Since man has looked up to the stars, we have always tried to understand why they move the way they do. The stars and planets make elliptical circles, which is against the First Law in which objects will continue to move straight. The answers explained motion in a linear fashion. Our motion became parabolic when we added a second dimension. When objects begin to move in a circular motion will be explored. We will have a better understanding of the Moon's position around the Earth.

The object's speed around its path should be constant. Although the speed may be constant, the direction of the velocity is always changing. There must be acceleration since the velocity is changing. This acceleration does not change the speed of the object, it only changes the direction of the velocity to keep it on its path. The object would move off in a straight line if there wasn't a force.

The figures are below. There is a figure on the left that shows an object moving along a circular trajectory.

The object's path is always tangential to the velocity vector. The magnitudes are the same.

Most objects don't undergo uniform circular motion. They follow ellipticals with different speeds.

This won't be tested for the AP physics 1 exam.

An object moving at constant speed in a circular path is undergoing uniform circular motion.

The magnitude of the force is given by this equation. The force that produces centripetal acceleration points to the center of the path.

Centrifugal force is not a real force. The net force from the physical forces on the object is called capillary force.

Identifying what forces produce the centripetal acceleration is the first thing to do in a problem like this. This is a horizontal circle.

The unit has changed from 80 cm to 0.80 m.

The centripetal force is provided by static friction. The centripetal force needed to keep him running in a circle would increase if the radius of the arcs were smaller. He would slip if the centripetal force increased enough.

The speed of the car is 15 m/s at the very top of the circle, where the people are upside down. If the diameter of the loop is 40 m and the total mass of the car is 1,200 kg, find the magnitude of the normal force by the track on the car at this point.

There are two forces acting on the car at its topmost point, both of which point downward. The normal force is directed downward by the surface of the track.

Force tells an object how to move. The car would fall straight down if it had zero velocity at this point.

The normal force pushes ninety degrees to the surface, even though the gravity still points downward. The forces are against one another. The centripetal force is still provided by the combination of these two forces. We will make anything that points toward the center of the circle positive and anything that points away from the circle negative, because the centripetal acceleration points inward.

You would feel little force between you and the seat at the top of the loop, but you would feel a big slam at the bottom of the loop.

The strength is proportional to the product of the objects' mass and the distance between them as measured from center to center.

The pulling force is gravity.

2-on-1 act along the line that joins the bodies and form an action/reaction pair.

The law was published more than a hundred years ago. The mass of the Earth and the radius of the Earth can be used to calculate gravity.

The mass of the Earth is determined by the radius of the Earth.

From above the North Pole, you can see the Earth.

It is possible to recognize the relationship between variables in formulas.

The centripetal force is provided by N.

The difference is so small that it can usually be ignored.

Satellites are often parked above Earth's surface. The satellites have the same position on Earth's surface because they have the same amount of time in the air. Determine the altitude that a satellite has to be above the equator.

The answer is that the Earth pulls.

Any object at the same distance from the Earth as the moon must move at the same speed.

There are questions about banking on the AP physics 1 exam. Engineers often use banked curves to design and build roads.

Banking allows for cars to travel around a curve at or below the posted speed limit, without relying on the tires and road.

The curve is banked at 11.8 degrees if the radius of curvature is 60 m.

The centripetal force that the car experiences as it rounds the curve is produced by the horizontal component of the normal force.

The recommended speed is 40 km/hour.

We covered objects that move in a circular motion. Taking those objects and spinning them is the next part of this chapter.

There were previous equations where objects were moved in a linear orientation. We need a new set of equations that are similar to the physics of linear motion.

An object's mass is its resistance to acceleration. The harder it is to change an object's speed, the more inertia it has. The greater the inertia, the greater the force that is required in order for an object to be moved. If the same force is applied on both objects, Object 1 will experience a smaller acceleration.

The force, mass, acceleration, and velocity are put in the linear model.

The relationship between the three rotational parameters and the linear parameters will be explored.

There are some basic definitions.

A toy car is going around a circle.

If you follow the path of the car, you will find that your fingers are counterclockwise. The direction of your thumb is determined by your thumb. It points out something on the page.

Many of the equations reflect linear equations.

Four children are on a carousel.

The objects were treated as a single particle in the preceding chapters. The force is being delivered at a single point on the object.

