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Analyzing Three Forces to Determine the Net Force

Methods of adding vectors were discussed earlier in Lesson 1 of this unit. During that discussion, the head to tail method of vector addition was introduced as a useful method of adding vectors that are not at right angles to each other. Now we will see how that method applies to situations involving the addition of force vectors.
A force board (or force table) is a common physics lab apparatus that has three (or more) chains or cables attached to a center ring. The chains or cables exert forces upon the center ring in three different directions. Typically the experimenter adjusts the direction of the three forces, makes measurements of the amount of force in each direction, and determines the vector sum of three forces. Forces perpendicular to the plane of the force board are typically ignored in the analysis.
Suppose that a force board or a force table is used such that there are three forces acting upon an object. (The object is the ring in the center of the force board or force table.) In this situation, two of the forces are acting in two-dimensions. A top view of these three forces could be represented by the following diagram.

The goal of a force analysis is to determine the net force and the corresponding acceleration. The net forceis the vector sum of all the forces. That is, the net force is the resultant of all the forces; it is the result of adding all the forces together as vectors. For the situation of the three forces on the force board, the net force is the sum of force vectors A + B + C.

One method of determining the vector sum of these three forces (i.e., the net force") is to employ the method of head-to-tail addition. In this method, an accurately drawn scaled diagram is used and each individual vector is drawn to scale. Where the head of one vector ends, the tail of the next vector begins. Once all vectors are added, the resultant (i.e., the vector sum) can be determined by drawing a vector from the tail of the first vector to the head of the last vector. This procedure is shown below. The three vectors are added using the head-to-tail method. Incidentally, the vector sum of the three vectors is 0 Newton - the three vectors add up to 0 Newton. The last vector ends where the first vector began such that there is no resultant vector.
The purpose of adding force vectors is to determine the net force acting upon an object. In the above case, the net force (vector sum of all the forces) is 0 Newton. This would be expected for the situation since the object (the ring in the center of the force table) is at rest and staying at rest. We would say that the object is at equilibrium. Any object upon which all the forces are balanced (Fnet = 0 N) is said to be at equilibrium.
Quite obviously, the net force is not always 0 Newton. In fact, whenever objects are accelerating, the forces will not balance and the net force will be nonzero. This is consistent with Newton's first law of motion. For example consider the situation described below.

 

 

An Example to Test Your Understanding

A pack of five Artic wolves are exerting five different forces upon the carcass of a 500-kg dead polar bear. A top view showing the magnitude and direction of each of the five individual forces is shown in the diagram at the right. The counterclockwise convention is used to indicate the direction of each force vector. Remember that this is a top view of the situation and as such does not depict the gravitational and normal forces (since they would be perpendicular to the plane of your computer monitor); it can be assumed that the gravitational and normal forces balance each other. Use a scaled vector diagram to determine the net force acting upon the polar bear. Then compute the acceleration of the polar bear (both magnitude and direction). When finished, check your answer by clicking the button and then view the solution to the problem by analyzing the diagrams shown below.
  
  
The task of determining the vector sum of all the forces for the polar bear problem involves constructing an accurately drawn scaled vector diagram in which all five forces are added head-to-tail. The following five forces must be added.
The scaled vector diagram for this problem would look like the following:



The above two problems (the force table problem and the polar bear problem) illustrate the use of the head-to-tail method for determining the vector sum of all the forces. The resultants in each of the above diagrams represent the net force acting upon the object. This net force is related to the acceleration of the object. Thus, to put the contents of this page in perspective with other material studied in this course, vector addition methods can be utilized to determine the sum of all the forces acting upon an object and subsequently the acceleration of that object. And the acceleration of an object can be combined with kinematic equations to determine motion information (i.e., the final velocity, the distance traveled, etc.) for a given object.

Sometimes 10 + 10 = 10 

In addition to knowing graphical methods of adding the forces acting upon an object, it is also important to have a conceptual grasp of the principles of adding forces. Let's begin by considering the addition of two forces, both having a magnitude of 10 Newton. Suppose the question is posed:
10 Newton + 10 Newton = ???
How would you answer such a question? Would you quickly conclude 20 Newton, thinking that two force vectors can be added like any two numerical quantities? Would you pause for a moment and think that the quantities to be added are vectors (force vectors) and the addition of vectors follow a different set of rules than the addition of scalars? Would you pause for a moment, pondering the possible ways of adding 10 Newton and 10 Newton and conclude, "it depends upon their direction?" In fact, 10 Newton + 10 Newton could give almost any resultant, provided that it has a magnitude between 0 Newton and 20 Newton. Study the diagram below in which 10 Newton and 10 Newton are added to give a variety of answers; each answer is dependent upon the direction of the two vectors that are to be added. For this example, the minimum magnitude for the resultant is 0 Newton (occurring when 10 N and 10 N are in the opposite direction); and the maximum magnitude for the resultant is 20 N (occurring when 10 N and 10 N are in the same direction).

