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11/03 1. Which moves faster on a merry-go-round, a horse near the outside rail or one near the inside rail? 2. If the hamster stops running does it rotate or does in revolve? Close reading procedure 1. FIRST READ (Key Ideas & Details) read text - Think-Pair-Share to check understanding 2. SECOND READ (Craft & Structure) Number the paragraphs Circle main vocabulary, underline main points, add question marks and exclamation Think Aloud, Shared, Paired, portions of text that will aid in citing text based evidence Discuss in small and whole group 3. THIRD READ (Integration of Knowledge and Ideas) Reread (with a group) selected chunk focusing on text dependent question use pencils to mark text find parts of text that will aid in citing – (text based evidence) 5.1 and 5.2 Uniform Circular Motion and Centripetal Acceleration Centripetal force keeps an object in circular motion. 10.1 Rotation and Revolution Earth undergoes both types of rotational motion. • It revolves around the sun once every 365 ¼ days. • It rotates around an axis passing through its geographical poles once every 24 hours. Uniform Circular Motion Period (T) – Time it takes to make one trip around the circle Circumference – distance around the circle – C = 2r – Object is traveling at a constant (uniform) speed on a circular path 10.2 Rotational Speed The turntable rotates around its axis while a ladybug sitting at its edge revolves around the same axis. Linear speed is the distance traveled per unit of time. • Tangential speed – the linear speed of an object along a circular path The greater distance from the axis the greater the tangential speed 10.2 Rotational Speed Tangential and Rotational Speed Tangential speed and rotational speed are related. Tangential speed is directly proportional to the rotational speed and the radial distance from the axis of rotation. Tangential Velocity ~ radial distance × rotational speed Vt = r * w 10.2 Rotational Speed In symbol form, v ~ r where v is tangential speed and (pronounced oh MAY guh) is rotational speed. • You move faster if the rate of rotation increases (bigger ). • You also move faster if you are farther from the axis (bigger r). Uniform Circular Motion Speed (v) – distance / time 1.2 m Find v v = 3.77 m/s T=2s Uniform Circular Motion Speed is constant Velocity is not constant Velocity is always changing This acceleration is “centripetal” acceleration 5.2 Centripetal Acceleration Object moves in circular path At time t0 it is at point O with a velocity tangent to the circle At time t, it is at point P with a velocity tangent to the circle The radius has moved through angle Centripetal Acceleration Draw the two velocity vectors so that they have the same tails. The vector connecting the heads is v Draw the triangle made by the change in position and you get the triangle in (b) Centripetal Acceleration Since the triangles have the same angle are isosceles, they are similar Centripetal Acceleration Centripetal Acceleration Know this Centripetal Acceleration Forces cause acceleration F=ma Ac = V2 / r Fc = m (v2 / r) centripetal acceleration centripetal force Centripetal acceleration – acceleration toward the center Centripetal force – a center directed force that causes an object to move in a curved path Gravity provides constant centripetal force 11/4 1. A 20 kg child is on the merry go round. If she is 3 m from the center of the merry go round and her tangential velocity is 2 m/s what is her centripetal acceleration? Which equation are you using? 2. When a can is twirled in a circle, what is the direction of acceleration? Today : Spinning stopper lab What are the variables that can be changed in the spinning stopper? What do you think affects the rate at which the stopper spins? Centripetal Acceleration At any given moment – v is pointing tangent to the circle – ac is pointing towards the center of the circle If the object suddenly broke from circular motion would travel in line tangent to circle 10.3 Centripetal Force Calculating Centripetal Forces Greater speed and greater mass require greater centripetal force. Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force. Centripetal force, Fc, is measured in newtons when m is expressed in kilograms, v in meters/second, and r in meters. 11/5 What two forces where acting on the stopper allowing it to stay suspended? What happens to the period (time to complete a rotation) as your radius decreases? What can you do if you want to know if your data is accurate? Spinning stopper lab write up Claim – how where you able to suspend the stopper (2 forces) Evidence – calulations, data table, observations Reasoning – discuss centripetal force, what was acting on the small mass to keep it orbiting? Vocabulary : Direction, gravity, Explain centripetal force, centripetal acceleration in terms of equations. 