* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Physics Chapter 7
Survey
Document related concepts
Classical mechanics wikipedia , lookup
Equations of motion wikipedia , lookup
Center of mass wikipedia , lookup
Coriolis force wikipedia , lookup
Jerk (physics) wikipedia , lookup
Hunting oscillation wikipedia , lookup
Fictitious force wikipedia , lookup
Seismometer wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Centrifugal force wikipedia , lookup
Work (physics) wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Classical central-force problem wikipedia , lookup
Transcript
Physics Chapter 7 Circular Motion and Gravitation Section 7.1 Day1 Objectives: • Solve problems involving centripetal acceleration. • Solve problems involving centripetal force. • Explain how the apparent existence of an outward force in circular motion can be explained as inertia resisting the centripetal force. Section 7.1 Circular Motion • Circular motion = any object revolving about a single axis • Axis of rotation = a line • Centripetal vs. centrifugal • Centripetal = center seeking • Centrifugal = center fleeing • Tangential speed = speed of an object that is tangent to the object’s circular path • When tangential speed is constant, the object is moving with uniform circular motion. • Tangential speed depends on the distance from the object to the center. • Example: 2 carousel horses (outer horse has greater tangential speed) Centripetal acceleration is due to a change in direction. • Remember that acceleration can change due to a change in magnitude of velocity or due to a change in direction or both. • Centripetal acceleration = acceleration directed toward the center of a circular path due to a change in direction • ac = vt2 r • Centripetal acceleration = (tangential speed)2 radius of circular path A test car moves at a constant speed around a circular track. If the car is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s2, what is the car’s tangential speed? r= 48.2 m vt = ? ac = 8.05 m/s2 Practice A p. 236 1. A rope attaches a tire to an overhanging tree limb. A girl swinging on the tire has a centripetal acceleration of 3.0 m/s2. If the length of the rope is 2.1 m, what is the girl’s tangential speed? 2. As a young boy swings a yo-yo parallel to the ground and above his head, the yo-yo has a centripetal acceleration of 250 m/s2. if the yo-yo’s string is 0.50 m long, what is the yo-yo’s tangential speed? 3. A dog sits 1.5 m from the center of a merry-goround. The merry-go-round is set in motion, and the dog’s tangential speed is 1.5 m/s. What is the dog’s centripetal acceleration? 4. A race car moving along a circular track has a centripetal acceleration of 15.4 m/s2. if the car has a tangential speed of 30.0 m/s, what is the distance between the car and the center of the track? • Tangential acceleration = an acceleration due to a change in speed of a circular object • Centripetal force = net force directed toward the center of an object’s circular path • Fc = mac • Fc = mvt2 r • Centripetal force = (tangential speed)2 radius of circular path • Centripetal force is necessary for circular motion. A pilot is flying a small plane at 56.6 m/s in a circular path with a radius of 188.5 m. The centripetal force needed to maintain the plane’s circular motion is 1.89 x 10 4 N. What is the plane’s mass? vt = 56.6 m/s Fc = mvt2 r r = 188.5 m Fc = 1.89 x 104 N Practice B p. 238 1. A 2.10 m rope attaches a tire to an overhanging tree limb. A girl swinging on the tire has a tangential speed of 2.50 m/s. If the magnitude of the centripetal force is 88.0 N, what is the girl’s mass? 2. A bicyclist is riding at a tangential speed of 13.2 m/s around a circular track. The magnitude of the centripetal force is 377 N, and the combined mass of the bicycle and the rider is 86.5 kg. What is the track’s radius? 3. A dog sits 1.50 m from the center of a merrygo-round and revolves at a tangential speed of 1.80 m/s. If the dog’s mass is 18.5 kg, what is the magnitude of the centripetal force on the dog? 4. A 905 kg car travels around a circular track with a circumference of 3.25 km. If the magnitude of the centripetal force is 2140 N, what is the car’s tangential speed? Section 7.2 Objectives: • Explain how Newton’s law of universal gravitation accounts for various phenomena, including satellite and planetary orbits, falling objects, and the tides. • Apply Newton’s law of universal gravitation to solve problems. Newton’s Law of Universal Gravitation • Newton realized that gravitational force was the centripetal force holding the planets in orbit. • Orbiting objects are in free fall. • Free fall = the motion of a body when only the force of