Chapter 1:Introduction and Mathematical Concepts

Transcription

1 Physics 11 Chapter 1:Introduction and Mathematical Concepts Units Vector Addition General Schedule: Mondays: 2 labs due every other Monday (1 formal) Tuesdays: PLC due by 4:00 pm Thursdays: HW due; Quiz Recipe for Success in Physics 11: 1) Read book and/or online notes before I lecture on the material. 2) After each lecture, review your notes, work on your cheat sheet, and do the appropriate HW problems. 3) Finish HW by Tues. night so you can ask me, a PLC tutor, or another student questions. 4) Review HW and notes on Wed. night for Thursday s quiz. Units Physics is a study of the fundamental laws of nature, which are the laws that underlie all physical phenomena in the universe. Physics is based upon the measurements of various physical quantities. We measure a physical quantity by comparing it with a standard. For example, the foot was originally defined to be the length of the royal foot of King Louis XIV. Metric mishap caused loss of NASA orbiter (CNN) -- NASA lost a $125 million Mars orbiter because a Lockheed Martin engineering team used English units of measurement while the agency's team used the more conventional metric system for a key spacecraft operation, according to a review finding released Thursday. Error points to nation's conversion lag Lorelle Young, president of the U.S. Metric Association, said the loss of Climate Orbiter brings up the "untenable" position of the United States in relation to most other countries, which rely on the metric system for measurement. She was not surprised at the error that arose. "Only the metric system should be used because that is the system science uses," she said. 1

2 Units SI units are an international agreement on the standard units countries will use when measuring physical quantities. length meter (m) SI unit of length: meter (m) In 1792, the meter was officially defined by the French Academy of Sciences to be one tenmillionth of the distance from the north pole to the equator. mass kilogram (kg) time second (s) A Earth C Equator B AB 1 m 10 7 SI unit of length: meter (m) (The standard meter in 1889) For practical reasons, in 1889, the meter was redefined to be the distance between two fine lines engraved near the ends of a platinum-iridium bar. SI unit of length: meter (m) In 1960, the meter was redefined as 1,650, wavelengths of a particular light emitted by an isotope of krypton (krypton-86). Finally, in 1983, the meter was redefined to the definition that we use today. Definition of the meter: The meter is the length of path traveled by light in a vacuum during a time interval of 1/299,729,458 of a second. 2

3 SI unit of mass: kilogram (kg) The standard mass is a particular platinum-iridium cylinder, kept at the International Bureau of Weights and Measures near Paris, France, whose mass is defined to be exactly 1 kg. SI unit of mass: kilogram (kg) When dealing with atoms and molecules, the atomic mass unit (u) is usually used. One atomic mass unit (u) is defined to be 1/12 the mass of the carbon-12 atom. 1 u = kg SI unit of time: second (s) For many years, the second was defined as 1/86,400 of a mean solar day. In 1967, the definition of the second was defined to be 9,192,631,770 oscillations of the light (of a specified wavelength) emitted by a cesium-133 atom. SI unit of time: second (s) A cesium atomic clock kept at the National Institute of Standards and Technology (NIST). This particular clock keeps time with an accuracy of ~ 3 millionths of a second per year. The atomic clocks that are currently being developed will be so accurate that they would have to run for more than 30 billion years before they were off by 1.0 second. 3

4 Vectors and Scalars Vector a quantity that has a direction as well as a magnitude ex: displacement, velocity, acceleration, force, momentum Scalar a quantity that only has a magnitude (number and units) ex: distance, speed, time, mass, energy, work, density, temperature Vectors vectors are represented with arrows the length of the vector is proportional to the magnitude of the vector (use an appropriate scale such as 1 cm = 10 N) the direction of the arrow is the direction of the vector 100 N force at 45 o 50 N force at 0 o tip tail Parallelogram Tail-to-Tip Adding Vectors Graphically Tail-to-tip method: Adding Vectors Graphically 1) Draw one of the vectors to scale and in the right direction. choose an appropriate scale (1 in. = 25 N) 2) Draw the second vector (to scale and in the right direction) starting from the tip of the first. 3) The resultant vector is drawn from the tail of the first vector to the tip of the second vector. 4

5 Adding Vectors Graphically Note that it does not matter what order you add the vectors in. Adding Vectors Graphically This tail-to-tip method can easily be extended to three or more vectors. A + B = B + A You simply draw the tail of the third vector starting at the tip of the second vector. Vectors Subtraction Vectors Subtraction Subtracting a vector is the same as adding the negative of the vector. The negative of a vector has the same magnitude as the vector but the opposite direction. 5

6 A component of a vector is really just a projection of the vector onto an axis. Components of a vector are two perpendicular vectors that add together to produce the original vector. Any vector can be expressed as the sum of its components. 6

7 Adding Vector Using Components Adding Vector Using Components Adding Vector Using Components Adding Vector Using Components 7