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7.3 Circular Motion and Gravity

7.3 Circular Motion and Gravity. pp. 260 - 265 Mr. Richter. Agenda. Warm-Up Intro to rotational motion. Refresh on Newton’s Laws Notes: Centripetal Force Centripetal Force and Inertia Circular motion The Myth of Centrifugal Force. Objectives: We Will Be Able To….

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7.3 Circular Motion and Gravity

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  1. 7.3 Circular Motion and Gravity pp. 260 - 265 Mr. Richter

  2. Agenda • Warm-Up • Intro to rotational motion. • Refresh on Newton’s Laws • Notes: • Centripetal Force • Centripetal Force and Inertia • Circular motion • The Myth of Centrifugal Force

  3. Objectives: We Will Be Able To… • Explain how a centripetal force causes circular motion • List the factors that affect centripetal force • Describe the relationship between gravitational force, mass, and distance • Relate centripetal force to orbital motion

  4. Warm-Up:

  5. Centripetal Force

  6. Centripetal Force • Usually we think of a force as changing the speed of an object. • But what else can forces do? • Centripetal force is any force that is applied that changes the direction of an object but not its speed.

  7. Centripetal Force • Centripetal force is applied perpendicular to the motion of an object. • It causes the object to move in a circular path. • Centripetal force always points toward the center of the circle.

  8. Centripetal Force Velocity Centripetal Force

  9. Centripetal Force and Inertia • Why doesn’t the ball get pulled in to the center? • Why doesn’t the ball go rocketing off in some direction? • Answer: • the ball has inertia to keep going the same speed if the force doesn’t speed it up or slow it down, and • the force is perpendicular to motion, so it only changes the ball’s direction toward the middle of the circle

  10. Centripetal Force and Inertia • Force and velocity are always perpendicular to each other. • If the string is suddenly cut (or if Mr. Richter lets go), then the ball will continue in a straight-line path at a 90° angle from the string.

  11. Warm-Up • A boy swings a ball in a circle on a string above his head. What factors do you think will make a difference in how much centripetal force he has to apply to keep the ball spinning in a circle? • Think and then discuss at your table. We will discuss as a class in a few minutes.

  12. Centripetal Force Video • http://www.youtube.com/watch?v=PBpe_LLlQJw

  13. Circular Motion

  14. Circular Motion • How does the centripetal force change with the radius of the circle? • As the radius increases, the object turns more gradually, so the force required to turn the object is less. Force is inversely proportional to radius. • How does the centripetal force change with the mass of the object? • As the mass of the object increases, more force is required to cause it to turn. Force is directly proportional to mass.

  15. Circular Motion • How does the centripetal force change with the speed of the object? • As the speed of an object increases, the amount of force required to turn the object increases. Force is directly proportional to the square of the speed. • Meaning: • twice as fast means four times the force required • three times as fast means nine times the force

  16. Warm-Up • If the radius of an object’s orbit is doubled, by what factor does the centripetal force increase or decrease? • If the speed of an object’s orbit is quadrupled, by what factor does the centripetal force increase or decrease?

  17. The Myth of Centrifugal Force

  18. The Rotor Ride • http://www.youtube.com/watch?v=Or0IFpRSTjM

  19. The Rotor Ride • Explain what you think is happening on the rotor ride you saw. Is there really a force coming from the middle of the ride, pushing people against the wall? If not, what do you think is really happening? • Discuss at your table and we will discuss in a few minutes.

  20. The Myth of “Centrifugal Force” • It might seem like as an object is rotating, there is a force pushing the object away from the center of the circle. • THIS IS NOT TRUE. THERE IS NO SUCH THING AS CENTRIFUGAL FORCE! There is no force pushing away from the center of the circle. • Objects just want to keep going in a straight line. Inertia, not force.

  21. Gravitational Force Does the moon pull on the earth?

  22. Gravitational Force • Newton observed that some centripetal force must be required to cause planets and moons to orbit in a circle. • He determined that this force must be gravity! • Gravity is a form of centripetal force! • The force of gravity between two objects is the same in both directions. • The moon pulls on Earth the same as Earth pulls on the moon.

  23. Gravitational Force • Gravitational force exists between ALL objects that have mass. • Your weight is the force of gravity between you and the Earth. • This force changes if you travel to another planet, get farther from the earth, or go to the moon. • It takes an enormous amount of mass to have a noticeable force of gravity.

  24. Gravitational Force • The gravitational force between two objects always lies along the line connecting their centers. • The size of the force depends on: • The mass of each object: as masses increase, the force of gravity increases. • The distance between the objects from center to center: force decreases with the square of the distance.

  25. Think About It • According to the Law of Universal Gravitation formula, will you weigh more or less (or the same) on the top of Mt. Everest?

  26. Note: Measuring Distance • We measure distance between two objects from their centers: • NOT because gravity comes from the center of objects. ALL of the object’s mass contributes to the force of gravity. • The center is your average distance to all parts of the object.

  27. Calculating the Force of Gravity • Newton’s Law of Universal Gravitation gives the relationship between gravitational force, distance, and the masses of any two objects. • G is the gravitational constant: • 6.67 x 10-11 Nm2/kg2 Note: because G is so small, at least one mass needs to be very large to have much gravitational force.

  28. Your Turn • Use the following information to calculate the force of gravity between Earth and the moon. • Mass of Earth: 5.97 × 1024 kg • Mass of moon: 7.34 × 1022 kg • Distance between centers of Earth and moon: 3.84×108m • Answer: 1.99 x 1020 N

  29. Practice • Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter. • A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 106 meters. Find the mass of the moon.

  30. Wrap-Up: Did we meet our objectives? • Explain how a centripetal force causes circular motion • List the factors that affect centripetal force • Describe the relationship between gravitational force, mass, and distance • Relate centripetal force to orbital motion

  31. Homework • Due Monday • p265 Gravitational Force #1-3 • p265 Section Review #1, 3 • p 270 #34, 36 • Boooooks!

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