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Gravitation – the mutual force of attraction between two particles of matter

Gravitation – the mutual force of attraction between two particles of matter. Gravitation. What happens if you fire a cannonball horizontally at greater and greater speeds?.

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Gravitation – the mutual force of attraction between two particles of matter

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  1. Gravitation – the mutual force of attraction between two particles of matter

  2. Gravitation What happens if you fire a cannonball horizontally at greater and greater speeds? • If the speed is just right, the cannonball will go into orbit like the moon, because it falls at the same rate as Earth’s surface curves. • Therefore, Earth’s gravitational pull extends to the moon.

  3. Law of Universal Gravitation • Fg is proportional to the product of the masses (m1m2). • Fg is inversely proportional to the distance squared (r2). • Distance is measured center to center. • G converts units on the right (kg2/m2) into force units (N). • G = 6.673 x 10-11 N•m2/kg2

  4. What happens to the gravitational force if…. • One of the Masses is doubled? • Both masses are doubled? • The distance is doubled? • The distance is halved?

  5. Law of Universal Gravitation

  6. Gravity is a Field Force • Earth, or any other mass, creates a force field. • Forces are caused by an interaction between the field and the mass of the object in the field. • The gravitational field (g) points in the direction of the force, as shown.

  7. Calculating the value of g • Since g is the force acting on a 1 kg object, it has a value of 9.81 N/m (on Earth). • The same value as free fall acceleration (g = 9.81 m/s2) • Using the radius and mass of the earth, calculate its gravitational field. (ME = 5.97*1024 kg, RE=6.38*106 m)

  8. Practice Problem 1: • Two .30 kg billiard balls are on a table as shown. Find the gravitational force on the cue ball (m1) as a result of the other ball. (G = 6.67 x 10-11 N m2/kg2) m2 F21 = 3.75 X 10-11 N .40 m m1

  9. Practice Problem 2: • Two .30 kg billiard balls are on a table as shown. Find the gravitational force on the cue ball (m1) as a result of the other ball. (G = 6.67 x 10-11 N m2/kg2) F31 = 6.67 X 10-11 N .30 m m1 m3

  10. Practice Problem 3: • Three .30 kg billiard balls are on a table making the corners of a right triangle. Find the gravitational force on the cue ball (m1) as a result of the other two balls. (G = 6.67 x 10-11 N m2/kg2) m2 F21 = 3.75 X 10-11 jN F31 = 6.67 X 10-11 iN .40 m Ftot = 7.65 x 10-11 N at 29.3° .30 m m1 m3

  11. Kepler’s Laws • Johannes Kepler built his ideas on planetary motion using the work of others before him • (Nicolaus Copernicus and Tycho Brahe)

  12. Kepler’s Laws • Kepler’s first law • Orbits are elliptical, not circular. • Some orbits are only slightly elliptical. • Kepler’s second law • Equal areas are swept out in equal time intervals.

  13. Physics is Phunny

  14. Kepler’s Laws • Kepler’s third law • Relates orbital period (T) to distance from the sun (r) • Period is the time required for one revolution. • As distance increases, the period increases. • Not a direct proportion • T2/r3 has the same value for any object orbiting the sun

  15. Equations for Planetary Motion • Using SI units, prove to yourself that the units are consistent for each equation shown above.

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