Aleks: Math Prep For College Physics
ALEKS is an artificial intelligence-based system that is able to determine what a student actually understands in mathematics and then is able to determine what the student is ready to learn next . Because it is completely individualized to each student, students are able to work at their pace and are therefore better able to master skills that once eluded them.
Some Special Cases Of Vector Addition
The following are some special cases to make vector calculation easier to represent.
1. =0° : Here is the angle between the two vectors. That is, if the value of is zero, the two vectors are on the same side. In this case, the value of the resultant vector will be
Thus, the absolute value of the resultant vector will be equal to the sum of the absolute values of the two main vectors. Notice the image below
2. =180° : Here, if the angle between the two vectors is 180°, then the two vectors are opposite to each other. That is, the value of cos here will be -1.
Here the absolute value of the resultant vector is equal to the absolute value of the subtraction of the two vectors. And the resultant vector will be oriented towards it whose absolute value is higher than the others.
3. a=b and =180° : Here the two vectors are of equal value and are in opposite directions to each other. In this case, the absolute value of the resultant vector will be zero. That is, the resolution vector is a null vector
2. =90° : If the angle between the two vectors is 90 degrees. The value of cos will be zero. So, here the resultant vector will follow the formula of Pythagoras
In this case, the two vectors are perpendicular to each other. And the resultant vector will be located at the specified angle with the two vectors. Suppose, here two vectors a, b are taken and the resultant vector c is located at angle with a vector Then the direction of the resultant vector will be
What Are Vectors In Physics
A physical quantity is a quantity whose physical properties you can measure. Such as mass, force, velocity, displacement, temperature, etc.
Suppose you are told to measure your happiness. In this case, you can never measure your happiness. That is, you cannot describe and analyze with measure how much happiness you have. So, happiness here is not a physical quantity.
Suppose you have a fever. And the doctor ordered you to measure your body temperature. Then you measured your body temperature with a thermometer and told the doctor. When you tell your doctor about your body temperature, you need to use the word degree centigrade or degree Fahrenheit.
So, the temperature here is a measurable quantity. So we will use temperature as a physical quantity.
In general, we will divide the physical quantity into three types
In this tutorial, we will only discuss vector quantity. But before that, lets talk about scalar.
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Top Physics Questions And Answers Learn The Basics Of Physics Part 4
76) A body is thrown vertically upward from the ground. It reaches a maximum height of 20 min 5 sec. After what time, it will reach the ground from its maximum height position? 2.5 sec 5 sec 10 sec 25 secAnswer: B.
77) What is the practical unit of loudness?Answer: Decibel .
78) Among the following, the unit of sound absorption is _Answer: Sabin.
79) What are the elements required for the sensation of hearing?Answer: A vibrating source, a propagating medium, and a receiver namely ear.
80) If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s, it covers a distance of 2880 m 1440 m 400 m 20 mAnswer: C.
81) What is supersonic?Answer: Supersonic refers to the speed of an object moving with a speed greater than that of sound.
82) 2 December 1942 is known for:Answer: The creation of the first controlled chain reaction.
83) What are the essential characteristics of a musical sound?Answer: Loudness, pitch, and quality are the characteristics of a musical sound.
84) A car moving with a speed of 40 km/h can be stopped by applying brakes at least after 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance? 8 m 6 m 4 m 2 mAnswer: A.
85) What is known as the study of sound?Answer: Acoustics.
86) The Standard Unit of measurement of magnetic field strength is _Answer: Ampère per meter.
87) What is the distance between a compression and its nearest rarefaction in a longitudinal wave?Answer: L/2.
Example : Subtracting Vectors Graphically: A Women Sailing A Boat
A woman sailing a boat at night is following directions to a dock. The instructions read to first sail 27.5 m in a direction\boldsymbolnorth of east from her current location, and then travel 30.0 m in a direction\boldsymbolnorth of east . If the woman makes a mistake and travels in the opposite direction for the second leg of the trip, where will she end up? Compare this location with the location of the dock.
We can represent the first leg of the trip with a vector\textbf,and the second leg of the trip with a vector\textbf.The dock is located at a location\boldsymbol\:+\:\textbf}.If the woman mistakenly travels in the opposite direction for the second leg of the journey, she will travel a distance\textbf in the direction\boldsymbolsouth of east. We represent this as\boldsymbol},as shown below. The vector\boldsymbol}has the same magnitude as\textbfbut is in the opposite direction. Thus, she will end up at a location\boldsymbol+},or\boldsymbol-\textbf}.
We will perform vector addition to compare the location of the dock,\boldsymbol+\textbf},with the location at which the woman mistakenly arrives,\boldsymbol+}.
To determine the location at which the woman arrives by accident, draw vectors\textbfand\boldsymbol}.
Place the vectors head to tail.
Draw the resultant vector\textbf.
Use a ruler and protractor to measure the magnitude and direction of\textbf.