gravity is acting on the body • Free-fall acceleration on Earth’s surface = 9.81 m/s2 Orbiting Objects • Newton realized that if an object were projected at just the right speed, the object would fall down toward Earth in just the same way that Earth curved out from under it. • Gravitational force depends on mass and distance. Newton’s Law of Universal Gravitation Fg = (G) m1 m2 r2 Gravitational force = constant x mass 1 x mass 2 (distance between masses)2 G = constant of universal gravitation = 6.673 x 10-11 N•m2 kg2 Mass of Object 1 (kg) Mass of Object 2 (kg) Separation Distance (m) Football Player 100 kg Earth 5.98 x1024 kg 6.38 x 106 m (on surface) Earth 5.98 x1024 kg 6.38 x 106 m (on surface) Earth 5.98 x1024 kg 6.60 x 106 m (low-height orbit) d. Physics Student 70 kg Physics Student 70 kg 1m e. Physics Student 70 kg Physics Student 70 kg 0.2 m f. Physics Student 70 kg Physics Book 1 kg 1m g. Physics Student 70 kg Moon 7.34 x 1022 kg 1.71 x 106 m (on surface) h. Physics Student 70 kg Jupiter 1.901 x 1027 kg 6.98 x 107 m (on surface) a. b. Ballerina 40 kg c. Physics Student 70 kg www.glenbrook.k12.il.us/.../circles/u6l3c.html Force of Gravity (N) Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of th egravitational force between them is 8.92 x 10-11 N. Practice C p. 242 1. What must be the distance between two 0.800 kg balls if the magnitude of the gravitational force between them is equal to that in the sample problem? 2. Mars has a mass of about 6.4 x 1023 kg, and its moon Phobos has a mass of 9.6 x 1015 kg. If the magnitude of the gravitational force between the two bodies is 4.6 x 1015 N, how far apart are Mars and Phobos? 3. Find the magnitude of the gravitational force a 66.5 kg person would experience while standing on the surface of each of the following planets: Planet Mass Radius a. Earth 5.97 x 1024 kg 6.38 x 106 m b. Mars 6.42 x 1023 kg 3.40 x 106 m c. Pluto 1.25 x 1022 kg 1.20 x 106 m Newton’s law of gravitation accounts for ocean tides. • • • • • • • • • • On the side of Earth that is nearest to the moon, the moon’s gravitational force is greater than it is at Earth’s center. This is because gravitational force decreases with distance. The water is pulled toward the moon, creating an outward bulge. On the opposite side of Earth, the gravitational force is less than it is at the center. On this side, all mass is still pulled toward the moon, but the water is pulled least. This creates another outward bulge. Two high tides take place each day because when Earth rotates one full time, any given point on Earth will pass through both bulges. When the sun and moon are in line, the combined effect produces a greater-than- usual high tide called a spring tide. When the sun and moon are at right angles, the result is a lower-thannormal high tide called a neap tide. Each revolution of the moon around Earth corresponds to two spring tides and two neap tides. www.this-magic-sea.com/TIDE.HTM • Other things influencing tides: depth of ocean, Earth’s tilt, rotation, friction between ocean floor and water, and sun. Why the moon not the sun? • Tidal forces arise from the differences between the gravitational forces at Earth’s near surface, center, and far surface. • As the distance (r) between two bodies increases, the tidal force decreases as 1/r3. For this reason, the sun, which has a greater mass than the moon does, has less effect on the Earth’s ocean tides than the moon does. • Tidal forces are exerted on all substances. • The amount of distortion depends on the elasticity of the body under gravitational influence. • If an orbiting body moves too close to a more massive body, the tidal force on the orbiting body may be large enough to break the body apart. • The distance at which tidal forces can become destructive is called Roche’s limit. • Gravity is a field force. • Gravitational force is an interaction between a mass and the gravitational field created by other masses. • Gravitational field strength equals free-fall acceleration. • Weight changes with location. • Gravitational mass equals inertial mass. • Gravitational mass = weight/ gravitational field strength at the location of measurement • Fg = (G) m1 m2 r2 • F = ma inertial mass Section 7.3 Day2 Objectives: • Describe Kepler’s laws of planetary motion. • Relate Newton’s mathematical analysis of gravitational force to the elliptical planetary orbits proposed by Kepler. • Solve problems involving orbital speed and period. Motion in Space • In 1543 – Polish Astronomer – Nicolaus Copernicus proposed that the earth and other planets orbit the sun in perfect circles • Kepler (1571- 1630) 3 laws of planetary motion Kepler’s 3 Laws of Planetary Motion 1. Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points. 2. An imaginary line drawn from the sun to any planet sweeps out equal areas in equal areas in equal time intervals. 3. The square of a plantet’s orbital period (T2) is proportional to the cube of the average distance (r3) between the planet and the sun, or T2 α r3. • First Law – orbits are elipses not circles • Second Law – planets travel faster when they are closer to the sun • Third Law – orbital period = time a planet takes to finish one full revolution (T) and distance (r) = mean distance between the planet and the sun (this also applies to satellites orbiting Earth, including the moon) T12 = r13 T22 r23 • Kepler’s laws are consistent with Newton’s law of gravitation. • Kepler’s third law describes orbital period • Another way of stating Kepler’s third law: T2 = 4π2 • r3 Gm • Assume a circular path. This is a close approximation for planets in our solar system, because most are nearly circular (except Mercury and Pluto) Period and Speed of an Object in Circular Orbit • T = 2π2 • v=G • • • • • r3 Gm m r T = orbital period v = orbital speed r = mean radius m = mass of central object G = gravitational constant Practice D p. 251 Use chart p. 250 1. Find the orbital speed and period that the Magellan satellite from the sample problem would have at the same mean altitude above Earth, Jupiter, and Earth’s moon. 2. At what distance above Earth would a satellite have a period of 125 min? Section Review p. 253 5. Find the orbital speed and period of Earth’s moon. The average distance between the centers of Earth and the moon is 3.84 x 108 m. Weight and Weightlessness • What is weight? • If a friend pushes down on you while you are on the scale, what will happen? • The scale reading is a reading of the normal force acting on you. Why? • In an elevator, the normal force will be smaller as the elevator accelerates downward. • If the elevator’s acceleration were equal to freefall, you would experience apparent weightlessness. • Astronauts in orbit experience apparent weightlessness. • The force due to gravity keeps the astronauts and shuttle in orbit, but the astronauts feel weightless because no normal force is acting on them. • Our bodies rely on this. Prolonged weightlessness produces weakened muscles and brittle bones. • Astronauts in orbit experience apparent weightlessness. • Actual weightlessness occurs only in deep space, far from stars and planets. • Gravity is never entirely absent, but if an object is far enough from any masses, gravity can become negligible. • If this were the case, the object would drift through space in a straight line at constant speed. Section 7.4 Objectives: • Distinguish between torque and force. • Calculate the magnitude of a torque on an object. • Identify the six types of simple machines. • Calculate the mechanical advantage of a simple machine. Torque and Simple Machines • Torque = a quantity that measures the ability of a force to rotate an object around some axis • Torque depends on the force and the lever arm. • Lever arm = the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. The Inclined Plane: Often referred to as a 'ramp' the inclined plane allows you to multiply your force over a longer distance. In other words, you exert less force but for a longer distance. You do the same amount of work, it just seems easier because you spread it over time. The Wedge: A wedge works in a similar way to the inclinded plane, only it is forced into an object to prevent it from moving or to split it into pieces. A knife is a common use of the wedge. The Screw: The screw is really just an inclined plane wrapped around a rod. It too can be used to move a load (like a corkscrew) or to 'split' and object (like a carpenter's screw). www.coolschool.ca/lor/SC9/unit16/U16L04.htm The Lever: The lever is simply a bar supported at a single point called the fulcrum. The positioning of the fulcrum changes the mechanical advantage of the lever. Look at how you can manipulate the position of the fulcrum relative to the heavier weight to lift the 200g mass with only 100g of force... The Wheel and Axle: Any large disk (the wheel) attached to a small diameter shaft or rod (the axle) can give you mechanical advantage. Turning a screw with a screwdriver is a simple example of a wheel and axle. Can you think of others we use everyday? The Pulley: A pulley is any rope or cable looped around a support. A very simple pulley system would be a rope thrown over a branch to hoist something into the air. Often, pulleys incorporate a wheel and axle system to reduce the friction on the rope and the support. www.coolschool.ca/lor/SC9/unit16/U16L04.htm