Physics I Workbook For Dummies with Online Practice
Overview
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 with online practice
CHEAT SHEET
Avoid difficulties when working on physics by knowing the common issues that can cause trouble in physics problems, understanding physical constants, and grasping principal physics equations.10 issues to avoid when solving physics problemsIf you get stumped working on physics formulas, take a deep breath, and recheck your work.
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Physics
The following list discusses the most common errors people make when working out physics problems. For those who teach 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.
Physics is the scientific study of the basic rules that govern the universe. Because physicists like to be precise, they often express their ideas as mathematical equations. What follow are ten of the most important ideas in physics. These ideas have had a profound impact on how scientists view the universe and on the technologies people use every day.
Physics
If you get stumped working on physics formulas, take a deep breath, and recheck your work. Go through these common physics-problem issues to make sure you have avoided them:
Mixing units
Expressing the answer in the wrong units
Swapping radians and degrees
Getting sines and cosines mixed up
Failin
Tons of physics tutorials are online, and some are very useful, not to mention fun. Take a look at these resources. There's a lot of physics just waiting for you out there.
The Physics Classroom: This famous physics tutorial and problem-solving site is touted as a high school physics tutorial, but it's a great resource for students at any level.
Physics constants, like the mass of a proton or speed of light, are physical quantities with fixed numerical values. This list contains the most common physics constants:
Avogadro's Number: NA = 6.022 × 1023 mol–1
Boltzmann's constant: k = 1.380 × 10–23 J/K
Coulomb's constant: k = 8.99 × 109 N–m2/C2
Gas constant: R = 8.
Suppose that you have a crate that has been mistakenly placed near the top of a long ramp, and it starts sliding down that ramp. How about calculating its acceleration down the incline?
The object is sliding down the ramp — you’re not pushing it — which means the force of kinetic friction is opposing (not adding to) the component of gravity along the ramp.
When you have a block of ice (read: frictionless) moving down a ramp, it’s being acted on by forces, which means that it’s accelerated. How fast is it being accelerated? When you know that F = ma, you can solve for the acceleration.
After you solve for the force along the ramp, you can get the acceleration (a = F/m) along the ramp.
In physics terms, acceleration is the amount by which your velocity changes in a given amount of time. In terms of equations, it works like this:
Given initial and final velocities, vi and vf, and initial and final times over which your speed changed, ti and tf, you can also write the equation like this:
To get the units of acceleration, you divide velocity by time as follows:
Displacement over time squared?
Kinetic friction is usually less than the force of friction you need to overcome static friction. Kinetic friction occurs when an object is already in motion.
Static friction is the force that must be overcome to get something to move, and it’s usually larger than kinetic friction, the force that pushes against a moving object.
There are analogs of every linear motion quantity (such as distance, velocity, and acceleration) in angular motion, and that’s one of the things that makes angular motion easier to work with after you have learned about linear motion. The velocity of an object in linear motion is shown in the following equation (this is actually a vector equation, of course, but you can look at this equation in scalar terms):
What’s the analog of this equation in angular terms?
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.
Friction is a force, and from physics, you know that forces can change an object's speed or direction. The force of friction from dry pavement on your car's tires is much greater than the force of friction from snow or ice. Why? Because ice produces much less friction with your car's tires than the dry pavement does.
The first step in working with ramps of any kind is to resolve the forces that you're dealing with, and that means using vectors. For example, take a look at the cart in the figure; it's on an inclined plane, ready to roll.
The force on the cart is the force due to gravity, Fg = mg. So how fast will the cart accelerate along the ramp?
Newton says sigmaF = ma, which means that you add all the force vectors together to get the net force. That’s how it usually works when you have to figure out F = ma problems in physics. Often, a number of force vectors are involved, and you have to solve for the net force to find the acceleration.
Take a look at the hockey puck in the figure.
In order to keep an object going around in a circle, that object must be pulled toward the center of the circle. Take a look at the Moon circling Earth in the following figure. The Moon is accelerated toward Earth along a radius from Earth to the Moon.