Imagine a bunch of experiments. We walk into a large room with a hammer and a small light. The light will be attached to the end of the hammer in the first experiment. We throw the hammer across the room after turning off the light.

We repeat the experiment again. The small light should be attached to the head of the hammer. We turn off the light, throw the hammer across the room, and trace the path of the hammer.

There was something important about that point.

The one point that gave a smooth path was the only one that gave spiraled trajectory. If we place that point on our fingers, we can see that the hammer is horizontal with the floor.

The center of mass is this point. It is possible to say that the center of mass is the point at which all the mass of the object can be concentrated.

The center of mass is the geometric center of the object.

The center of mass is motionless as every other point moves around it.

Pick a location that is convenient.

The formula above can be used to calculate the center of mass.

The stick matters. If the stick has mass, it must be taken into account to determine its center position.

We could either palm the ball or put our hands on the opposite side of the ball and push one hand forward and the other backward. In both cases, we need to exert force to make the object's center of mass accelerate. We need to exert a Torque in order to make an object spin.

The measure of a force's effectiveness is called Torque. Something must have a Torque if it starts to spin after being at rest. If an object is spinning, something has to exert a Torque to stop it.

The systems that can spin have a "center" of turning. While the rest of the object is rotating, the point that does not move becomes the center of the circle. There are many different terms used to describe this point.

Students have difficulty understanding the topic of Torque.

There is a door with a pivot point on the left side of the drawing. Some examples can be tried at home on a door to get a better understanding.

The door will close the fastest in the first situation.

In both situations, the door will close the fastest. The door will not close in situation 3.

If you try this at home, you will see that it will be easier to close the door if you push it like Situation 2.

There were a few points that mattered when trying to close the door. The amount of force used to close the door mattered. The angle in which we pushed the door mattered. In scenario 3, the place in which we pushed mattered.

Our force's effectiveness at rotating was determined by a few factors.

This is a cross product between your force and your radius.

The unit is called a newton-meter.

Torque is not a force because it is not in newtons. There was a force being applied to the door straight into the pivot point. The force was not enough to close the door. It's the equivalent of force in trying to accelerate something.

A newton-meter became a joule in the previous chapter. This isn't the case with Torque.

Torque problems can involve putting systems in equilibrium.

A student pulls down a rope with a force of 40 N and a pulley of 5 cm.

The two forces produce a Torque, but they don't like each other. The Torque of F1 is counterclockwise and the Torque of F2 is counterclockwise. Imagine the effect of each force if the other wasn't there.

It's important to balance one force's effectiveness at turning something clockwise with another force's effectiveness at turning it counter-clockwise.

The wall is connected to the bar's center by a wire.

The wall on the bar exerts contact force. The components are sin 55deg.

When using center-of- mass, some problems are easier than others.

You can choose which one is easier.

This system can't be solved as is. The second condition for equilibrium requires that the sum of the Torques about any point is zero.

cot 55o is what we use here.

We can put together the pieces of making an object spin now that we've studied Torque and rotation. The moment of inertia is the tendency of an object in motion to rotate until acted upon by an outside force.

We are taking a ball at rest and speeding it up, which is rotational acceleration. A force is needed to achieve this. In terms of inertia, Torque is required. We need to apply a force that works.

Some key relationships are made by this equation. The larger the inertia, the smaller the value for an object. It will be more difficult to rotation Object 1 than it will be to rotation Object 2. If the same Torque is applied to both objects, Object 1 will undergo a smaller rotational acceleration.

There is more to it than the object's mass. There are two objects that have the same mass. How the mass is distributed in an object affects rotational inertia.

The greater the rotation inertia, the farther away the mass is from it.

Imagine a barbell with weights near each end and an identical barbell with weights near the middle of the bar. The barbells have the same mass, but their inertias are different. The first barbell has its attached mass farther away from the axis of rotation than the second barbell. It was more difficult to rotation the first barbell than the second one.

Chapter 13 contains Review Questions Answers and Explanations.

A bucket is whirled in a vertical circle with a rope tied to it. The bucket has a mass of 3 kilograms.

A uniform meter stick of mass 1 kilogram is hanging from a thread.

If the distance between two point particles is doubled, then the force between them decreases by a factor of 4 and increases by a factor of 2.

The mass of the dwarf planet is 1/600 and the distance from Earth is 1/15.

You are looking at a planet that is in the middle of the sun.

