Slides for Week 6 - SFSU Physics & Astronomy
Transcription
Slides for Week 6 - SFSU Physics & Astronomy
3/6/15 Announcements • Today: Centripetal force and gravity • Wednesday: Finish Gravity • Reading for Wednesday: Chapter 10, focus on figs. 10.3, 10.17, & 10.31 • I am working on the midterms! They should be ready by the end of this week, or next Monday at the latest. Scores will be posted on iLearn, and you’ll be able to come pick up your tests in my office. Centripetal Force Centripetal Force • Centripetal means “towards the center.” Whenever an object moves along a circular path, there must be a force on that object in the direction of the center of the circle. • In such a case, the force is said to be centripetal Example: The spin cycle! • Any force directed toward a fixed center is called a centripetal force. – Centripetal means “center-seeking” or “toward the center.” F = mv2/r r = radius of circle v = tangential velocity Example Chapter 9: Gravity You are riding at the very edge of a merrygo-round with a radius of 2 m. Your friend runs alongside, pushing the merry-go-round so that it’s tangential speed is 3 m/s. a. What force is keeping you from sliding off? b. If you have a mass of 75 kg, what is the strength of that force? 1 3/6/15 Newton’s Law of Gravity • Everything with mass pulls on everything else with mass • Gravity is always attractive • The closer the object, the stronger the pull Newton’s Law of Gravity F = GMm/r2 • M = mass of 1st object • m = mass of 2nd object • r = distance between objects • G = gravitational constant M r m = 6.67 × 10-11 N m2/kg2 Newton’s Law of Gravity Inverse-Square Laws • Applies to gravitational strength, light, and other phenomena F = GMm/r2 • Force grows or shrinks with distance squared – If you get 2x closer, force is 4x stronger – If you get 3x farther away, force is 9x weaker • Called Inverse-square relation The Moon and Earth pull on each other with equal strength and in opposite directions You and Earth pull on each other with equal strength and in opposite directions Fg Moon Earth Fg Fg Fg Earth 2 3/6/15 At which point does the satellite feel the strongest gravitational force from Earth? (C is exactly half-way between Earth and the Moon) At which point does the satellite feel the strongest total (or net) gravitational force from both Earth and the Moon? Moon C Earth D Moon E B A Announcements • Today: Finish Gravity, Projectile Motion • Friday: Orbits, maybe start CH 11 • Reading: Sections 12.1-12.3 and 13.1, focus on density and pressure C Earth B A Moon C • On the surface of the Earth, we are about 6,380 km from the center of the Earth. The astronauts on the ISS are about 6,720 km from the center of the Earth. Compare the gravitational force on two people: one on Earth’s surface, and one in the ISS. E If the satellite is at location C halfway between the Moon and Earth, in what direction will the net force on the satellite point? Earth Example: The ISS D D E B A Application: Ocean Tides • Tides are primarily due to the moon’s gravitational pull on our oceans. • Sun contributes too, but the Earth-Sun distance doesn’t change very much. 3 3/6/15 Application: Black Holes Chapter 10: Projectile Motion • Black holes are not cosmic vacuum cleaners, they’re just very very compact! • From “Foxtrot” by Bill Amend Projectile Motion • A ball thrown across the room follows an arced trajectory. • Both vertical and horizontal motion Projectile Motion vs. Free-Fall At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground. Which strikes the ground first? Projectile Motion Combines uniform horizontal motion with free-fall vertical motion. Launching at an Angle • With no gravity, projectile would follow a straight line. • Due to gravity, projectile falls beneath this line, just as if released from rest. No a Gr y vi t 4 3/6/15 Range • Range depends on both horizontal speed and angle (Maximum at 45º) Projectile Motion & Curvature • For initial speeds that are faster and faster, the range of the projectile is farther and farther. • For very large speeds, the curvature of Earth starts to be noticeable. Distance