The acceleration needed to keep an object (here, it's the Moon) going around in a circle is called the centripetal acceleration, and it's always perpendicular to the object's travel.
To give an object moving in a circle the centripetal acceleration needed to keep moving, it needs a force applied to it. Any force that causes an object to move in a circle is a centripetal force. Gravity, tension, friction, and other forces can all act as centripetal forces; all of these forces can act to pull or push an object into a circle.
Collisions can take place in two dimensions. For example, soccer balls can move any which way on a soccer field, not just along a single line. Soccer balls can end up going north or south, east or west, or a combination of those. So you have to be prepared to handle collisions in two dimensions.
Sample question
In the figure, there’s been an accident at an Italian restaurant, and two meatballs are colliding.
Physics
You know that you can relate velocity with displacement and time. And you know that you can relate velocity and time to get acceleration. You also can relate displacement with acceleration and time:
If you don’t start off at zero velocity, you use this equation:
Sample question
You climb into your drag racer, waving nonchalantly at the cheering crowd.
Physics
You can connect angular displacement, angular velocity, and angular acceleration. The corresponding equation for linear motion is vf2 – vo2 = 2as. Substituting omega for v, alpha for a, and theta for s gives you:
Use this equation when you want to relate angle to angular velocity and angular acceleration.
Sample question
A merry-go-round slows down from 6.
Physics
You can connect angular velocity, angular acceleration, and time to angular displacement. This is very similar to the way that you connect linear velocity, linear acceleration, and time to linear displacement. Recall that you can connect displacement to the original velocity and linear acceleration like this:
And you can make the substitution from linear to angular motion by putting in the appropriate symbols:
Using this equation, you can connect angular velocity, angular acceleration, and time to the angle.
Physics
You use the following equation to relate velocity, acceleration, and distance. Suppose you have a drag racer whose acceleration is 26.6 m/s2, and his final speed is 146.3 m/s. What is the total distance traveled? This scenario sets you up to use a handy motion equation:
vf2 – vo2 = 2as = 2a (xf – xo)
Sample question
A drag racer’s acceleration is 26.
In some types of collisions, called elastic collisions, kinetic energy and momentum are conserved. What do elastic collisions look like? In general, there’s no permanent deformation of any of the objects from an elastic collision. The objects involved might initially deform, but they immediately spring back to their original shape.
The major tool you have in calculating what’s going to happen in collisions is the knowledge that momentum is conserved. You know that the total momentum before the collision is the same as the total momentum after the collision as long as there are no significant outside forces.
When you have two objects that collide (one is initially at rest and the other is moving), and you know the final velocity and mass of one object after the collision, you can calculate the final velocity of the other object.
Study in physics usually begins with linear motion, which is motion in straight lines. Much of physics focuses on angular motion, however, which is the motion of objects around circles or parts of circles. In order to study angular motion you must know how to measure that motion. You use radians, not meters, and you have to know what that means.
There’s often more than one force involved when you’re dragging a mass over a distance. Just think of the forces of friction and gravity for an object on an inclined plane. For example, take a look at the figure, where a couch is being dragged up an incline. If you’re applying force F, how much work is done as the couch is dragged up the incline?
Displacement occurs when something moves from here to there. For example, suppose that you have a ball at the zero position, as in the top of the following figure.
Now suppose that the ball rolls over to a new point, 3 meters to the right, as you see in bottom half of the image. The ball is at a new location, so there's been displacement.
Force, like displacement, velocity, and acceleration, is a vector quantity, which is why Newton’s Second Law is written as sigmaF = ma. Put into words, it says that the vector sum of the forces acting on an object is equal to its mass (a scalar) multiplied by its acceleration (a vector).
Because force is a vector quantity, you add forces together as vectors.
In the real world, when things slide down ramps, friction is involved, and the force of friction opposes the motion down the ramp. The force of friction is proportional to the force from the ramp that balances the component of gravity that is perpendicular to the ramp. (If this force were not present, the object would sink into the ramp.
You’re frequently asked to add vectors when solving physics problems. To add two vectors, you place them head to tail and then find the length and magnitude of the result. The order in which you add the two vectors doesn’t matter.
