Download Presentation
## Mathematics and Physics

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Section**Mathematics and Physics 1.1 What is Physics? • Physics is a branch of science that involves the study of the physical world: energy, matter, and how they are related. • Learning physics will help you to understand the physical world. • Any problem that deals with temperature, size, motion, position, shape or color involves physics.**Review Questions:**• 1. Identify the area of physics that is most relevant to each of the following situations. Explain your reasoning. • A. High school football game • B. Food preparation for the prom • C. Playing in the school band • D. Lightning in a thunderstorm • E. Wearing sunglasses outside in the sun**Question #1 Answer**• A. High school football game: mechanics • B. Food preparation for the prom: thermodynamics • C. Playing in the school band: waves • D. Lightning in a thunderstorm: electromagnetism • E. Wearing sunglasses outside in the sun: optics**Question #2**• Identify the area of physics involved in each of the following tests of a lightweight metal alloy proposed for use in sailboat hulls: • A. Testing the effects of a collision on the alloy • B. Testing the effects of extreme heat and cold on the alloy • C. Testing whether the alloy can affect a magnetic compass needle**Answer #2**• A. Testing the effects of a collision on the alloy: mechanics • B. Testing the effects of extreme heat and cold on the alloy: thermodynamics • C. Testing whether the alloy can affect a magnetic compass needle: electromagnetism**Section**Mathematics and Physics 1.1 SI Units • The Système International d’Unités, or SI, uses seven base quantities, which are shown in the table below.**Measurement**Derived units • Area – square meter, m2 • Volume – cubic meter, m3 • Force – newton, N • Pressure – pascal, Pa • Energy – joule, J • Power – watt, W • Voltage – volt, V • Frequency – hertz, Hz • Electric charge – coulomb, C**Section**Mathematics and Physics 1.1 SI Units • Measuring standards for kilogram and meter are shown below. • International Bureau of Weights and Measures in Sèvres, France and the National Institute of Science and Technology (NIST) in Gaithersburg, Maryland • http://www.surveyhistory.org/the_standard_meter1.htm**Great (giga)**Magnificent (mega) King (kilo) Hector (hecto) Drinks (deka) Ultra (unit) Delicious (deci) Chocolate (centi) Milk (milli) Most (micro) Nights (nano) Mnemonic device for remembering prefixes**1. 30 Gm = ___ µm**2. 1 Mg = ___ ng 3. 0.052 mL = ___ ML 4. 0.58 Mm = ___ nm 5. 597 ng= ____ mg Conversion practice**Section**Mathematics and Physics 1.1 Dimensional Analysis • This method of treating the units as algebraic quantities, which can be cancelled, is called dimensional analysis. • Dimensional analysis also is used in choosing conversion factors. • A conversion factor is a multiplier equal to 1. For example, because 1 kg = 1000 g, you can construct the following conversion factors:**Section**Section Check 1.1 Question 1 The potential energy, PE, of a body of mass, m, raised to a height, h, is expressed mathematically as PE = mgh,where g is the gravitational constant. If m is measured in kg, g in m/s2, h in m, and PE in joules, then what is 1 joule described in base unit? • 1 kg·m/s • 1 kg·m/s2 • 1 kg·m2/s • 1 kg·m2/s2**Section**Section Check 1.1 Answer 1 Answer:D Reason:**Section**Section Check 1.1 Question 2 A car is moving at a speed of 90 km/h. What is the speed of the car in m/s? (Hint: Use Dimensional Analysis) • 2.5×101 m/s • 1.5×103 m/s • 2.5 m/s • 1.5×102 m/s**Section**Section Check 1.1 Answer 2 Answer:A Reason:**Section**Section Check 1.1 Question 3 Which of the following representations is correct when you solve 0.030 kg + 3333 g using scientific notation? • 3.4×103 g • 3.36×103 g • 3×103 g • 3363 g**Section**Section Check 1.1 Answer 3 Answer:A Reason:0.030 kg can be written as 3.0 101 g which has 2 significant digits, the number 3 and the zero after 3. In number 3333 all the four 3’s are significant hence it has 4 significant digits. So our answer should contain 2 significant digits.**Section**Mathematics and Physics 1.1 Significant Digits • A meterstick is used to measure a pen and the measurement is recorded as 14.3 cm. • This measurement has three valid digits: two you are sure of, and one you estimated. • The valid digits in a measurement are called significant digits. • However, the last digit given for any measurement is the uncertain digit.**Section**Mathematics and Physics 1.1 Scientific Methods • Observe (this may lead to or be the result of a question) • A scientist often works with an idea that can be worded as a hypothesis, which is an educated guess about how variables are related. • Test with an experiment (record & analyze all data) • Draw a conclusion from experiment (may lead to new hypothesis & more experiments)**Section**Mathematics and Physics 1.1 Models, Laws, and Theories • A scientific law is a rule of nature that sums up related observations to describe a pattern in nature. • A scientific theory is an explanation based on many observations supported by experimental results.**Section**Graphing Data 1.3 Identifying Variables • The independent variable is the factor that is changed or manipulated during the experiment. (x axis) • The dependent variable is the factor that depends on the independent variable. (y axis)**Section**Graphing Data 1.3 Linear Relationships • When the line of best fit is a straight line, the dependent variable varies linearly with the independent variable.**Section**Graphing Data 1.3 Nonlinear Relationships: Quadratic Relationship • A quadratic relationship exists when one variable depends on the square of another.**Section**Graphing Data 1.3 Nonlinear Relationships: Inverse Relationship • In an inverse relationship,a hyperbola results when one variable depends on the inverse of the other.**Section**Section Check 1.3 Question 1 Which type of relationship is shown following graph? • Linear • Inverse • Parabolic • Quadratic**Section**Section Check 1.3 Answer 1 Answer:B Reason:In an inverse relationship a hyperbola results when one variable depends on the inverse of the other.**Section**Section Check 1.3 Question 2 What is line of best fit? • The line joining the first and last data points in a graph. • The line joining the two center-most data points in a graph. • The line drawn close to all data points as possible. • The line joining the maximum data points in a graph.**Section**Section Check 1.3 Answer 2 Answer:C Reason:The line drawn closer to all data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one or two points that help to determine the line.