A robot probe lands. The diameter of the planet is 8 x 106 m.

You can write your answer in both m/s2 and g's.

The Earth has a mass of 6 x 1000 km and is in a constant circle around the Sun.

An amusement park ride consists of a large cylinder that rotates around its central axis as passengers stand against the inner wall of the cylinder.

The passengers feel pinned against the wall of the cylinder as it rotates.

Don't include friction.

The centripetal force is given by and the centripetal acceleration is given by.

A force that makes an object rotate is called Torque. Torques can be clockwise or counterclockwise.

Universal gravitation can be linked up with circular motion.

Robert Hooke was a British physicist who helped pave the way for simple motion. Newton's laws of static equilibrium made it possible to show a relationship between stress and strain. Hooke's Law is one of the laws he developed after building upon these. The concise mathematical relationship of a spring was discovered by Hooke.

In this section, we will focus on periodic motion that is simple and easy to understand.

There is a fixed block on the left side of the wall. The spring is said to be in its equilibrium position when it is not stretched or compressed.

The net force on the block is zero when the block is in equilibrium.

There is a spring at rest. When we pull the block to the right, it will experience a force pulling back toward equilibrium. The block will once again be pushed toward the equilibrium position by a force. The block passes through the equilibrium position again, but this time it is traveling to the right. This back-and-forth motion will continue indefinitely if this is taking place in ideal conditions, and the block will oscillate from these positions in the same amount of time. The block at the end of this spring has a physical example of SHM.

Since the block is decelerating, there must be some force behind it. The spring exerts a force on the block that is proportional to its displacement from its equilibrium point.

This is called Hooke's Law. Hooke's Law states that the force is a restoring force. The force wants to return the object to its equilibrium position. The force was to the right when the block was on the left, and it was to the left when the block was on the right. In all cases of the extreme left or right, the spring tends to return to its original position. The force helps to maintain the movement of the body.

We would have to exert a lot of force to keep the spring in this state.

The number tells us how far away from equilibrium the block will travel.

The block's motion can be described in terms of energy transfers.

The more work you have to do, the more potential energy that's stored.

The block's energy transfers can be described as follows. The elastic energy of the system increases when you pull the block out. The block moves when the potential energy turns into energy. All the energy is in motion. As the block continues through equilibrium, it transforms the spring's energy into elastic potential energy.

The magnitude of the event is 4 cm.

This method can only calculate the maximum velocity in a spring.

The AP physics 1 exam won't ask you to calculate other velocities at other points because it's not uniform accelerated motion.

The result is a oscillations of 8.0 cm. Determine the total energy and speed of the block when it's less than 4 cm from equilibrium.

The total energy is the sum of the two energies.

The block is at rest. The block has an initial speed of 2.0 m/s.

When the spring's potential energy has been transformed into the block's initial energy, it will come to rest.

The number of cycles that can be completed in a given time interval is a way of indicating the rapidity of the oscillations.

You can always get the frequencies if you have the period. The period and Frequency are inverses of each other.

A block on the end of a spring moves from maximum spring stretch to maximum spring compression in 0.25 s.

The time required for one full cycle is defined as the period.

It's only half a cycle when you move from one end of the region to the other. 2 s is 1/(0.5 s)

A student is observing a block. Determine its frequencies in hertz and seconds.

The force constant of the spring and the mass of the block are two of the defining properties of the spring-block oscillator.

Let's look at the equations. If we had a small mass on a very stiff spring, we would expect that the strong spring would cause the mass to change shape quickly.

A block is attached to a spring and set into motion.

A student is doing an experiment. In the first trial, the amplitude is 3.0 cm, while in the second trial it is 6.0 cm. The values of the period, Frequency, and maximum speed of the block can be compared.

The period and Frequency are not dependent on the amplitude. The period and frequencies in the second trial will be the same as in the first trial, because the same spring and block were used. The maximum speed of the block will be greater in the second trial. The second system has more energy to convert to kinetic when the block is passing through equilibrium.

The force constant of a single spring is the same force on the block as the pair of springs shown in each case.

The second spring is stretched.

The simple motion follows this cycle.

We've seen a block sliding back and forth on a table, but it could also move vertically. The only difference would be that gravity would cause the block to move downward, to an equilibrium position at which the spring would not be at its natural length.

There is a spring hanging from a support. The upward force of the spring is balanced by the downward force of gravity as the block is in equilibrium.

