge
coulomb
C
These are the measuring sticks that will become familiar to you as you solve problems and triumph over the math in this workbook. Also for reference, Table 1-2 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 1-2 CGS Units of Measurement
Measurement
Unit
Abbreviation
Length
centimeter
cm
Mass
gram
g
Time
second
s or sec
Force
dyne
dyn
Energy
erg
erg
Pressure
barye
Ba
Electric current
biot
Bi
Magnetism
gauss
G
Electric charge
franklin
Fr
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.
1 You’re told to measure the mass of a marble using the CGS system. What unit(s) will your measurement be in?
2 You’re asked to measure the time it takes the moon to circle the Earth using the MKS system. What will your measurement’s units be?
3 You need to measure the force a tire exerts on the road as it’s moving using the MKS system. What are the units of your answer?
4 You’re asked to measure the amount of energy released by a firecracker when it explodes using the CGS system. What are the units of your answer?
Putting Scientific Notation to Work
Physics deals with some very large and very small numbers. To work with such numbers, you use scientific notation. Scientific notation is expressed as a number multiplied by a power of 10.
For example, suppose you’re measuring the mass of an electron in the MKS system. You put an electron on a scale (in practice, electrons are too small to measure on a scale — you have to see how they react to the pull of magnetic or electrostatic forces to measure their mass), and you measure the following:
What the heck is that? That’s a lot of zeros, and it makes this number very unwieldy to work with. Fortunately, you know all about scientific notation, so you can convert the number into the following:
That is, 9.1 multiplied by a power of 10, . Scientific notation works by extracting the power of 10 and putting it on the side, where it’s handy. You convert a number to scientific notation by counting the number of places you have to move the decimal point to get the first digit in front of that decimal point. For example, 0.050 is because you move the decimal point two places to the right to get 5.0. Similarly, 500 is because you move the decimal point two places to the left to get 5.0.
Check out this example question about scientific notation:
Q. What is 0.000037 in scientific notation?
A. The correct answer is . You have to move the decimal point five times to the right to get 3.7.
5 What is 0.0043 in scientific notation?
6 What is 430,000.0 in scientific notation?
7 What is 0.00000056 in scientific notation?
8 What is 6,700.0 in scientific notation?
Converting between Units
Physics problems frequently ask you to convert between different units of measurement. For example, you may measure the number of feet your toy car goes in three minutes and thus be able to calculate the speed of the car in feet per minute, but that’s not a standard unit of measure, so you need to convert feet per minute to miles per hour, or meters per second, or whatever the physics problem asks for.
For another example, suppose you have 180 seconds — how much is that in minutes? You know that there are 60 seconds in a minute, so 180 seconds equals three minutes. Here are some common conversions between units:
The conversion between CGS and MKS almost always involves factors of 10 only, so converting between the two is simple. But what about converting to and from the FPI and other systems of measurement? Here are some handy conversions that you can come back to as needed:
Length:
Mass:
Force:
Energy:
Power:
Because conversions are such an important part of physics problems, and because you have to keep track of them so carefully, there’s a systematic way of handling conversions: You multiply by a conversion constant that equals 1, such that the units you don’t want cancel out.
Q. A ball drops 5 meters. How many centimeters did it drop?
A. The correct answer is 500 centimeters. To perform the conversion, you do the following calculation:
Note that 100 centimeters divided by 1 meter equals 1 because there are 100 centimeters in a meter. In the calculation, the units you don’t want — meters — cancel out.
9 How many centimeters are in 2.35 meters?
10 How many seconds are in 1.25 minutes?
11 How many inches are in 2.0 meters?
12 How many grams are in 3.25 kg?
Converting through Multiple Units
Sometimes you have to make multiple conversions to get what you want. That demands multiple conversion factors. For example, if you want to convert from inches to meters, you can use the conversion that 2.54 centimeters equals 1 inch — but then you have to convert from centimeters to meters, which means using another conversion factor.
Try your hand at this example question that involves multiple conversions:
Q. Convert 10 inches into meters.
A. The correct answer is 0.254 m.
You know that
, so start with that conversion factor and convert 10 inches into centimeters:
Convert 25.4 cm into meters by using a second conversion factor:
13 Given that there are 2.54 centimeters in 1 inch, how many centimeters are there in 1 yard?
14 How many centimeters are in a kilometer?
15 How many inches are in an angstrom, given that ?
16 How many inches are in 3.0 meters, given that there are 2.54 cm in 1 inch?
Converting Times
Physics problems frequently ask you to convert between different units of time: seconds, minutes, hours, and even years. These times involve all kinds of calculations because measurements in physics books are usually in seconds, but can frequently be in hours.