In this case,\boldsymbol=23.0\textbf}and\boldsymbolsouth of east.
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Medieval European And Islamic
The Western Roman Empire fell in the fifth century, and this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, and continued to advance various fields of learning, including physics.
Book of Opticscamera obscura
In sixth-century Europe John Philoponus, a Byzantine scholar, questioned Aristotle‘s teaching of physics and noted its flaws. He introduced the theory of impetus. Aristotle’s physics was not scrutinized until Philoponus appeared unlike Aristotle, who based his physics on verbal argument, Philoponus relied on observation. On Aristotle’s physics Philoponus wrote:
Philoponus’ criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries later, during the Scientific Revolution. Galileo cited Philoponus substantially in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus. It was a step toward the modern ideas of inertia and momentum.
Components Of A Vector
A vector that points in a random direction in the x-y plane has x and y components: it can be split into two vectors, one entirely in the x-direction and one entirely in the y-direction . Added together, the two components give the original vector.
The easiest way to add or subtract vectors, which is often required in physics, is to add or subtract vector components knowing how to break up a vector into its componenets is therefore a useful thing to know, and it involves nothing more complicated than the trigonometry associated with a right-angled triangle.
Consider the following example. A vector, which we will call A, has a length of 5.00 cm and points at an angle of 25.0 degrees above the negative x-axis, as shown in the diagram. The x and y components of A, Ax and Ay are found by drawing right-angled triangles, as shown. Only one right-angled triangle is actually necessary the two shown in the diagram are identical.
Knowing the length of A, and the angle of 25.0 degrees, Ax and Ay can be found by re-arranging the expressions for sin and cos.
Note that this analysis, using trigonometry, produces just the magnitudes of the vectors Ax and Ay. The directions can be found by looking on the diagram. Usually, positive x is to the right of the origin Ax points left, so it is negative:
Ax = -4.53 cm in the x-direction
Positive y is generally up Ay is directed up, so it is positive:
Ay = 2.11 cm in the y-direction
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What Is A Vector Anyway
In this course, we’ll be dealing with two kinds of quantities, scalars and vectors. A scalar is something that can be specified as just a number, like temperature or mass . A vector requires both a number and a direction. A velocity is a good example of a vector…if you came to campus on the T today, at some point you may have been travelling 20 km/hr east. Velocity is a combination of a scalar and a direction .
One crucial difference between scalars and vectors involves the use of plus and minus signs. A scalar with a negative sign means something very different from a scalar with a plus sign +30 C feels an awful lot different than -30 C, for example. With a vector, however, the sign simply tells you about the direction of the vector. If you’re travelling with a velocity of 20 km/hr east, it means you’re travelling east, and your speed is 20 km/hr. A velocity of -20 km/hr east also means that you’re travelling at a speed of 20 km/hr, but in the direction opposite to east…20 km/hr west, in other words.
Note that a vector will normally be written in bold, like this : A. A scalar, like the magnitude of the vector, will not be in bold face .
Carolyn Bertozzi Recipient Of The Nobel Prize In Chemistry
Carolyn Bertozzi, currently a professor at Stanford University, spent her formative years at UC Berkeley and taught on campus until 2015. She earned her Ph.D. in chemistry from the university in 1993 and joined UC Berkeleys chemistry faculty, and Berkeley Lab, in 1996, after working as a postdoctoral fellow at UCSF. She was also the first director of Berkeley Labs Molecular Foundry, a cutting-edge nanoscience research facility. She developed and named a field called bioorthogonal chemistry, which stages chemical reactions in cells that do not interfere with biological processes.
For 19 years, until 2015 the year she left to help lead Stanfords Sarafan ChEM-H institute developed at Berkeley the chemical biology techniques for which she received the Nobel Prize. She calls these techniques bioorthogonal chemistry, building off the click chemistry developed by her Nobel Prize co-winners, K. Barry Sharpless of Scripps Research in La Jolla, California, and Morten Meldal of the University of Copenhagen in Denmark.
Berkeley Lab, whose Molecular Foundry flourished under Bertozzis leadership, also offered its praises.
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Three Remarkable Scientists With Uc Connections Win Nobel Prizes
The Nobel Prizes were announced this week, and three of the extraordinary recipients have important connections to UC.
The Nobel Prize was established by Swedish businessman Alfred Nobel in 1895 and is designed to honor those whose work shall have conferred the greatest benefit to humankind. First awarded in 1901, they are announced on an annual basis, and include the categories of physics, chemistry, physiology or medicine, literature and peace, with economics added in Nobels memory in 1968 by Swedens central bank, SverigesRiksbank.
This year, the winners in medicine, physics and chemistry all share one important distinction: important foundational time spent at UC, a cradle of inventiveness, experimentation and learning. They are:
Solved Examples On Resultant Vector Formula
Example 1: Find the resultant of the vectors 4i + 3j -5k and 8i + 6j – 10k.