11/6 How many cm long is your pinky? How many meters is in 10 cm? Due today – circular motion write up See metric mania Untitled – ne measurement myth busters full episodes circular motion http://www.youtube.com/watch?v=torrlSW6Vn A http://www.youtube.com/watch?v=B5LCTVK8 kDs&list=PL78DB5CFC40BE2225 http://www.youtube.com/watch?v=d3FrvV3It5 U can you do a 360 degree swing? This claims that you can http://www.youtube.com/watch?v=PBpe_L LlQJw Example 1 Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do either of the cars make the curve? (hint find the ac) Yes, 100m 50 m 100 m Problems Try this Concept development practice page 9-2 Which arrow indicates the direction of the gravitational force the star exerts on the comet when the comet is in the position shown? 1 2 3 4 A tin can spun around on the end of a string moves in circle because a. once the can starts moving, that is its natural tendency b. the can continually pulls on the string c. there is a force on the can pulling outward d. the string continually pulls inward on the can (8.4) Suppose a 30kg child is riding a merry go round. If she is 2.00m from the center of the merry go round and her tangential velocity is 2.50 m/s, what is her centripetal acceleration? a. 5.00m/s2 b. 3.12m/s2 c. 281m/s2 d. 1.25m/s2 Due today: Stopper lab CER 4/14 What determines how fast a planet revolves around the sun? mass, size, or distance from the sun? How long does it take the moon to orbit the earth? What would happen to the period if the moon where farther from the earth? 14.2 Circular Orbits Describe the motion of a satellite in relation to Earth’s surface and gravity. 14.3 Elliptical Orbits A simple method of constructing an ellipse is shown here. 14.3 Elliptical Orbits What happens if you launch a satellite at 9 km/s Satellite speed varies in an elliptical orbit. • When the initial speed is more than 8 km/s, the satellite overshoots a circular path and moves away from Earth. • It loses speed due to the pull of gravity. • The satellite slows to a point where it no longer recedes, and begins falling back toward Earth. 14.3 Elliptical Orbits A satellite moves in an elliptical orbit. a. When the satellite exceeds 8 km/s, it overshoots a circle. 14.3 Elliptical Orbits A satellite moves in an elliptical orbit. a. When the satellite exceeds 8 km/s, it overshoots a circle. b. At its maximum separation, it starts to come back toward Earth. 14.3 Elliptical Orbits A satellite moves in an elliptical orbit. a. When the satellite exceeds 8 km/s, it overshoots a circle. b. At its maximum separation, it starts to come back toward Earth. c. The cycle repeats itself. 14.3 Elliptical Orbits The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses. a. For relatively low speeds, the center of Earth is the far focus. 14.3 Elliptical Orbits The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses. a. For relatively low speeds, the center of Earth is the far focus. b. For greater speeds, the near focus is Earth’s center. 14.4 Energy Conservation and Satellite Motion For a satellite in circular orbit, no force acts along the direction of motion. The speed, and thus the KE, cannot change. 14.3 Elliptical Orbits think! The orbit of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the greatest speed? The least speed? Answer: The satellite has its greatest speed as it whips around A. It has its least speed at C. Beyond C, it gains speed as it falls back to A to repeat its cycle. 14.3 Elliptical Orbits think! The orbit of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the greatest speed? The least speed? 14.3 Elliptical Orbits What is the shape of the path of a satellite in an orbit around Earth? Conservation of energy total energy stays the same Total energy = kinetic energy + potential energy Kinetic energy = energy due to speed Potential energy = energy due to distance 14.4 Energy Conservation and Satellite Motion • The PE is greatest when the satellite is at the apogee and least when the satellite is at the perigee. • The KE will be least when the PE is most; and the KE will be most when the PE is least. • At every point in the orbit, the sum of the KE and PE is constant. 14.4 Energy Conservation and Satellite Motion For a satellite in circular orbit, no force acts along the direction of motion. The speed, and thus the KE, cannot change. 