Fallen The distance fallen is the same whether falling straight down or in projectile motion. Earth’s Curvature • Curvature of the Earth is about 5 meters over a distance of 8000 meters (which is about 5 yards over 5 miles). Missing the Ground Orbits and Centripetal Force • Suppose you throw a ball at a speed of 8000 m/s (about 18,000 mph). • After one second, ball travels 8000 meters and falls 5 meters. In that distance, Earth curves by same amount (5 meters). • Gravity provides the centripetal force required for planets & satellites to move in orbit 5 3/6/15 Which of the following is true? A. Satellites orbit at least 150 km above the surface of Earth because there is almost no gravity there. B. Satellites orbit at least 150 km above the surface of Earth because there is almost no air resistance there. Elliptical Orbits • For speeds higher than 8 km/s, the orbit is elliptical instead of circular. Application: Black Holes • Black holes are not cosmic vacuum cleaners, they’re just very very compact! • Getting into Orbit • Rocket needs to lift above the atmosphere and then fire thrusters to acquire the required orbital speed of about 8 kilometers per second. • Returning to Earth, air resistance slows the spacecraft during reentry Escape Velocity If speed exceeds 11.2 km/s then object escapes Earth because gravity weakens (as object gets further away) and never slows the object enough to return it back towards Earth. Imagine a planet in its orbit around the Sun. Rank the four positions shown (A-D) in order of the gravitational force from greatest to least. A. A, B, C, D B. A, B=C, D C. D, C=B, A D. D, C, B, A E. D=C=B=A 6 3/6/15 Imagine a planet in its orbit around the Sun. Rank the four positions shown (A-D) in order of the planet’s acceleration from greatest to least. A. A, B, C, D B. A, B=C, D C. D, C=B, A D. D, C, B, A E. D=C=B=A Chapter 11: The Atomic Nature of Matter Announcements: • Today: Atoms and structure of matter • Monday: More on density and pressure • Reading: Finish Chapter 13, focus on buoyancy and flotation • Midterm scores & grade update will get posted this afternoon! Average score was right in the middle of the C range. What is the structure of matter? Electron Cloud Atom Atomic Structure All matter is made of atoms • Characteristics of Atoms: – Very tiny – Very numerous – Always in motion • Substances made of only 1 type of atom are called elements Nucleus An atom is composed of • Nucleus – Contains most of the atomic mass – made up of protons (+ electric charge) and neutrons (no electric charge) – Very, very small (<10-14 m) • Electrons – even smaller than nucleus – 2000 times less massive than nucleus – negative electric charge (same amount as proton) – may be thought of as “orbiting” nucleus Number of electrons in a neutral atom is equal to number of protons in nucleus 7 3/6/15 Atomic Terminology Elements & The Periodic Table • Atomic Number = # of protons in nucleus • Atomic Mass Number = # of protons + neutrons • Molecules: consist of two or more atoms (H2O, CO2) Relative Sizes of Atoms Atomic Terminology • Isotope: same # of protons but different # of neutrons. (4He, 3He) Examples: Dark matter & Antimatter • Antimatter – atoms with opposite electrical charge (or some other property). – Antiprotons, positrons – Antimatter and regular matter destroy each other & release energy • Dark matter – Detected via the gravitational force that it exerts on stars & galaxies, but invisible – Dark matter makes up almost ¼ of all the matter in the universe 8 3/6/15 Chapters 12-14: Phases of Matter Density Sequence of increasing molecule motion (and kinetic energy) Solid Liquid Gas Example: Density • Compute density of a gold brick. • Dimensions: (20.5 cm)x(10 cm)x(5 cm) • Mass: 19.8 kg • The densities of most liquids and solids vary slightly with changes in temperature and pressure • Densities of gases vary greatly with changes in temperature and pressure Mass Density vs. Weight Density • Mass density = mass/volume (kg/m3) • Weight density = weight/volume (N/m3) • What is the weight density of the gold brick from the previous example? 9