11A Section: Describing Position PDF

Section 11A: Describing Position 11A Questions Ø Ø Ø Ø Why use Newtonian mechanics if newer models are better? How do we study motion? How can tools help us study motion? Aren’t distance and displacement the same thing? pp. 244–252 mechanics the study of motion kinematics the study of how t...

Section 11A: Describing Position 11A Questions Ø Ø Ø Ø Why use Newtonian mechanics if newer models are better? How do we study motion? How can tools help us study motion? Aren’t distance and displacement the same thing? pp. 244–252 mechanics the study of motion kinematics the study of how things move What is the history of mechanics? Section 11.1 Greek Philosophical Thought • Aristotle believed that things move as they do because it is their nature. • Earth and water move downward. • Air and fire move upward. • Heavenly bodies move around. • Planets appear to “wander.” Early Scientific Thought • Early 1600s: Tycho Brahe and Johannes Kepler studied the motion of planets. • Brahe made highly accurate observations of the planets’ positions over time. • Kepler used those observations and applied mathematics to explain retrograde motion, the apparent reversal of the planets in their orbits. Early Scientific Thought • Kepler’s work resulted in the three laws of planetary motion. • Galileo studied falling objects. • He came to the conclusion that all objects would fall at the same rate in a vacuum. Classical Mechanics • Isaac Newton developed the first truly mathematical model of motion in the late 1600s. • His three laws of motion – and his law of universal gravitation – form the basis for classical mechanics. Modern Motion Models • Quantum mechanics developed from the study of subatomic particles. • Albert Einstein developed relativistic mechanics to explain the motion of high-speed objects. Modern Motion Models • These models are more workable than Newtonian mechanics, but also far more complex. • Newtonian mechanics explains observations and makes predictions accurately enough for most objects without being overly complex. What is a “frame of reference”? Section 11.2 frame of reference a coordinate system used to describe the motion of an object Your frame of reference determines who you say is “moving” inside this airplane. system a portion of a larger motion that we are interested in studying Anything that is not part of the selected system is considered part of the environment. What is the difference between distance and displacement? Section 11.3 distance (d ) how far an object moves during a time interval displacement (Δx) a vector quantity that describes a change in position Displacement (Δx) • When getting directions, knowing the distance to your destination is not enough; you also need to know which direction to go. • Displacement includes both the distance and direction involved in a change in position. Displacement (Δx) • The formula for calculating displacement is Δx = xf – xi where Δx is the displacement (change in position), xf is the final position, and xi is the initial position. Displacement (Δx) • In this example, the trips to and from home are equal distances, but opposite directions. Distance is always positive, while displacement may be positive or negative. Displacement (Δx) • Distance is typically larger than displacement, since distance includes any side roads you may have to travel to get to the destination, while displacement measures the change in position “as the crow flies.” Moving in One Dimension AàB Starting from A (10 m east) and moving to B (40 m east), we travel 30 m, and our displacement is Δx = 40 m – 10 m = 30 m which means 30 m east or 30 m to the right. Moving in One Dimension AàBàC Continuing from B (40 m east) to C (40 m west), our distance traveled from A to C is 110 m and our displacement is Δx = –40 m – 10 m = –50 m which means 50 m west, or 50 m to the left. Moving in One Dimension AàBàCàD Turning around again and traveling from C (40 m west) to D (20 m west), our total distance from A to D is 130 m, and our displacement is Δx = –20 m – 10 m = –30 m which means 30 m west, or 30 m to the left. Moving in Two Dimensions AàB Starting from A and moving to B (8 km east), we have traveled 8 km and our displacement is 8 km east. Moving in Two Dimensions AàBàC Continuing from B (8 km east) to C (6 km south), our distance traveled from A to C is 14 km. Use the Pythagorean theorem to find the displacement value. c2 = a2 + b2 Moving in Two Dimensions AàBàC c2 = a2 + b2 c = 𝑎2 + 𝑏2 = 8 km 2 = 100 km2 = 𝟏𝟎 𝐤𝐦 + (6 km)2 Moving in Two Dimensions AàBàCàD Distance = 22 km Displacement = 6 km to the south Moving in Two Dimensions AàBàCàDàA Distance = 28 km Displacement = 0 EXAMPLE 11-1 Calculating Distance and Displacement While hiking in the national forest, you start at the ranger station and hike 4.5 km east. On the second leg of the hike, you travel 2.3 km south. Finally, you travel 5.7 km to the west. What is your total distance traveled? What is your displacement from the ranger’s station? p. 252 EXAMPLE 11-1 Calculating Distance and Displacement Write what you know. Δx1 = 4.5 km east Δx2 = 2.3 km south Δx3 = 5.7 km west Draw three displacement vectors end to end, using arrows to indicate direction. p. 252 EXAMPLE 11-1 Calculating Distance and Displacement Distance: 12.5 km Use the Pythagorean theorem: c2 = a2 + b2 c = 𝑎2 + 𝑏2 = 2.3 𝑘𝑚 2 + (1.2 𝑘𝑚)2 = 6.73 𝑘𝑚2 = 2.6 𝑘𝑚 Displacement: 2.6 km southwest p. 252 What are scalars and vectors? Section 11.4 scalar a measurable quantity that consists of magnitude (size) only Scalar Quantities • • • • Distance (35 m) Temperature (22 °C) Pressure (101 325 Pa) Speed (115 kph) vector upward force (muscle) downward force (gravity) a measurable quantity with both magnitude and direction Scalar Quantities • • • • Distance (35 m) Temperature (22 °C) Pressure (101 325 Pa) Speed (115 kph) Vector Quantities • • • • Displacement (35 m north) Velocity (115 kph northwest) Acceleration (9.8 m/s2 downward) Force (45 N upward)