Our net force is zero since it is not moving up or down.

The vertical spring can be treated the same as the horizontal spring at this point.

If a question asks about the total length of the spring at a given moment, you don't need to worry about this.

The block is pulled down a distance of 2.0 cm after it comes to rest.

When the block is at the lowest position in its cycle, the spring is stretched a maximum of 7 cm, and a minimum of 5 cm when the block is at its highest position.

The simple pendulum has many of the same features as the spring-block oscillator, but the displacement of the pendulum is measured by the angle that it makes with the vertical, rather than by its linear distance from the equilibrium position.

The equilibrium position has zero displacement.

The pendulum's energy and speed are maximized when it passes through the equilibrium position.

There is one important difference despite the similarities. There is a restoring force that is proportional to the displacement.

The motion of a simple pendulum is not simple.

The periods and frequencies are not dependent on the mass of the weight.

There is a period of 1 s on Earth.

Chapter 9 Review Questions Answers and Explanations can be found in chapter 13.

A block is attached to a spring. The maximum speed at which the block can be accelerated is A, the minimum is B, and the restoring force is D.

The maximum speed of the block will decrease by a factor of 4 and by a factor of 2 if the block is replaced with one with twice its mass. A spring-block simple harmonic oscillator is set up.

Blocks of different amounts are used in different trials and the corresponding frequencies are recorded.

The block is pushed so that the spring is compressed to 1/3 of its natural length. Half of Block 1's energy is lost to heat when it collides with Block 2, while the other half is divided between Block 1 and Block 2.

If Block 1 did not collide with Block 2, the period of the oscillations that Block 1 would have had would be 0.

The bullet is embedded in the block.

Support your answer for a moment.

Support your answer for a moment.

Hooke's Law holds for most springs.

It would not make sense to describe everything scientifically.

Imagine holding the end of a rope in your hand and attaching it to a wall. You can create a wave from your hand to the wall by moving your hand up and down. Waves and their characteristics will be discussed in this chapter.

A long rope is being looked at.

A wave travels in a direction that is parallel to the direction in which the median is vibrating. The wave is related to the direction of travel.

Imagine the visible point on the rope moving from its crest position down to its trough position, and then back up to the crest position, when you look at the second figure on the previous page.

Ocean waves are similar to compressional waves.

Matter moves in large circles near the surface of the ocean and smaller circles deeper down as the energy in the system dwindles.

It's the most basic equation in wave theory.

A wave on a rope has a Frequency of 2.5 Hz.

2 s is 1/(0.5 s)

The wave speed, wavelength, and period have nothing to do with the amplitude.

We can derive an equation for the speed of a wave on a stretched string or rope.

The wave's speed depends on a number of factors. The speed of the wave we create will be constant, because we can wiggle the end at any frequencies we want.

The speed of a wave is determined by the type of wave and the characteristics of the medium.

Both travel at the speed of sound.

Sound and light can move through air with different speeds, for example.

When a wave passes from one medium to another, we have a second wave rule. A change in the medium causes a change in wave speed, but the frequencies won't change.

When a wave passes into another medium, its speed changes, but its Frequency doesn't.

The non-attached end is oscillated with a Frequency of 4.

There are 11 m/s and 4 m.

A wave is created in the rope on the left which travels to the interface with the heavier rope.

Some of the wave's energy is reflected and some is transmitted when a wave strikes a new medium. The transmitted wave has the same frequencies, but it has different speeds and wavelength.

The wave will have a new wave speed after entering a new medium.

When two or more waves meet, the displacement at any point of the medium is equal to the sum of the individual waves. The figure on the next page shows two waves traveling in opposite directions.

The relative phase of the two waves affects the amplitude of the combined wave. The waves will interfere completely if the crest and trough meet, and the combined wave will be the sum of the individual waves. If crest meets trough and trough meet crest, then they will interfere completely, and the wave will have a difference between the individual waves. The waves will be between in phase and out of phase.

When the waves are in phase, the maximum amplitude is 8 cm + 3 cm. When the waves are out of phase, the minimum amplitude is 8 cm - 3 cm. All we can say is that the amplitude will be at least 5 cm and no greater than 11 cm, without more information about the relative phase of the two waves.