14.4 Energy Conservation and Satellite Motion The sum of KE and PE for a satellite is a constant at all points along an elliptical orbit. 14.4 Energy Conservation and Satellite Motion Clicker question, think! The orbital path of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the most KE? Most PE? Most total energy? 14.4 Energy Conservation and Satellite Motion think! The orbital path of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the most KE? Most PE? Most total energy? Answer: The KE is maximum at A; the PE is maximum at C; the total energy is the same anywhere in the orbit. 4/16 1. Draw a satellite in circular motion and a satellite in an elliptical orbit, what is the difference in terms of speed and acceleration? 2. Why doesn't gravitational force change the speed of a satellite in circular motion? Ellipse – an oval where the sums of the distances from the foci to any point is constant Ellipse – an oval where the sums of the distances from the foci to any point is constant Eccentricity = distance between foci / length of major axis (or behavior deviating from the norm, eccentric) d = distance between foci L = length of major axis E = eccentricity e = d/l 4/16 Agenda - Orbital stopper lab CER (Past due) - Ellipse lab Kepler’s 3 law = 1. Which orbit has a greater eccentricity (purple or blue)? 2. At what point does the orbit from the blue planet have the greatest kinetic energy? Potential energy? Total energy? 4/17 Why do satellites have to be far above earth to keep their orbit? When is the amount of energy of a satellite in elliptical orbit the greatest? Tomorrow: Quiz and notebook check dates from 4/7 Assessment Questions 1. When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it follows a. matches the curve of planet Earth. b. results in a straight line. c. spirals out indefinitely. d. is within 150 kilometers of Earth’s surface. Assessment Questions 1. When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it follows a. matches the curve of planet Earth. b. results in a straight line. c. spirals out indefinitely. d. is within 150 kilometers of Earth’s surface. Answer: A Assessment Questions 2. When a satellite travels at constant speed, its shape is a(n) a. circle. b. ellipse. c. oval that is almost elliptical. d. square. Assessment Questions 2. When a satellite travels at constant speed, its shape is a(n) a. circle. b. ellipse. c. oval that is almost elliptical. d. square. Answer: A Assessment Questions 3. A satellite in elliptical orbit about Earth travels a. fastest when it moves closer to Earth. b. fastest when it moves farther from Earth. c. slowest when it moves closer to Earth. d. at the same rate for the entire orbit. Assessment Questions 3. A satellite in elliptical orbit about Earth travels a. fastest when it moves closer to Earth. b. fastest when it moves farther from Earth. c. slowest when it moves closer to Earth. d. at the same rate for the entire orbit. Answer: A Assessment Questions 4. Energy is conserved when an Earth satellite travels a. in either a circular or elliptical orbit. b. in only an elliptical orbit. c. away from Earth. d. toward Earth. Assessment Questions 4. Energy is conserved when an Earth satellite travels a. in either a circular or elliptical orbit. b. in only an elliptical orbit. c. away from Earth. d. toward Earth. Answer: A Assessment Questions 5. Kepler is credited as being the first to discover that the paths of planets around the sun are a. circles. b. ellipses. c. straight lines most of the time. d. spirals. Assessment Questions 5. Kepler is credited as being the first to discover that the paths of planets around the sun are a. circles. b. ellipses. c. straight lines most of the time. d. spirals. Answer: B http://www.phy.ntnu.edu.tw/ntnujava/index. php?topic=9 14.6 Escape Speed 14.6 Escape Speed Pioneer 10, launched from Earth in 1972, escaped from the solar system in 1984 and is wandering in interstellar space. 4/18 Why is mercury the fastest moving planet? Notebook check from 4/7 Due today Ellipse lab What would happen to the length of the month if the moon moved further out? Create a diagram of the kinetic and potential energy of a planet traveling in an ellipse Test tomorrow How does the distance between the two foci affect the eccentricity of an ellipse? To get a lower number would you move the tacks closer or further? Which planet was the hardest to do, why? What remains constant for a satellite in an elliptical orbit? What if we lost the moon? http://www.phy.ntnu.edu.tw/ntnujava/index.p hp?topic=9 http://www.youtube.com/watch?v=DgD4nV Qim-Y