The given two vectors are:A = 4i + 3j – 5k and B = 8i + 6j – 10kThe direction ratios of the two vectors are in equal proportion and hence the two vectors are in the same direction.The following resultant vector formula can be used here.R = A + B= + = 12i + 9j – 15kAnswer: Hence the resultant of the two vectors is 12i + 9j – 15k.
Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees.
The two vectors are A = 5 units, B = 6 units and the angle Ø = 60°.The resultant vector can be obtained by the following formula.R2 = A2 + B2 + 2ABCosØ= 52 + 62 + 2×5×6×Cos60°= 25 + 36 + 60 × 1/2Answer: Therefore the resultant vector is 91.
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Watch The Video To Find Out What Base Measurements Are
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Nobel Prize In Physics
2022 Nobel Prize in Physics was conferred to scientists Alain Aspect, John Clauser and Anton Zeilinger for the research in the field of quantum mechanics.
About Nobel Prize in Physics
The Nobel Prize in Physics was conferred to 221 Nobel Prize laureates between the years 1901 to 2022. John Bardeen is the only individual to receive this prestigious award twice, in 1956 to 1972. It is bestowed by the Royal Swedish Academy of Sciences to give recognition to those who have made noteworthy contributions for humanity in the field of physics. The first to receive this award was German scientist Wihelm Rontgen for the discovery of X-rays.
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John F Clauser Recipient Of The Nobel Prize In Physics
In 1971, Clauser, a postdoctoral researcher working with the late UC Berkeley physicist Stuart Freedman, then a graduate student, got up to an exciting and revolutionary new experiment inside a UC Berkeley basement: testing one of the strangest aspects of quantum mechanics, what Einstein called spooky action at a distance. What Clauser and Freedman revealed about the quantum world, namely quantum entanglement, paved the way for stunning new advances in the field and led directly to the Nobel Prize in physics that Clauser received on Oct 4. .
Learn more about Clausers work as a young scientist in this UC Berkeley piece, quoted below: Physics Nobel recognizes Berkeley experiment on spooky action at a distance:
That experiment was the first to show that quantum mechanics really is weird. Two particles, once linked quantum mechanically, or entangled, can be separated by large distances even the diameter of the universe and still know what happens to one another.
The research was Freedmans Ph.D. dissertation in 1972, but he subsequently moved onto a broad range of subfields of physics, all related to quantum mechanics, and died tragically in 2012. Clauser continued to refine the experiment to provide more convincing proof that nature violates whats called Bells inequality and prove that the quantum mechanical description of entangled particles is right.
What Ever Does This Thing Do
DaveC426913 said:The bottom device is more mysterious and has a ratio more like 1:20-ish with the crank,
Maybe it was used for winding under-thread, with a preset tension, onto the bobbin of a sewing machine.
The OP instrument does not test tension, it measures the small change in length of a spun yarn as it is twisted. Procedure: The spindle counter dials are set to zero. The yarn to be tested is clamped at the spindle and at the length gauge, with a weight beyond the length gauge, to apply a constant tension. The spindle is then turned to remove the twist, which lengthens the yarn, but turning is continued until the length gauge shows the yarn length has reduced again to the same reading as initially set, . Half that spindle turns counter reading is the number of twists per length tested. No magnifying glass is needed to examine the yarn to determine the average point of zero twist at different positions along the sample.
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Virtual Labs For Physics
With Connect Virtual Labs for Physics, the Lab is Always Open. These virtual physics labs provide a flexible online lab solution for preparation, supplement, replacement, or make-up lab to bridge the gap between the lecture and lab. The experiments help students learn the data acquisition and analysis skills needed, then check for understanding and feedback. With pre-lab and post-lab assessments available, instructors can customize each assignment. Want to check out Virtual Labs in other science disciplines?
Learn more on how Virtual Labs meets Accessibility guidelines
Resolving A Vector Into Components
In the examples above, we have been adding vectors to determine the resultant vector. In many cases, however, we will need to do the opposite. We will need to take a single vector and find what other vectors added together produce it. In most cases, this involves determining the perpendicular componentsof a single vector, for example the x andy-components, or the north-south and east-west components.
For example, we may know that the total displacement of a person walking in a city is 10.3 blocks in a direction\boldsymbolnorth of east and want to find out how many blocks east and north had to be walked. This method is called finding the components of the displacement in the east and north directions, and it is the inverse of the process followed to find the total displacement. It is one example of finding the components of a vector. There are many applications in physics where this is a useful thing to do. We will see this soon in Chapter 3.4 Projectile Motion, and much more when we cover forces in Chapter 4 Dynamics: Newtons Laws of Motion. Most of these involve finding components along perpendicular axes , so that right triangles are involved. The analytical techniques presented in Chapter 3.3 Vector Addition and Subtraction: Analytical Methods are ideal for finding vector components.
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