The wave will travel back toward us when it strikes the wall. The string supports two waves; the wave we generated at our end and the reflected wave. There are two oppositely directed traveling waves that have the same wavelength and Frequency on the string. The pattern will remain fixed if the string is just right. The crests and troughs are no longer traveling down the string.

The right end is fixed to the wall, and the left end is oscillated so that we can consider both ends to be essentially fixed. The interference of the two waves results in destructive interference at some points and constructive interference at other points.

The points have different frequencies between the extremes. The difference between a standing wave and a traveling wave is that each point on the string has an individual amplitude.

The opposite of that is antinodes.

This information can be used to generate standing waves. The three simplest waves that our string can support are shown in the figures. The first, second, and third waves have one antinode.

A standing wave will form on a string if we create a traveling wave with the same frequencies.

All the other frequencies and wavelengths can be determined by knowing the fundamental frequency.

A string of length 12 m that's fixed at both ends supports a standing wave with a total of 5 nodes.

Draw a picture.

A string of 10 m and 300 g is fixed at both ends and has a tension of 40 N.

If you attached a rope or string to a ring that could slide up and down a pole, you would make a rope that is fixed at one end but free at another. The closed end and open end would be created with this. There are some possible examples.

Sound waves can be produced by an object such as a jackhammer or vocal cords. Human ears can detect the sound of the vibrations if they are between 20 and 20,000hertz.

In the figure on the next page, there is a sound wave in an airfilled tube.

All of the basic characteristics of a wave apply to sound waves as they did for waves on a string.

The medium through which a sound wave travels has an effect on its speed. A medium that is easily compressed, like a gas, has a low bulk modulus. Sound travels faster through liquids than through gases.

The mean pressure of the air can be used to calculate the speed of sound through it. As air warms, this value increases.

A change in wavelength is caused by a change in Frequency.

1,500 m/s.

If two sound waves with different frequencies interfere, the resulting sound becomes loud, soft, and soft. The individual waves travel in phases, then out of phase, then in phase again, and so on. When the waves are constructive, the sound is loud, and when they are destructive, the sound is soft. 2 matches, the combined wave doesn't change in amplitude, and no beats are heard.

A tuning fork is used to adjust the key that plays the A note above middle C. The tuning fork has a perfect tone. When the tuning fork and piano key are struck, the beats of frequencies are heard.

The piano string has to emit a tone of either 437 or 443 Hz since the fork emits a tone of 440. We can't determine which without more information.

The pianist should loosen the string and listen for beats again.

A vibrating source at one end of an air-filled tube produces sound waves that travel the length of the tube.

The waves reflect off the far end, and the superposition of the forward and reflected waves can produce a standing wave pattern if the length of the tube and the frequencies of the waves are related in a certain way.

The air molecule at the far end of the tube can't move horizontally because they're against a wall. The far end of the tube is a displacement point. The vibrating source is located at the other end of the tube.

Although sound waves in air are longitudinal, we'll show the wave in a way that makes it easier to determine the wavelength.

Our condition for resonance was that the closed end and the open end have an antinode.

Standing waves can be established in the tube if the far end is sealed. An open end is a displacement antinode.

An open-ended tube can support any harmonic, while a closed-end tube can only support odd ones.

The temperature of the air in the tube is 20degC, and it conducts sound at a speed of 343 m/s.

1 is the amount of time it takes to reach 1,320 Hz.

2 is equal to 880.0 Hz.

When a source of sound waves and a detector are not in motion, the frequencies that the source emits matches the frequencies that the detector receives.

If the detector moves toward the source, it will intercept the waves at a higher rate than the one at which they were emitted. If the source moves toward the detector, the wavefronts will pile up and the detector will receive waves with different frequencies and wavelength.

The source's speed is S. The directions in which the source and detector are moving affect the signs in the numerator and denominator.

There are four most common situations in which only one object moves.

We can use logic when the detector and source are moving.

If the source is moving faster than the detector, we would expect the detector's frequencies to decrease.

If the source was moving away from the detector at the same speed, it would decrease by a factor of less than if it were stationary.

We can learn from this. A police car and a sports car are examples. Both are moving relative to the road, but not relative to each other. There should be no shift if there is no relative motion between the source and the detector.

A source of sound waves travels at the speed of sound toward a detector that is moving at the speed of sound.

The wavelength will shift down by the same factor since the Frequency shifted up by a factor. A person yells as he runs towards a brick wall at 5 m/s.