For example, suppose you’re headed to the big physics convention and have been told that you go 20 miles due north and then 20 miles due east to get there.
Physics
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.
Physics
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.
A vector is a combination of exactly two values: a magnitude (like the speed of an object in motion) and a direction (such as the direction of an object in motion). All kinds of things can be described with vectors, including velocity, acceleration, displacement, magnetic fields, electric fields, and many more.
You can convert from the magnitude/angle way of specifying a vector to the coordinate way of expression. Doing so is essential for the kinds of operations you can expect to execute on vectors, such as when adding vectors.
For example, you have one vector at 15 degrees and one at 19 degrees, and you want to add them together.
In physics, when you’re given the vector components, such as (3, 4), you can easily convert to the magnitude/angle way of expressing vectors using trigonometry.For example, take a look at the vector in the image.Suppose that you’re given the coordinates of the end of the vector and want to find its magnitude, v, and angle, theta.
Velocity is a vector, and as such, it has a magnitude and a direction associated with it. Suppose you’re in a car traveling east at 88 meters/second when you begin to accelerate north at 5.0 meters/second2 for 10.0 seconds. What is your final speed?
You may think you can use this equation to figure out the answer:
vf= vo + a x t
But that’s not a vector equation; the quantities here are called scalars (the magnitude of a vector is a scalar).
Two kinds of friction — static and kinetic — mean that you have to handle ramp problems where kinetic friction is involved as well as problems where static friction is involved. Kinetic friction is involved any time an object is moving up or down a ramp.. You can solve problems with kinetic friction as easily as those that involve static friction.
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.
Momentum is the most important quantity when it comes to handling collisions in physics. Momentum is a physical quantity defined as the product of mass multiplied by velocity. Note the definition says velocity, not speed, so momentum is a vector quantity. This means that a 1,000-kg car moving north at 20 m/s has a different momentum from a 1,000-kg car moving south at 20 m/s.
Whether you're asked to give it in physics class or not, you need to be familiar with Isaac Newton's First Law of Motion: “An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force.”
What's the translation? The idea is that if you don't apply a force to something in motion, it will stay in that same motion along a straight line.
Force saves you from the monotony of everything moving at the same speed and direction forever. Force can act on objects, changing their direction and/or speed. The relationship between force, mass, and acceleration is primary in physics classes.
To start, you need to know Newton’s Second Law of Motion, which is a big one in physics: “When a net force sigmaF acts on an object of mass m, the acceleration of that mass can be calculated by sigmaF = ma.
Newton’s Third Law of Motion is a famous one: “Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body.” If that doesn’t ring a bell, try this on for size: “For every action, there is an equal and opposite reaction.”
Put simply, this law of motion says that if your car pushes against Earth, then Earth pushes back against your car with the same amount of force.
When describing the way things go in circles, you don’t just use radians; you also can specify the time it takes. The time it takes for an object to complete an orbit is referred to as the period of its motion. Period is generally measured in seconds, but it can be measured using other units of time, including milliseconds, minutes, and years.
Avoid difficulties when working on physics by knowing the common issues that can cause trouble in physics problems, understanding physical constants, and grasping principal physics equations.10 issues to avoid when solving physics problemsIf you get stumped working on physics formulas, take a deep breath, and recheck your work.
Physics
You've probably seen an electromagnet in action. This is a coil of current-carrying wire that acts like a magnet. But why does this happen? And how are electricity and magnetism related? To understand this concept, you must start by understanding that there are two types of electric charge: positive and negative.
Physics
The law of conservation of energy is one of the most important ideas in science. It states that energy can be transferred or transformed but never created or destroyed. But what is this thing that can never be created or destroyed? What is energy?
Energy comes in several forms, including two kinds of mechanical energy: kinetic energy and potential energy.
Physics
Thermodynamics is the study of how thermal energy (heat energy) and mechanical energy are related. It's an important topic in physics as well as in engineering. Engineers must employ thermodynamic principles whenever heat is involved. This includes the design of refrigerators, air conditioning units, automobiles, jet engines, and even computers.
