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Warm Up

Warm Up Find the centripetal Force, the centripetal acceleration, and the period of a 5kg ball (radius 0.5m) being swung through the air by a 5 m long string, if it is traveling at 8 m/s. .

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Warm Up

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  1. Warm Up Find the centripetal Force, the centripetal acceleration, and the period of a 5kg ball (radius 0.5m) being swung through the air by a 5 m long string, if it is traveling at 8 m/s. AP PhysicsMonday 14.02.03Standards: 1d2 Motion in a vertical circle (e.g., mass swinging on the end of a string, cart rolling down a curved track, rider on a Ferris wheel.Objective: SWBAT solve vertical circle problems. Agenda • Warm Up • Collect HW • Vertical Circle Problems • HW #C2 Homework #C2 Lab Write Up

  2. AP PhysicsTuesday 14.02.04Standards: F4b determine strength of gravitational force outside a mass. Objective: SWBAT solve gravitational force problems. Warm Up An astronaut in an orbiting space craft attaches a mass m to a string and whirls it around in uniform circular motion. The radius of the circle is r, the speed of the mass is v, and the tension in the string is F. If the mass, radius , and speed were to all double, the tension required to maintain uniform circular motion would be... A) F/2 B) F C) 2F D) 4F E) 8F Agenda • Warm Up • Review Homework • Gravitation Notes • Gravitation Practice • Gravitation Guided Practice Homework C#3

  3. AP PhysicsWednesday 14.02.05 Standards: Derive Kepler’s Third Law for the case of circular orbits. Objective: SWBAT derive Kepler’s third Law Warm Up A person weighing 800 N on Earth travels to another planet with twice the mass and twice the radius of Earth. The person’s weight on this other planet is most nearly. A) 400 N B)800/√2 C)800N D)800√2 E) 1,600N Agenda • Warm Up • Review HW • Read Kepler’s 3rd Law • Circular Orbits • C#5 Homework C#5 Equations Quiz Friday

  4. Warm Up 29. A hypothetical planet orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit? (A) 1/2 (B) 1/√2 (C) 1 (D) √2 (E) 2 AP PhysicsThursday 14.02.06Standards: Determine the strength of the gravitational field at a specified point outside a spherically symmetrical mass. Objective: SWBAT solve problems involving Gravitational Fields Agenda • Warm Up • Review HW • Gravitational Fields • Gravitational Field Practice Homework C#6 Equations Quiz Friday

  5. Warm Up Find the gravitational field that I produce when I curl up in a ball and my mass is 68kg and my average radius is 0.5m? AP PhysicsFriday 14.02.07Standards: F2 bApply the expression of the period of oscillation of a mass on a spring.Objective: SWBAT demonstrate understanding of the motion of an oscillating spring through problem solving. Agenda • Warm Up • Review HW • Equations Quiz • Mass on a spring Notes • Mass on a spring guided practice. Homework C#7

  6. Centripetal Motion C#1 • (A6)In 1995, Cathy Marsal of France cycled 47.112 km in 1.000 hour. Calculate the magnitude of the centripetal acceleration of Marsal with respect to Earth’s center. Neglect Earth’s rotation, and use 6.37x103 km as Earth’s radius. • (B5) In 1992, a team of 12 athletes from Great Britain and Canada rappelled 446 m down the CN Tower in Toronto, Canada. Suppose an athlete with a mass of 75.0 kg, having reached the ground, took a joyful swing on the 446 m-long rope. If the speed of the athlete at the bottom point of the swing was 12 m/s, what was the centripetal force? What was the tension in the rope? Neglect the rope’s mass. A. Fc=? m=20kg r=40m v=5m/s B. Fc=40N m=4kg r=40m v=? C. Fc=40N m=2kg r=6m T=?

  7. Vertical Circular Motion Guided Practice. A roller coaster spins its riders in a circular loop of radius 12m. If the cart full of riders is 4000 kg and the tangential velocity is 30 m/s, find the force that the tracks must put on the cart to keep it in a circle at the top of the track and at the bottom of the track? (Free Body Diagrams are required!)

  8. Centripetal Motion C#3 b. Vertical Circle a. Horizontal Circle Fnet=? Fc=? FT (top)=? FT (bottom)=? m=2kg v=8m/s r=4m ac? Fnet=? Fc=? m=2kg v=8m/s r=4m ac=? • 1 (28.) A 4.0 kg mass is attached to one end of a rope 2 m long. If the mass is swung in a vertical circle from the free end of the rope, what is the tension in the rope when the mass is at its highest point if it is moving with a speed of 5 m/s? (A) 5.4 N (B) 10.8 N (C) 21.6 N (D) 50 N (E) 65.4 N • 2(29.) A ball of mass m is fastened to a string. The ball swings at constant speed in a vertical circle of radius R with the other end of the string held fixed. Neglecting air resistance, what is the difference between the string’s tension at the bottom of the circle and at the top of the circle? (A) 1·mg (B) 2·mg (C) 4·mg (D) 6·mg (E) 8·mg

  9. Centripetal Motion Lab r 1. Write a procedure. Objective: Create a graph whose slope is acceleration due to gravity and is equal to g. Compare this value to g=9.80 m/s2 using % error. m1 2.. Fill in the table below: binder clip 3. Graph F vs. v2/r(the right 2 columns), find the best fit line, the slope, and the equation of the line. m2 F(N) mtotal(kg) 4. slope = acceleration due to gravity of the ball, so we will compare the acceleration due to gravity with our measured value to find its accuracy

  10. Gravitational Force Guided Practice. The sun has a mass of 2.0x1030kg and a radius of 7.0x105km. What mass must be located at the sun’s surface for a gravitational force of 470N to exist between the mass and the sun?