When the waves reach the runner, we need to know what the frequencies are. The person is the source of the sound and the wall is the detector.

Chapter 13 contains Review Questions Answers and Explanations.

A string is fixed at both ends and supports a standing wave.

A string has a length of 6 m and is fixed at both ends.

Two speakers, S1 and S2, emit sound waves of wavelength 2 m in phase with each other.

A > 0 9. A closed organ pipe has a length of 17 cm.

A bat emits a 40 kHz "chirp" with a wavelength of 8.25mm toward a tree and receives an echo of 0.4 s later.

A car is travelling at 20 m/s.

A rope is stretched. The points are fixed.

Waves of lengths 4 m and 3.2 m can be supported by the rope.

Students are brought to a racetrack for a physics lab experiment. The goal of the experiment is for the students to observe the pitch of the car's horn.

The diagram shows a long straight track where the car is being driven. The students are standing by the track.

A group of students perform a set of physics experiments using two tuning forks, one with a Frequency of 400 and the other with a Frequency of 440.

The medium through which a wave travels has an effect on the wave's speed.

The speed won't be affected by changing frequencies or wavelength, as long as the medium remains the same.

The amount of energy present in the waves is more important than the speed of the wave. A traveling wave can be described by Superposition as when parts of waves interact so that they interfere.

The sound is a wave.

The speed of sound is 343 m/s at room temperature and normal atmospheric pressure.

If the tube is closed on one end or open on the other, the sound will be different.

If there is a relative motion between the source of the sound and the detector, the frequencies of the sounds will vary. The relative motion of the objects will affect the Frequency. The relative motion will be perceived as lower if it is away from each other.

The most important product of man's creative brain is electric forces and fields.

Many people were aware of the electric force. The Greeks, Egyptians, and Romans reported on electricity. English scientist William Gilbert made a study of electricity and magnetism in the 16th century. Ben Franklin is known for his metal key and kite experiment in a storm. In the 19th century, real progress was made with regard to electricity and magnetism. The concept of electromagnetism would be linked to them by James Clerk Maxwell.

The components of atoms are protons, neutrons, and electrons.

The electrons would be five meters away if the nucleus was the size of the period at the end of this sentence. Positive and negative electric charge can be found. Positive and negative particles repel each other. electrons are negatively charged

Bulk matter is not charged with protons and electrons.

This is because the amount of charge on a protons balances the charge on an electron, which is quite remarkable in light of the fact that protons and electrons are very different particles. The electric charge of most atoms is zero because the negative charges cancel out the positive charges.

If you add electrons to the object, it becomes negatively charged.

Net charge can't be created or destroyed.

The transfer of electricity is done by negative electrons. The electrons are in the outer shells of the atom, whereas the protons and neutrons are in the nucleus. Any transfer of electric charge is either a loss or gain.

The electric force between two charged particles obeys a law that is very similar to the law that describes the force between two objects.

The electric force is stronger than the gravitational force.

Matters are kept together by electric force.

The relative strengths of the electric and gravitational forces are shown by the relative sizes of these fundamental constants.

Consider two small spheres, one carrying a charge of + 1.5 nC and the other a charge of -2.0 nC, separated by a distance of 1.5 cm.

The line that joins the charges is the force between the spheres. Two forces form an action/reaction pair.

There is an attraction between two objects.

The objects are pointing away from each other.

Remember to add the electric forces in a geometric way.

Four equal, positive point charges are located at the edge of a square. There is a negative point charge placed at the square's center.

The net force on the center charge is zero.

Each side of the square has a positive charge and a negative charge.

The center of the line that joins the two positive charges is the direction of the net force.

There are three forces that act on each ball.

The net force feels zero when the balls are in equilibrium.

The presence of a massive body such as the Earth causes objects to experience a force directed toward the Earth's center. The force varies with the square of the distance and the mass of the source.

Any mass that's placed in this field experiences a force.

The electric force is described using the same process. A force will be experienced by another charge placed in the field.

The test charge is the reason for dividing.

The factors of 2 would cancel when we divided the force by the test charge, leaving the ratio the same as before.

The ratio tells us if the field is strong because of the source charge, or if it is weak because of the test charge.

The electric field would point away from the source charge if the test charge was positive. If the source charge is positive, the electric field vectors point away from it; if the source charge is negative, they point toward it. The electric field and so does the electric field. The electric field is shorter farther from the source charge.

