4.7 Further Applications of Newton's Laws of Motion

It is important to determine whether the system is moving in a particular direction before you write net force equations.

The net force is zero if the acceleration is zero in a particular direction.

The net force is described by the equation if the acceleration is nonzero.

You will need this information to figure out what is happening in the system.

Check the solution to see if it's reasonable.

This is obvious in some cases.
It is reasonable to conclude that the object slides down the incline more slowly when there is no friction.
It becomes easier to judge whether an answer is reasonable with experience.
You can check the units to check your solution.
If you end up with units of m/s, you have made a mistake.

There are many interesting applications ofNewton's laws of motion presented in this section.

To help build problem-solving skills, these serve as an example of some further subtleties of physics.

The first tugboat exerts a force in the x-direction, while the second tugboat exerts a force in the y-direction.

The weight of the barge and the force of the water supporting it are not shown.

The problem is a one-dimensional problem since it is in the opposite direction.

The directions and magnitudes of the applied forces are given.

The system of interest here is the barge, since the forces on it are given.

Our strategy is to find the magnitude and direction of the net applied force and then applyNewton's second law to solve for the drag force.

The net external force is in the same direction, but its magnitude is less.

The problem is not two-dimensional.

The direction has been determined to be in the opposite direction to the south of the west.

The numbers used in this example are reasonable.

Small speeds are desirable to avoid running the barge into the docks, as it is difficult to get larger accelerations with tugboats.
The answer to this example is where the drag is less than 1/600th of the weight of the ship.

The angles on either side of wires supporting a mass were equal in the earlier example of a tightrope walker.

The angles are not equal in the following example.

Find the tension in the wires.

A traffic light is out of commission.

The traffic light diagram is also shown.
The weight of the traffic light is equal to the weight of the horizontal components of the tensions.

The three forces are not parallel, so they must be projected onto a coordinate system.

Two equations are needed to find two unknowns in this problem.

Newton's second law states that the net external force is zero along the horizontal and vertical axes.

The magnitude is determined using the relationship between them.

If the angles on either side are the same as they were in the earlier example of a tightrope walker, the tensions will be equal.

The bathroom scale is an example of a force acting on a body.

A quantitative reading of how much it must push upward to support the weight of an object is provided.
Consider the following example.

The broken arrows are correct when the elevator is speeding upward.

The magnitude of the force the person exerts downward on the scale will be equal if it is accurate.

The analysis of the free-body diagram can give answers to both parts of the example, as well as some other questions.

The person's weight and the scale's upward force are the only forces acting on him.
In order to find what the scale reads, we need to know that the third law is equal in magnitude and opposite in direction.

This solution should be valid for a variety of accelerations in addition to the ones in this exercise because no assumptions were made about the acceleration.

This is about 185 lbs.

The scale reading in the elevator is larger than his weight.

The scale must push up on the person with a force greater than his weight in order to accelerate him upward.
The scale reading is consistent with what you feel in fast elevators versus slow elevators.

The person's weight is determined by the scale reading.

Whenever the elevator has a constant velocity, this will be the case.

The solution to the previous example applies to the elevator.

When an elevator is negative and the scale reading is less than the weight of the person, until a constant downward velocity is reached, the scale reading becomes equal to the person's weight.
The scale reading will be zero if the elevator is in free-fall and the person is weightless.

When applied to general situations that involve more than a narrow set of physical principles, physics is most powerful.

The laws of motion can be used with other concepts to solve problems of motion.

Which physical principles are involved?

You can identify the principles involved by listing the givens and the quantities to be calculated.

Strategies outlined in the text can be used to solve the problem.

Refer to them if they are available for the specific topic.
Refer to the sections of the text that deal with the topic.
The following example shows how these strategies are applied.

The air resistance of the player is negligible.

To solve an integrated concept problem, we need to identify the physical principles involved and identify the chapters in which they are found.

The example considers acceleration along a straight line.
This is a topic of physics.
This chapter deals with force, a topic of dynamics.

The following solutions show how problem-solving strategies are applied.

Identifying knowns and unknowns involves checking to see if the answer is reasonable.

The initial and final velocities are zero and 8.00 m/s forward.

The elapsed time is given to us.

An athlete in good condition can achieve this acceleration.

We are asked to find the average force the player exerts backward.

The player's acceleration is caused by the net external force on the player, which is equal in magnitude to air resistance.
We can use the second law to find the force since we know the player's acceleration and mass.