 

The above diagram shows what is occasionally a difficult concept to believe. Many students find it difficult to see how 10 N + 10 N could ever be equal to 10 N. For reasons to be discussed in the next section of this lesson, 10 N + 10 N would equal 10 N whenever the two forces to be added are at 30 degrees to the horizontal. For now, it ought to be sufficient to merely show a simple vector addition diagram for the addition of the two forces (see diagram below).

 


 

We Would Like to Suggest ...

Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Name That Vector Interactive, our Vector Addition Interactive, or our Vector Guessing Game Interactive. All three Interactives can be found in the Physics Interactive section of our website and provide an interactive experience with the skill of adding vectors.

 
 

 

Check Your Understanding

Answer the following questions and then view the answers by clicking on the button.
1. Barb Dwyer recently submitted her vector addition homework assignment. As seen below, Barb added two vectors and drew the resultant. However, Barb Dwyer failed to label the resultant on the diagram. For each case, that is the resultant (A, B, or C)? Explain.





2. Consider the following five force vectors.
Sketch the following and draw the resultant (R). Do not draw a scaled vector diagram; merely make a sketch. Label each vector. Clearly label the resultant (R).
A + C + D

B + E + D

'Ring of exceptional points' appears on a Dirac cone



A material with exotic optical properties that make it both transparent and reflective to light has been created by physicists in the US and Singapore. The material, which resembles a thin piece of glass with tiny holes drilled in it, could be used to boost the output of some lasers and detect extremely small quantities of biological and chemical materials.
When light travels through a transparent material without losing energy, the system can be described by a set of energy states with values that are real numbers. In contrast, if light is absorbed during transmission, the energy states are described by complex numbers – with the imaginary part describing the absorption process. One fascinating element of complex energy states is that it is possible to have "exceptional points" where two or more energy states have the same value. Where this happens, the interplay between the energy states can cause the system to behave as if no energy loss occurs. An example of this that has been observed in the lab is "loss-induced optical transparency", whereby a material that is normally opaque can transmit light in specific directions.

Distorted cone

Now, Marin Soljačić, John Joannopoulos and colleagues at the Massachusetts Institute of Technology (MIT) have created a photonic crystal with exceptional points in its "Dirac cone" – which is the cone-shaped function that describes the relationship between the frequency and momentum of light in the material (see figure). Their crystal is a thin layer of silicon nitride that is drilled to create a square lattice of holes (diameter 218 nm) separated by 336 nm. The size and separation of the holes was chosen so that the system is described by a Dirac cone. A true Dirac cone has real energy states, so the team needed to distort the cone so that the states are complex. This was done by simply making a silicon-nitride layer with a finite thickness of 180 nm. In this case, the imaginary component corresponds to light being radiated out of the photonic crystal, rather than light being absorbed.
Calculations and simulations done by the team suggest that when the photonic crystal is immersed in a liquid with a specific index of refraction, a ring of exceptional points should appear around its distorted Dirac cone (see figure). This was confirmed by firing light at the crystal and measuring how much was reflected at different incident angles and frequencies. The data reveal a sharp drop in the reflectivity for incident light that is on the ring of exceptional points. This effect is called "coupled-resonator-induced transparency" – or CRIT – and the team believes that it could be used to boost the performance of some optical devices.
Soljačić believes the effect could be used to boost the output of photonic-crystal-based lasers by a factor of 10. "Photonic-crystal surface-emitting lasers are a very promising candidate for the next generation of high-quality, high-power compact laser systems," he says.
"Our system could also be used for high-precision detectors for biological or chemical materials, because of its extreme sensitivitym," adds team member Chia Wei Hsu. This is because a tiny change in the immersion fluid will have a large effect on the CRIT.

source:www.physicsworld.com(http://physicsworld.com/cws/article/news/2015/sep/18/ring-of-exceptional-points-appears-on-a-dirac-cone )


 publisher: Sivar .A.Baiz                                                                            Hawler@Kurdistan - Iraq(22/9/2015)

The 10 best physicists(Great Scientists)

Isaac NewtonCo-inventor of calculus, a major contributor to the science of optics and a gifted mathematician, Isaac Newton (1643-1727), who was born in Lincolnshire, outlined the laws of mechanics that now underpin vast swaths of classical physics. Most important of all, Newton outlined theprinciple of gravity, which explained how the planets revolve round the sun. During his life, he was showered with honours, including the presidency of the Royal Society. He is renowned as a supreme rationalist, though he actually wrote more about alchemy and religion, including a 300,000-word treatise that attempted to prove the pope was really the Antichrist and an “apocalyptic whore”.


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Niels BohrBorn in Copenhagen, Bohr (1885-1962) developed the modern idea of an atom, which has a nucleus at the centre with electrons revolving round it. When electrons move from one energy level to another, they emit discrete quanta of energy. The work won Bohr a Nobel prize in 1922. For his achievements, Carlsberg brewery gave Bohr a special gift: a house with a pipeline connected to its brewery next door, thus providing him with free beer for life. In 1954, Bohr helped establish Cern, the European particle physics facility. In 1975, his son, Aage, won a Nobel for research on atomic nuclei.