Your first thought might be that obliterating the individual field vectors deprives us of information, since the length of the field was what told us how strong the field was. The strength of the field can be figured out by looking at the density of the field lines. The field is stronger where the field lines are denser.

The electric field can be added in any other way. A third charge would feel the effect of the combined field if we had two source charges.

The electric field lines can be sketched.

Electric field lines always point away from positive source charges and toward negative ones.

The electric fields are sketched from the point of view of a positive test charge.

Finally, notice that electric field lines don't cross.

The electric field strength is 400 N/C.

3 x 10-9 C)( 400 N/C) is 1.2 x 10-6 N.

The two point charges are separated by a distance of 6.0 cm.

The force it would feel was described in the previous example.

One way to create a uniform field is to have two large sheets of conducting that are separated by distance. For all practical purposes, the field is uniform if it is near the edges of each sheet. If you have a uniform field, you can use the same equations and laws as if you had a uniform one.

Positive charge is distributed uniformly over a large horizontal plate, which acts as the source of a vertical electric field. There is an object of mass 5 g above the plate.

The electric force would be repulsive if the object carried a positive charge.

The electric field of 20 N/C is caused by two large charged plates that are 30 cm apart. The particles don't interact with each other because they are so far apart. They are released from the rest.

The electron and the protons have the same magnitude, so they will experience the same force. The electron travels in the opposite direction of the electric field if you want to know the direction.

Although the charges have the same magnitude of force, the electron's mass is almost 2000 times smaller than the proton's.

The particles will travel 0.15 m if they are midway between the 30 cm plates.

Even though the force is the same and the same work is done on both charges, there is a significant difference in final velocities due to the large mass difference. The same answers would have been obtained by you.

Chapter 13 contains Review Questions Answers and Explanations.

The three point charges are all positive.

Justify your answer.

Explain briefly if not.

Explain briefly if not.

According to the figure below, 2 is fixed in place.

The strategies you used in the chapter can be used to solve these problems.

The electric force and field are quantitives and therefore all the rules for addition are applicable.

The lighting in our houses, as well as the computing in our personal computers, are all powered by electricity. These are powered by complex circuits. The basics of simple direct current circuits will be studied in this chapter.

Within the metal, electrons are travelling at a million meters per second in random directions, colliding with other electrons and positive ion in the lattice. There is no current if there is no net movement of charge. If we created a potential difference between the ends of the wire, the electrons would experience an electric force, and they would start to drift through the wire.

We are moving water at a rate in the river and electric charge at a rate in the current.

To measure the current, we need to know how much charge crosses a plane per unit time.

Current is expressed in coulombs per second. So 1 A is 1 C/s.

The current points toward the left if the electrons drift to the right.

Let's say we had a copper wire and a glass fiber that had the same length and cross-sectional area, and that we hooked up the ends of the metal wire to a source of potential difference and measured the resulting current. The glass gave more resistance to the charge.

We can think of resistance as a portion of the river that zigzags. Resistance to the flow of water is provided by this.

It's known as Ohm's Law. If the current is large, the resistance is low, and if the current is small, the resistance is high. It's also called potential difference.

The resistance is expressed in volts per Amp. 1 V/A is 1

One answer is to say that there's an electric field inside the wire, and since negative charges move in the opposite direction to the electric field lines, electrons would drift opposite the electric field.

There is a potential difference between the ends of the wire. Positive charges move from higher potential to lower potential.

If the river is flat, it won't flow. A river can flow from higher ground to lower ground. We can think of a mountain as the height of the river.

A current is created by the amount of voltage.

It is not uncommon to see the cause of the current that creates it, since it is the cause that sets the charges into motion. The battery provides the voltage in a circuit.

The emf is the work done per unit charge, and it's measured in volts.

Let's follow one of the charge carriers that is drifting through the pathway to see what's happening in a circuit in which a steady-state current is maintained. The electric field pushes the charge into the wire from the positive terminal of the battery. It encounters resistance, bumping into the relatively stationary atoms that make up the metal's lattice and setting them into greater motion. The charge left the battery and turned into heat. All of the original electrical potential energy is lost when the charge reaches the negative terminal. In order to keep the current going, the voltage source has to do positive work on the charge and move it from the negative terminal to the positive terminal. The charge is ready to travel around the circuit again.