Average force is about 50 pounds.

Identifying the physical principles involved in the problem is the first step.

The second step is to find a solution to the unknown.
Many worked examples show how to use these strategies in a single topic.
These techniques are useful in applications of physics outside of a physics course, such as in your profession, in other science disciplines, and in everyday life.
Problems will build your skills in applying physical principles.

Only four distinct forces account for all known phenomena, which is one of the most remarkable simplifications in physics.

Almost all of the forces we experience are due to one force, called the electromagnetic force.
Only a few of the many forces we can list were discussed in the previous section.
The basic forces are thought to act through the exchange of carrier particles, and the characteristics of the basic forces are determined by the types of particles exchanged.

The strong nuclear force is one of the four basic forces.

The properties are summarized in Table 4.1.

The weak and strong nuclear forces are very important to the structure of matter, but we don't experience them directly.
The release of energy in nuclear reactions is dependent on the stability and decay of the nuclei.
Nuclear forces determine the relative abundance of elements in nature.
The chemistry of the atom is determined by the properties of the nucleus of the atom.
There will be more on these topics in later chapters.

As you progress through the text, the basic forces will be encountered in more detail.

Nuclear forces, magnetic force in Magnetism, and electric force in Electric Charge and Electric Field are included in the definition of the gravitational force.
The basis for all forces is electromagnetism and gravity.
Nuclear forces are important to the substructure of matter, but they are not directly experienced on the scale.

The force is weak because gravity is always attractive.

Our weight is caused by the Earth acting on us.
The dominant force determining the motions of moons, planets, stars, and galaxies is the gravitational force.
The nature of space and time is affected by the force of gravity.
The graviton is a proposed particle, though it has not yet been observed by scientists.
In this section, you can read about the discussion of the waves.

The existence of eight types of gluons is indicated by meson exchange in the nucleus of atoms.

There are either attractive or repulsive magnetic forces.

They are long-range forces, which act over large distances.
If they didn't cancel, the forces would overwhelm the force.
There are electrical and magnetic forces that affect a compass needle.
Scientists discovered that the two forces are different manifestations of the same force in the 19th century.
The unification of forces is the classical case of this discovery.

All of the forces we experience directly are due to the interaction of atoms and Molecules.

The ways in which these forces manifest themselves make it convenient to consider them separately in specific applications.

In relation to elementary particles, attempts to unify the four basic forces are discussed.

"Unify" means finding connections between the forces that show that they are different manifestations of a single force.
If unification is achieved, the forces will retain their separate characteristics on the macroscopic scale and may be identical under extreme conditions.

Physicists are looking into whether the four basic forces are related.

There has been some success in recent years with attempts to unify all forces under the rubric of Grand Unified Theories.
The nuclear forces are indistinguishable under high density and temperature, as was seen in the early universe.
They can now be seen as different manifestations of the same force.
The list has been reduced to three.
The inclusion of the gravitational force, which has special characteristics of affecting the space and time in which the other forces exist, is proving difficult to unify.

While the unification of forces will not affect how we discuss forces in this text, it is fascinating that such underlying simplicity exists in the face of the overt complexity of the universe.

Nature is simple.

All forces are far away.

It's obvious for the force.
Earth and the Moon are not in contact.
It is true for all other forces.
Friction is a force between atoms that isn't touching.
A test object placed in this field will experience a force that is a function of location and other variables.
The force from one object to another is carried by the field.

The field is defined to be a characteristic of the object that it is created from.

The mass of Earth and the distance from its center are the main factors in the Earth's gravitational field.

The concept of a field is useful because equations can be written for force fields surrounding objects, and motions can be calculated from these equations.

There is an electric force field between two particles.

A positive test charge will cause a force in the direction of the force field lines.

The concept of a force field is also used in connection with electric charge and is presented in or all the basic forces.

Fields help us to visualize forces and how they are transmitted, as well as to describe them with precision.

The field concept can be used to calculate motions and describe nature.

The field concept leaves unanswered the question of what carries the force.
In 1935, Hideki Yukawa's work on the strong nuclear force proposed that all forces are transmitted by the exchange of elementary particles.
Particle exchange is similar to a basketball game in that two people pass the ball back and forth without touching one another.

The exchange of people leads to repulsive forces.

If person 2 pulled the basketball away from the first person as he tried to retain it, the force between them would be attractive.

The idea of particle exchange deepens rather than undermines field concepts.