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Galileo GalileiBorn in Pisa, Galileo (1564-1642) initially trained as a doctor. On hearing of the invention of the telescope in 1609, he built his own and turned it to the heavens, revealing the existence of sunspots and a pitted, mountainous surface on the moon: the heavens were not incorruptible. His studies also provided support for the idea that the Earth revolves round the sun. This got Galileo into considerable trouble with the Catholic church and he was forced to abandon that backing in 1633. His work on falling bodies also laid the groundwork for Newton’s subsequent theories.


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Albert EinsteinThree great theories define our physical knowledge of the universe: relativity, quantum mechanics and gravitation. The first is the handiwork of German-born Albert Einstein (1879-1955), who remains the physicist with the greatest reputation for originality of thought. His work showed that space and time are not immutable but are fluid and malleable. Einstein, who took US citizenship in 1940, also provided the world with its most famous equation, E=mc2, which demonstrates the equivalence of mass and energy. His name has become synonymous with the idea of genius and he died a celebrity. He was awarded the 1921 Nobel prize for physics.
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James Clerk MaxwellIn contrast to Newton and Einstein, Edinburgh-born Maxwell (1831-79) is virtually unknown to the general public. Yet his contribution to physics was every bit as significant, particularly his discovery of the theory of electromagnetism. This showed that electricity, magnetism and light are all manifestations of the same phenomenon, the electromagnetic field. The development of radio, TV and radar were the direct consequences. Maxwell also carried out pioneering work in optics and colour vision. However, in his later years, his God-fearing Scottish upbringing brought him into dispute with the evolutionary thinking of Darwin and others and he wrote papers denouncing natural selection.


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Michael FaradayLargely self-educated, Faraday (1791-1867) became one of the greatest scientists of his day thanks to the patronage of the eminent English chemist Humphry Davy, who hired him as an assistant in 1813. Faraday went on to establish the idea of the electromagnetic field and discovered electromagnetic induction and the laws of electrolysis. His electromagnetic devices formed the foundation of electric motor technology. He twice rejected offers of a knighthood and when asked to advise on chemical weapons for the Crimean war effort, refused on ethical grounds. Einstein kept a picture of Faraday on his study wall (alongside pictures of Newton and Maxwell).

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Marie CurieThe first woman to win a Nobel and the first person to win two separate Nobels, Curie (1867-1934) was born in Poland and won her first Nobel in 1903 with husband, Pierre, for discovering radioactivity. However, she was not allowed to participate in the keynote lecture winners give because she was a woman. After Pierre died in a road accident in 1906, she won her second Nobel in 1911 for discovering radium, though an attempt was made to rescind it when news emerged of her affair with married colleague Paul Langevin. After collecting the prize, Curie was pilloried by the French press. Langevin was ignored.

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Richard FeynmanOne of the 20th century’s most influential and colourful physicists, Feynman (1918-88) played a key role in the development of quantum electrodynamics, the theory that describes how light and matter interact, earning him a Nobel prize in 1965. Feynman also contributed to the fields of quantum computing and nanotechnology and was a member of the Rogers Commission that lambasted Nasa over the destruction of space shuttle Challenger in 1986. He was a keen drummer, experimented with drugs and often worked on physics problems in topless bars because he said they helped him concentrate. Feynman died in 1988, aged 69.

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Ernest RutherfordNew Zealand-born Rutherford (1871-1937) is considered one of the greatest of all experimental physicists. He discovered the idea of radioactive half-life and showed that radioactivity involved the transmutation of one chemical element to another. He was awarded a Nobel in 1908 “for his investigations into the disintegration of the elements”. Rutherford later became director of the Cavendish Laboratory at Cambridge University where, under his leadership, the neutron was discovered by James Chadwick in 1932 and the first experiment to split the nucleus was carried out by John Cockcroft and Ernest Walton. The element rutherfordium was named after him in 1997.


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Paul DiracOne of the most revered – and strangest – figures in physics. The son of a Swiss father and English mother, Dirac (1902-84) was born in Bristol. He predicted the existence of antimatter, created some of quantum mechanics’ key equations and laid the foundations for today’s micro-electronics industry. Dirac won a Nobel in 1933 but remained “an Edwardian geek”, according tobiographer Graham Farmelo. He turned down a knighthood because he didn’t want people using his first name, while his daughter, Monica, never once remembered him laughing. “This balancing on the dizzying path between genius and madness is awful,” Einstein said of him.

source:http://www.theguardian.com/culture/gallery/2013/may/12/the-10-best-physicists
                                                                                                                                                                    Sivar  A.Baiz                                                                                          Hawler@Kurdistan 8-9-2015

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