When it comes to work in physics, you’re sure to see problems involving power, which is the amount of work being done in a certain amount of time. Here’s the equation for power, P:
W equals force along the direction of travel times distance, so you could write the equation for power this way:
where theta is the angle between the force and the direction of travel.
Physics
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 between 1 and 10 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:
0.
It turns out that there’s a direct connection between impulse and momentum. If you hit a pool ball with a cue, the cue imparts a certain impulse to the ball, causing the ball to end up with a particular momentum.
How can you relate impulse to momentum? Easy. The impulse you impart to an object gives it a change in momentum equal to that impulse, so
You might be confused about the units here.
When objects slide (frictionlessly) down a ramp, they’re acted on by a force, which means that they’re accelerated and therefore their speed changes. The equation to use in physics problems like these is
vf2 – vo2 = 2as
Finding the object’s final speed under these circumstances is easy when you remember that
s is the length of the ramp, and vo is usually 0.
One of the forces you’re asked to deal with frequently in physics is the force on an object from a gravitational field. Near Earth or another large mass (such as the Moon), all objects experience a downward force from gravity; on the surface of Earth, every kilogram of mass experiences a downward force of 9.8 N.
In physics terms, what is speed? It’s the same as the conventional idea of speed: Speed is distance divided by time, which is what a speedometer measures. The related term velocity refers to a speed with an associated direction. To measure velocity, you might use a speedometer in combination with a compass. Sometimes, you are interested in the average velocity over a period of time instead of velocity at a particular instant.
Two coefficients of friction correspond to two different physical processes. The first, called the coefficient of static friction, applies when you start pushing something at rest to get it moving. When you already have something moving and need to keep applying a force to keep it in motion, that’s called the coefficient of kinetic friction.
The figure shows a box on a ramp. Suppose that the box contains a new flat-screen TV that you’re pushing up the ramp and into your house.
A number of forces are acting on the box, including both gravity and friction, and you need to take both into account. There’s also the force exerted upon the box as you push it up the ramp.
Objects can have energy at rest simply by having a force act on them. For example, an object at the end of a stretched spring has energy because when you let the object go and it accelerates because of the spring, it can convert that stored energy into kinetic energy.
The energy that an object has by virtue of a force acting on it is called potential energy.
When you place a book on a table, it doesn’t accelerate down toward Earth, even though Earth’s gravity is pulling the book down, because a second force, from the table, is pushing up on the book and balancing the force from gravity. The book is in equilibrium. An object is in equilibrium if all the forces on it exactly cancel out.
Physics problems sometimes require you to have some trigonometry under your belt. To see what kind of trig you need, take a look at the figure, which shows a right triangle. The long side is called the hypotenuse, and the angle between x and y is 90 degrees.
Physics problems require you to be able to work with sines, cosines, and tangents.
When you apply a force for a certain amount of time, you create an impulse. In fact, that's the definition of impulse — impulse equals the force applied multiplied by the time it was applied. Here's the equation:
Impulse = Ft
Note that this is a vector equation because the force has a direction; therefore the impulse does as well.
When you have objects in motion, you have kinetic energy. When, for example, you slide an object on a frictionless surface, the work you do goes into the object’s kinetic energy:
W = KEf – KEi
If you have an object with mass m moving at speed v, its kinetic energy is
That’s the energy of motion.
Sample question
Say that you push a spaceship, mass 1,000.
In physics, physical work is defined as the applied force multiplied by the component of the displacement that is in the same direction as the force. So if you’re pushing a refrigerator 2.0 m across the floor, and you need to apply 900 N, you’ve done this much work:
(900)(2.0) = 1,800
1,800 what? Work in the MKS system is measured in joules, J, so that’s 1,800 J.
Just as with linear motion, you can have acceleration when you’re dealing with angular motion. For example, the line in the figure may be sweeping around the circle faster and faster, which means it’s accelerating.
In linear motion, the following is the equation for acceleration, the rate at which the object’s velocity is changing:
As with all the equations of motion, you need only to substitute the correct angular quantities for the linear ones.
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