  11. Gravitational Force Practice C#4 1.Deimos, a satellite of Mars, has an average radius of 6.3 km. If the gravitational force between Deimos and a 3.0 kg rock at its surface is 2.5x10-2N, what is the mass of Deimos? 2. A 3.08x104kg meteorite is on exhibit in New York City. Suppose this meteorite and another meteorite are separated by 1.27x107m (a distance equal to the Earth’s average diameter). If the gravitational force between them is 2.88x10-16N, what is the mass of the second meteorite? 3. Jupiter, the largest planet in the solar system, has a mass 318 times that of Earth and a volume that is 1323 times greater than Earth’s. Calculate the magnitude of the gravitational force exerted on a 50.0 kg mass on Jupiter’s surface. Volume=4/3πr3 Fg=? m1=40kg m2=20kg r=3x105m B. Fg=4x1040N m1=8x1035 kg m2=4x1030kg r=?

  12. Guided Practice: Kepler’s 3rd Law • A satellite in geostationary orbit rotates at exactly the same rate as Earth, so the satellite always remains in the same position relative to Earth’s surface. the period of Earth’s rotation is 23 hours, 56 miutes, and 4 seconds. What is the altitude of a satellite in geostationary orbit.

  13. Kepler’s 3rd Law C#5 m2=4x1021 r=4x106m T=? • (1) The period of Mars’ rotation is 24 hours, 37 minutes, and 23 seconds. At what altitude above Mars would a “Mars-stationary” satellite orbit? • (4,5) Earth’s moon orbits the Earth at a mean distance of 3.84x108m. What is the moon’s orbital speed? What is the moon’s orbital period. Use your book to find the mass of the earth and moon if required. • The asteroid (45) Eugenia has a small moon named S/1998(45)1. The moon orbits Eugenia once every 4.7 days at a distance of 1.19x103km. What is the mass of (45) Eugenia? m2=? r=4x1020m T=5 years 2. Derive Kepler’s 3rd Law from the concepts of Gravitational Force & CentripetalForce

  14. C#6 Gravitational Fields 1 (5.) Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the surface of Mars is most nearly (A) 0.25 m/s2 (B) 0.5 m/s2 (C) 2 m/s2 (D) 4 m/s2 (E) 25 m/s2 2.(9.) The planet Mars has mass 6.4 x1023kilograms and radius 3.4 x106 meters. The acceleration of an object in free-fall near the surface of Mars is most nearly (A) zero (B) 1.0 m/s2 (C) 1.9 m/s2 (D) 3.7 m/s2 (E) 9.8 m/s2 3. (30.) A hypothetical planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly (A) 2.9 m/s2 (B) 5.7 m/s2 (C) 17.5 m/s2 (D) 35 m/s2 (E) 122 m/s2 a. g=ag=? m=3x1019kg r=1.5x105m b. Fg=400 N mplanet=3x1019kg mshuttle=4x104kg g=ag=? c. g=ag=4 m/s2 m=? r=6x1011 m

  15. Force & Energy in Springs Guided Practice The pygmy shrew has an average mass of 2.0 g. If 49 of these shrews are placed on a spring scale with a spring constant of 24 N/m, what is the springs displacement? How much energy is stored in the spring?

  16. C#7 Force & Energy in Springs. Object hanging on spring Fsp=? Fnet=? ms=20 kg k=10 N/m x=? Usp=? b. Object hanging from elastic band Fnet=? Fsp=? ms=5 kg k=? x=2 m Usp=? • (1) The largest meteorite of lunar origin reportedly has a mass of 19 g. If the meteorite is placed on a sale whose spring constant is 83 N/m, what is the compression of the spring? How much energy is stored in the spring through its compression? • (3) The largest tigers, and therefore the largest members of the cat family, are the Siberian tigers. Male Siberian tigers are reported to have an average mass of about 389 kg. By contrast, a variety of very small cat that is native to India has an average adult mass of only 1.5 kg. Suppose this small cat is placed on a spring scale, causing the spring to be extended from its equilibrium position by 1.2 mm. How far would the spring be extended if a typical male Siberian tiger were placed on the same scale? How much more energy will be stored in the spring with the Tiger than with the cat?

  17. AP Weekly Equations Quiz 1 • List correctly two equations used to describe the motion objects in elastic and inelastic collisions. • List correctly two equations used to find the motion of a satellite around a star. • List correctly two equations used to find the period of an object spinning in circles on a massless string.

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