It is more satisfying to think of something moving between objects.
The search for Yukawa's proposed particle found it and a number of others that were completely unexpected, stimulating yet more research.
The proposal of quarks as the underlying substructure of matter is a basic tenet of GUTs.

The structure of matter will be explained by these theories.

The real world is where the test of these theories must lie.
Scientists at the Large Hadron collider in Switzerland are starting to test theories using the world's largest particle collider.
Two high-energy protons can be sent in opposite directions by this accelerator.
Fourteen trillion electron volts will be available.
Some new particles are expected to be found.
The researchers hope to detect the force carriers of high interest.
The properties of the particles might tell us something.

The border between Switzerland and France is marked by the world's largest particle accelerator.

Two beams travelling in opposite directions collide in a tube similar to the central tube shown here.
The beam's path is determined by external magnets.

Particles will be analyzed by special detectors.

Questions like the origin of mass and the first few seconds of our universe will be explored.
The preliminary operation of this accelerator began in 2008.
Let's consider gravity to better understand force-carrier particles.
The search for waves has been going on for a long time.
Einstein predicted the existence of these waves almost 100 years ago.

During the collision of massive stars, black holes, or in supernova explosions--like shock waves--grittational waves are created.

These waves will travel through space at the speed of light, like a pebble dropped into a pond.
LIGO is a facility that uses the Laser Interferometer.
Each installation is designed to use optical lasers to look at the relative positions of the two masses.
The two sites allow simultaneous measurement of these small effects to be separated from other natural phenomena.
The initial operation of the detectors began in 2002.
Similar installations have been built in Italy, Germany, and Japan.

The EU/US project LISA is moving into space with international collaboration.

Earthquakes and other Earthly noises will not be a problem for these monitoring satellites.
LIGO will complement LISA by looking at more massive black holes.
Three satellites will be placed in space.
The relative positions of each satellite will be measured.
It will be necessary to detect waves with an accuracy of 10% of the size of an atom.
The launch of this project could be in the year 2018?

LIGO will tell us something we didn't know before.

The history of science shows that when you go where you haven't been before, you usually find something that really shakes the scientific paradigm of the day.
There is a drawing of LISA.

The distance between each satellite's test mass will be measured by the lasers.

Information about passing waves will be provided by the relative motion of these mass.

The ideas presented in this section are a glimpse into the topics that will be covered in later chapters.

An object's mass is related to inertia.

Inertia the system, as opposed to internal forces, which act between components.

Problem-Solving Strategies are used to solve problems involvingNewton's laws of motion.

Draw a picture of the problem.

The force of the system of interest is the weight of an object.

Draw a diagram of gravity acting on an object.
The object is a sketch showing all of the forces acting on it.
If the only force acting on an object is due to gravity, the directions from the dot are different.
The object is in free fall if the vectors act in a certain direction.

Add the forces acting on the object to the horizontal and Symmetry in Forces law.

Whenever one body.
The object exerts force on the first body if it does accelerate in that direction.

Check your answer.

Cars are pushed forward by a thrust reaction force.

In 4.5 Normal, Tension, and Other situations, the laws of motion can be applied to solve problems of motion.

There are examples of forces acting in different directions on an object.

When objects rest on a surface, the surface applies a draw diagrams, resolve all force into horizontal force to the object that supports the weight of the and vertical components, and draw a free-body object.
The supporting force acts in line with the diagram.
Determine the direction in which you are going away from the surface.
It's called a normal force.

When an object rests on an inclined plane that makes more than the weight of the object, the normal force will be less than.

The normal force can be resolved into components that act less than the full weight of the object if the object angle is horizontal.

The components that can be calculated are forces, acceleration, velocity, or position.

The problems of motion can be solved by applying concepts from dynamics and kinematics.

The pulling force that acts along a stretched flexible connector is called tension.

The various types of forces that are categorized for use object are all manifestations of the four basic forces in nature.

In any frame of reference, the properties of these forces are summarized in Table accelerated or rotated.

There are attempts to show that all four forces are related.

Different manifestations of a single unified force are responsible for the nuclear forces.

An example of a direction of the net external force on a stretched spring is discussed in the text.

The standard basketball must be able to produce the same force repeatedly.

When the second law of motion kicks in, why does an ordinary rifle recoil?

The rifle's barrel is open at both ends.

A rock is thrown.

If one pair of forces cancels, the system is not external.