The power in a circuit is related to the heat given off. The light bulb becomes hot if we touch it. The brighter the light bulb, the hotter it is.

This equation works for the power delivered by a battery to the circuit.

When current passes through them, they become hot.

A way of specifying the current, voltage, and power associated with each element in a circuit will be developed. The circuits will contain batteries, resistors and connecting wires.

It's easy to determine the current in this case because there's only oneresistor.

To simplify the circuit, our goal is to find the equivalent resistance of combinations. If the total voltage drop across them is equal to the sum of the individual voltage drops, then the Resistors are in series.

In a series circuit, the current is the same. The voltage drop is the same in a parallel circuit.

The total current entering the combination is split between the resistors if they all share the same voltage drop.

Current travels through the path of least resistance in parallel resistors. If two resistors are in parallel and one has more resistance, the other will have more current running through it.

Each time we replace a combination of resistors, you might want to change the circuit.

We can return to the original circuit. Back to diagram 2. In diagram 2, the current is 2 A.

A simple circuit with a battery and an equivalent is the most common method of working a circuit problem. We work backwards to build the circuit back to its original form after we solve for individual values.

We moved the diagram to the left to make the circuit simpler. We went from 3 to 2 to 1.

The total voltage drop across the two resistors is 12 V, which matches the drop across the 4 resistors.

Going from diagram 2 to diagram 1.

There is nothing that needs to be done with the 4resistor and the 2resistor in diagram 2 goes back to the parallel combination. Back to diagram 1. The two parallel resistors in diagram 1 have a 4 V drop across them.

The current through the 3 and 6 are equal to A. The total current passing through the individual resistors is equal to the current entering the parallel combination.

We will calculate the dissipated power by the heat of the resistors.

If the resistors are dissipating a total of 24 J every second, then they need a lot of power. 24 W is 2 A)(12 V)

Two people want to send current counterclockwise. The current will flow counterclockwise if 2 is the more powerful battery.

8 W is 2 A)(4 V)

The power delivered is equal to the power taken.

There is no conducting pathway from the positive terminal of the battery to the negative terminal before the switch is closed.

There is a distinction between the emf of the battery and the actual voltage it provides once the current has begun. The ideal voltage is higher than it is.

20 V - 4 V is 16 V.

A student has an ideal battery. Compare the current drawn from and the power supplied by the battery.

The equivalent resistance that's greater than any of the individual resistances is always provided by the resistors in series.

The number is 9 A and 90 V.

90 W. is the number of A and 90 V.

Determine the readings on the ammeter in the circuit below.

The ammeter is ideal because it doesn't alter the current that it's trying to measure. The voltmeter draws negligible current away from the circuit because it has an extremely high resistance.

We want to find the equivalent resistance in the circuit. The 600 and 300 resistors are in close proximity. The current splits at the junction.

The ammeters measure current and current stays the same in series.

The voltage stays the same in parallel because we connect them in parallel.

We need another method for analyzing the circuit when the resistors are not in series or parallel.

The total current that leaves the junction must be equal to the total current that enters the junction.

Any closed loop in a circuit must have zero potential differences.

It's a good idea to know that the total drops must equal the total rise in potential. No more and no less must be used if 60 V came out of a battery.

By the time we get back to the same point by following any closed loop, we have to be back to the same potential. The total rise in potential must be equal to the total drop in potential. The Loop Rule says that all the decreases in electrical potential energy must be balanced by all the increases in electrical potential energy. The loop rule is a restatement of the law of energy.

The charge that goes into a junction must be equal to the charge that comes out. This is a statement about the law of charge.

The Junction Rule is easy to apply.

Let's start with the points in the circuit.

Each branch has a current.

2 is equal to 0.64 A.

The direction of the currents at the beginning of the solution was arbitrary. Don't worry about trying to guess the direction of the current in a branch. Pick a direction and follow it. When you solve for the values of the branch current, a negative value will alert you that the direction of the current is different to the direction you chose in the diagram.

Chapter 13 contains Review Questions Answers and Explanations.

If you double the voltage without changing the resistance, the current will decrease by a factor of 4 and the resistance will increase by a factor of 2.

A 40 V battery has an internal resistance of 5.

Three identical light bulbs are connected to a source of emf.

Three light bulbs are connected to a battery.

The loop rule tells us that the potential differences in a closed loop must be zero.

The total current that enters a junction must be equal to the total current that leaves it.