Chapter 1: Units, Physical Quantities in addition to Vectors About Physics What is Physics
Mollenkamp, Aida, Food Editor has reference to this Academic Journal, PHwiki organized this Journal Chapter 1: Units, Physical Quantities in addition to Vectors About Physics What is Physics Physics [Gr. Physika, physical or natural things] Originally, natural sciences or natural philosophy The science of dealing with properties, changes, interaction, etc., of matter in addition to energy Physics is subdivided into mechanics, thermodynamics, optics, acoustics, etc. From Webster’s Unabridged Dictionary
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Science Science [Latin scientia – knowledge] Originally, state of fact of knowing; knowledge, often as opposed to intuition, belief, etc. Systematized knowledge derived from observation, study in addition to experimentation carried on in order to determine the nature or principles of what is being studied. A Science must have PREDICTIVE power Physics: Like a Mystery Story Nature presents the clues Experiments We devise the hypothesis Theory A hypothesis predicts other facts that can be checked – is the theory right Right – keep checking Wrong – develop a new theory Physics is an experimental science The Ancient Greeks Aristotle (384-322 B.C.) is regarded as the first person to attempt physics, in addition to actually gave physics its name. On the nature of matter: Matter was composed of: Air Earth Water Fire Every compound was a mixture of these elements Un as long as tunately there is no predictive power
On the Nature of Motion Natural motion – like a falling body Objects seek their natural place Heavy objects fall fast Light objects fall slow Objects fall at a constant speed Unnatural motion – like a cart being pushed The moving body comes to a st in addition to still when the as long as ce pushing it along no longer acts The natural state of a body is at rest Aristotelian Physics Aristotelian Physics was based on logic It provided a framework as long as underst in addition to ing nature It was logically consistent It was wrong !!! Aristotelian physics relied on logic – not experiment The Renaissance Galileo Galilei (1564 -1642) was one of the first to use the scientific method of observation in addition to experimentation. He laid the groundwork as long as modern science.
Classical Mechanics Newtons Laws work fine as long as Large Objects – Balls, planes, planets, Small objects (atoms) Quantum Mechanics Slow Objects – people, cars, planes, Fast objects (near the speed of light) Relativity Classical Mechanics – essentially complete at the end of the 19th Century Mechanics: the study of motion Galileo (1564 -1642) laid the groundwork as long as Mechanics Newton (1642-1727) completed its development (~almost~) Why is Physics Important Planetary motion Steam Engines Radio Cars Television Newtons Laws in addition to Classical Physics Quantum Mechanics The Next Great Theory Microwaves Transistors Computers Lasers Teleportation Faster than light travel (cant exist today) “Heavier-than-air flying machines are impossible.” Lord Kelvin, president, Royal Society, 1895. Mechanics Physics is science of measurements Mechanics deals with the motion of objects What specifies the motion Where is it located When was it there How fast is it moving Be as long as e we can answer these questions We must develop a common language
Units Fundamental Units Length [L] Foot Meter – Accepted Unit Furlong Time [T] Second – Accepted Unit Minute Hour Century Mass [M] Kilogram – Accepted Unit Slug Derived Units Single Fundamental Unit Area = Length Length [L]2 Volume = Length Length Length [L]3 Combination of Units Velocity = Length / Time [L/T] Acceleration = Length / (Time Time) [L/T2] Jerk = Length / (Time Time Time) [L/T3] Force = Mass Length / (Time Time) [M L/T2]
Units SI (Système Internationale) Units: mks: L = meters (m), M = kilograms (kg), T = seconds (s) cgs: L = centimeters (cm), M = grams (g), T = seconds (s) British Units: Inches, feet, miles, pounds, slugs We will switch back in addition to as long as th in stating problems. Unit Conversion Useful Conversion Factors: 1 inch = 2.54 cm 1 m = 3.28 ft 1 mile = 5280 ft 1 mile = 1.61 km Example: convert miles per hour to meters per second: Orders of Magnitude Physical quantities span an immense range Length size of nucleus ~ 10-15 m size of universe ~ 1030 m Time nuclear vibration ~ 10-20 s age of universe ~ 1018 s Mass electron ~ 10-30 kg universe ~ 1028 kg
Physical Scale Orders of Magnitude Set the Scale Atomic Physics ~ 10-10 m Basketball ~ 10 m Planetary Motion ~ 1010 m Knowing the scale lets us guess the Result Q: What is the speed of a 747 Distance – New York to LA 4000 mi Flying Time 6 hrs = 660 mph Dimensional Analysis Fundamental Quantities Length – [L] Time – [T] Mass – [M] Derived Quantities Velocity – [L]/[T] Density – [M]/[L]3 Energy – [M][L]2/[T]2 Physical Quantities Must always have dimensions Can only compare quantities with the same dimensions v = v(0) + a t [L]/[T] = [L]/[T] + [L]/[T]2 [T] Comparing quantities with different dimensions is nonsense v = a t2 [L]/[T] = [L]/[T]2 [T]2 = [L]
Provides Solution Sometimes Period of a Pendulum Period is a time [T] – t Can only depend on: Length [L] – l Mass [M] – m Gravity [L/T2] – g Which of these could be correct Solving Problems Problem Solving Strategy Each profession has its own specialized knowledge in addition to patterns of thought. The knowledge in addition to thought processes that you use in each of the steps will depend on the discipline in which you operate. Taking into account the specific nature of physics, we choose to label in addition to interpret the five steps of the general problem solving strategy as follows:
Problem Solving Strategy A. Everyday language: 1) Make a sketch. 2) What do you want to find out 3) What are the physics ideas B. Physics description: 1) Make a physics diagram. 2) Define your variables. 3) Write down general equations. D. Calculate solution: 1) Plug in numerical values. E. Evaluate the answer: 1) Is it properly stated 2) Is it reasonable 3) Answered the question asked C. Combine equations: 1) Select an equation with the target variable. 2) Which of the variables are not known 3) Substitute in a different equation. 4) Continue as long as all of the unknown variables . 5) Solve as long as the target variable. 6) Check units. Problem Solving Strategy, Step A A. Everyday language description: In this step you develop a qualitative description of the problem. Visualize the events described in the problem by making a sketch. The sketch should indicate the different objects involved in addition to any changes in the situation (e.g. changes in as long as ce applied, collisions, etc.) First, identify the different objects that are relevant to finding your desired category. Next, identify whether there is more than one stage (part) to the behavior of the object during the time from the beginning to the end that is relevant as long as what you are trying to find out. Things that would indicate more than one part would include key in as long as mation about the behavior of the object at a point between start in addition to end of movement, collisions, changes in the as long as ce applied or acceleration of an object. Write down a simple statement of what you want to find out. This should be a specific physical quantity that you could calculate to answer the original question. Write down verbal descriptions of the physics ideas (the type of problem). Identify the physics idea as long as each stage of each object. If the physics idea is a vector quantity (motion, as long as ce, momentum, etc.) identify how many dimensions are involved. Problem Solving Strategy, Step B B. Physics description: In this step you use your qualitative underst in addition to ing of the problem to prepare as long as the quantitative solution. First, simplify the problem situation by describing it with a diagram in terms of simple physical objects in addition to essential physical quantities. Make a physics diagram. You will need a diagram as long as each physics idea as long as each object, in addition to possibly one as long as each stage in addition to as long as each dimension. Define your variables (make a chart) of know quantities in addition to unknown quantities. Identify the variable you will solve as long as . Make sure variables are defined as long as each object, stage, idea in addition to dimension. Pay attention to units, to make sure you have the right kind of units as long as each type of variable. Using the physics ideas assembled in A-3 in addition to the diagram you made in B-1, write down general equations which specify how these physical quantities are related according to the principles of physics or mathematics.
Problem Solving Strategy, Step C C. Combine equations: In this step you translate the physics description into a set of equations which represent the problem mathematically by using the equations assembled in step 2. Select an equation from the list in B3 that contains the variable you are solving as long as (as specified in B2). Identify which of the variables in the selected equation are not known. For each of the unknown variables, select another equation from the list in B3 in addition to solve it as long as the unknown variable. Then substitute the new equation in as long as the unknown quantity in the original equation. Continue steps 2 & 3 until all of the unknown variables (except the variable you are solving as long as ) have been replaced or eliminated. Solve as long as the target variable. Check your work by making sure the units work out. Problem Solving Strategy, Steps D & E D. Calculate solution: In this step you actually execute the solution you have planned. Plug in numerical values (with units) into your solution from C-5. E. Evaluate the answer: Finally, check your work. Is it properly stated Is it reasonable Have you actually answered the question asked Problem Solving Strategy Consider each step as a translation of the previous step into a slightly different language. You begin with the full complexity of real objects interacting in the real world in addition to through a series of steps arrive at a simple in addition to precise mathematical expression. The five-step strategy represents an effective way to organize your thinking to produce a solution based on your best underst in addition to ing of physics. The quality of the solution depends on the knowledge that you use in obtaining the solution. Your use of the strategy also makes it easier to look back through your solution to check as long as incorrect knowledge in addition to assumptions. That makes it an important tool as long as learning physics. If you learn to use the strategy effectively, you will find it a valuable tool to use as long as solving new in addition to complex problems.
Unit Vectors Unit vectors provide a convenient means of notation to allow one to express a vector in terms of its components. Unit vectors always have a magnitude of 1 (with no units). Unit vectors point along a coordinate direction. Unit vectors are written using a caret (or “hat”, ^ ) to distinguish them from ordinary vectors. Unit Vectors
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