Q. An SUV is traveling . What’s that in kilometers per hour?
A. The correct answer is 100 km/hr.
You know that there are 60 minutes in an hour, so start by converting from kilometers per second to kilometers per minute:
Because there are 60 minutes in an hour, convert this to kilometers per hour using a second conversion factor:
17 How many hours are in 1 week?
18 How many hours are in 1 year?
Counting Significant Figures
You may plug numbers into your calculator and come up with an answer like 1.532984529045, but that number isn’t likely to please your instructor. Why? Because in physics problems, you use significant digits to express your answers. Significant digits, also often called significant figures, represent the accuracy with which you know your values.
For example, if you know only the values you’re working with to two significant digits, your answer should be 1.5, which has two significant digits, not 1.532984529045, which has 13! Here’s how it works: Suppose you’re told that a skater traveled 10.0 meters in 7.0 seconds. Note the number of digits: The first value has three significant figures, the other only two. The rule is that when you multiply or divide numbers, the result has the number of significant digits that equals the smallest number of significant digits in any of the original numbers. So if you want to figure out how fast the skater was going, you divide 10.0 by 7.0, and the result should have only two significant digits — 1.4 meters per second.
On the other hand, when you’re adding or subtracting numbers, the rule is that the last significant digit in the result corresponds to the last significant digit in the least accurate measurement. How does that work? Take a look at this addition example:
So is the result 24.83? No, it’s not. The 12 has no significant digits to the right of the decimal point, so the answer shouldn’t have any either. That means you should round the value of the result up to 25.
Zeros used just to fill out values down to (or up to) the decimal point aren’t considered significant. For example, the number 3,600 has only two significant digits by default. That’s not true if the value was actually measured to be 3,600, of course, in which case it’s usually expressed as 3,600; the final decimal indicates that all the digits are significant.
Rounding numbers in physics usually works the same way as it does in math: When you want to round to three places, for example, and the number in the fourth place is a five or greater, you add one to the third place (and ignore or replace with zeros any following digits).
Q. You’re multiplying 12.01 by 9.7. What should your answer be, keeping in mind that you should express it in significant digits?
A. The correct answer is 120.
The calculator says the product is 116.497.
The number of significant digits in your result is the same as the smallest number of significant digits in any of the values being multiplied. That’s two here (because of 9.7), so your answer rounds up to 120.
19 What is 19.3 multiplied by 26.12, taking into account significant digits?
20 What is the sum of 7.9, 19, and 5.654, taking into account significant digits?
Coming Prepared with Some Algebra
It’s a fact of life: You need to be able to do algebra to handle physics problems. Take the following equation, for example, which relates the distance something has traveled (s) to its acceleration and the time it has been accelerated:
Now suppose that the physics problem asks you for the acceleration, not the distance. You have to rearrange things a little here to solve for the acceleration. So when you multiply both sides by 2 and divide both sides by , here’s what you get:
Cancelling out and swapping sides, you solve for a like this:
So that’s putting a little algebra to work. All you had to do was move variables around the equation to get what you wanted. The same approach works when solving physics problems (most of the time). On the other hand, what if you had to solve the same problem for the time, t? You would do that by rearranging the variables like so:
The lesson in this example is that you can extract all three variables — distance, acceleration, and time — from the original equation. Should you memorize all three versions of this equation? Of course not. You can just memorize the first version and use a little algebra to get the rest.
The following practice questions call on your algebra skills:
Q. The equation for final speed, — where the initial speed is , the acceleration is a, and the time is t — is . Solve for acceleration.
A. The correct answer is
To solve for a, divide both sides of the equation by time, t.
21 The equation for potential energy, PE, for a mass m at height h, where the acceleration due to gravity is g, is . Solve for h.
22 The equation relating final speed, , to original speed, , in terms of acceleration a and distance s is . Solve for s.
23 The equation relating distance s to acceleration a, time t, and speed v is . Solve for .
24 The equation for kinetic energy is . Solve for v.
Being Prepared with Trigonometry
Physics problems also require you to have some trigonometry under your belt. To see what kind of trig you need, take a look at Figure 1-1, which shows a right triangle. The long side is called the hypotenuse, and the angle between x and y is 90°.
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FIGURE 1-1: A triangle.
Physics problems require you to be able to work with sines, cosines, and tangents. Here’s what they look like for Figure 1-1:
You can find the length of one side of the triangle if you’re given another side and an angle (not including the right angle). Here’s how to relate the sides:
And here’s one more equation, the Pythagorean theorem. It gives you the length of the hypotenuse when you plug in the other two sides:
25 Given the hypotenuse h and the angle , what is the length x equal to?
26 If and , what is the length of h?
Answers to Problems about Physics Basics
The following are the answers to the practice questions presented earlier in this chapter. You see how to work out each answer, step by step.
1grams
The unit of mass in the CGS system is the gram.
2seconds
The unit of time in the MKS system is the second.
3newtons
The unit of force in the MKS system is the newton.
4ergs
The unit of energy in the CGS system is the erg.
5
You have to move the decimal point three places to the right.
6
You have to move the decimal point five places to the left.
7
You have to move the decimal point seven places to the right.
8
You have to move the decimal point three places to the left.
9235 cm
Convert 2.35 meters into centimeters:
