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Universal Gravitation and Circular Motion

Universal Gravitation and Circular Motion. Honors. Unit AKS. Part 1. 13) explain Newton's Law of Universal Gravitation (GPS, HSGT) 13a) explain the concept of gravity and gravitational force in relationship to mass (GPS)

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Universal Gravitation and Circular Motion

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  1. Universal Gravitation and Circular Motion Honors

  2. Unit AKS Part 1 • 13) explain Newton's Law of Universal Gravitation (GPS, HSGT) • 13a) explain the concept of gravity and gravitational force in relationship to mass (GPS) • 13a1) explain gravity is a force dependent on mass and the distance between objects (GPS) • 13a2) demonstrate understanding of the proportional relationships between mass, distance, and gravitational force • 13b) solve problems that relate gravitational force, mass, distance, the Universal Gravitation constant, and acceleration due to gravity (GPS) • 13c) Extension – explain Kepler’s three laws of planetary motion • 12h) identify, measure and calculate centripetal force (GPS) • 12i) explain centrifugal force as a fictitious force resulting from the object’s inertia Part 2 Part 3

  3. Part 1: Gravity

  4. Relationship between mass and weight • Your weight (on earth) is the force felt between you and earth • There are two ways to calculate the force of weight • Using the mass of two objects, distance between, and G Bob : m1= 89 kg d = Earths radius = 6.4 x 106 m Earth : m2= 6.0 x 1024 kg

  5. Relationship between mass and weight 2. Using the mass of one if g (the acceleration due to gravity) is known Bob : m1= 89 kg

  6. Relationship between mass and weight

  7. Newton's Law of Universal Gravity • The force of gravity is universal • All things in the universe are attracted to all other things with mass.

  8. Ok its more like this • Newton's law of universal gravitation is not as romantic

  9. Gravity is the weakest fundamental force • It can only be felt when you have an object or objects with substantial mass

  10. Gm1m2 d2 Fg = Newton's Law of Universal Gravity • This equation relates mass and distance to force

  11. Gm1m2 d2 Fg= Newton's Law of Universal Gravity Force of Gravity Fg

  12. Gm1m2 d2 Fg= Newton's Law of Universal Gravity Mass of object 1 Mass of object 2

  13. Gm1m2 d2 Fg= Newton's Law of Universal Gravity Mass is directly proportional to Fg: If either of the masses increase the overall Fg will go up

  14. Gm1m2 d2 Fg= Newton's Law of Universal Gravity Distance: remember it is squared and has a greater effect on force

  15. Gm1m2 d2 Fg= Newton's Law of Universal Gravity Distance is inversely proportional to Fg: if d is larger the Fg decreases

  16. Gm1m2 d2 Fg= Newton's Law of Universal Gravity A constant that relates mass and distance to force G = 6.67 x 10-11Nm2/kg2 A constant G is not g g = -9.8 m/s2 Acceleration due to gravity G = 6.67 x 10-11 Nm2/kg2

  17. Gm1m2 d2 Fg= Specifically, how do changes in masses or distance change Fg? • Law of ones. • Can be used with any equation

  18. Gm1m2 d2 Fg= How do changes in masses or distance change Fg? • Ex.A: How does the force of gravity change if you double the distance between masses?

  19. Gm1m2 d2 Fg= • Use the Law of ones. • Can be used with any equation • Start by isolating the variable you want to compare on the left Its Isolated (by itself)

  20. Gm1m2 d2 Fg= (1)(1)(1) 12 Fg= = 1 • Next plug in ones for every variable on the right side. • If everything stayed the same Fg would equal 1

  21. Gm1m2 d2 Fg= (1)(1)(1) 22 = = ¼ Now double the distance between masses? • If everything stayed the same Fg would equal 1 • Now change only the variables that change: d becomes a 2 (since it is double) • This tells me the force is ¼ of 1 • or ¼ original

  22. Problem Set #1 • What would happen to the force of gravity if you tripled the distance between the objects? • What would happen to the force of gravity if you doubled the mass of one object? • What would happen to the force of gravity if you doubled the mass of one object and doubled the distance?

  23. Problem Set #1 • What would happen to the force of gravity if you tripled the distance between the objects?

  24. Problem Set #1 2. What would happen to the force of gravity if you doubled the mass of one object?

  25. Problem Set #1 3. What would happen to the force of gravity if you doubled the mass of one object and doubled the distance?

  26. The Earth • Earth’s mass = 6.0 x 1024 kg • Earths radius = 6.4 x 106 m • Fw of an object on earth can be also calculated using the Fg equation and the givens above.

  27. Gm1m2 d2 Fg= Ex B. What is the weight of a 56 kg woman on earth? (use the Fg equation to solve for this) Assumed Givens: Earth’s mass = 6.0 x 1024 kg Earths radius = 6.4 x 106 m

  28. Gm1m2 d2 Fg= Ex B. What is the weight of a 56 kg woman on earth? Assumed Givens: Earth’s mass = 6.0 x 1024 kg Earths radius = 6.4 x 106 m

  29. Problem set #2 • Consider the graph above showing the force between two objects as a function of the distance between them. This graph can be best explained using which of Newton’s Laws? • 1st Law • 2nd Law • 3rd Law • Law of Universal Gravitation

  30. Problem set #2 • Consider the graph above showing the force between two objects as a function of the distance between them. This graph can be best explained using which of Newton’s Laws? • 1st Law • 2nd Law • 3rd Law • Law of Universal Gravitation

  31. Gm1m2 d2 Fg= Problem Set #2 #2 A 85.00 kg boy is sitting 0.25 meters away from a 65.00 kg girl. How much attraction (Fg) do they have for each other? G = 6.67 x 10-11 Nm2/kg2

  32. Gm1m2 d2 Fg= Problem Set #2 #2 A 85.00 kg boy is sitting 0.25 meters away from a 65.00 kg girl. How much attraction (Fg) do they have for each other? G = 6.67 x 10-11 Nm2/kg2

  33. Gm1m2 d2 Fg= Problem Set #2 #3 What is the average force between the earth and moon? The average distance of the moon to earth is 3.84 x 108 m. The moon has a mass of 7.35 x 1022 kg and the earth has a mass of 6.0 x 1024 kg G = 6.67 x 10-11 Nm2/kg2

  34. Gm1m2 d2 Fg= Problem Set #2 #3 What is the average force between the earth and moon? The average distance of the moon to earth is 3.84 x 108 m. The moon has a mass of 7.35 x 1022 kg and the earth has a mass of 6.0 x 1024 kg G = 6.67 x 10-11 Nm2/kg2

  35. Gm1m2 d2 Fg= Problem Set #2 #4 A 6.00 x 104 kg mass is separated from a newly discovered object by a distance of 2.00 x 103 m. If the force of gravity between them is 4.00 x 104 N, what is the mass of the newly discovered object? G = 6.67 x 10-11 Nm2/kg2

  36. Gm1m2 d2 Fg= Problem Set #2 #4 A 6.00 x 104 kg mass is separated from a newly discovered object by a distance of 2.00 x 103 m. If the force of gravity between them is 4.00 x 104 N, what is the mass of the newly discovered object? G = 6.67 x 10-11 Nm2/kg2

  37. Honors Addition All objects in nature apply a force on all other objects. They apply equal and opposite forces on each other. + F, the gravitational force exerted on particle 1 by particle 2 - F, the gravitational force exerted on particle 2 by particle 1

  38. The earth and moon apply equal and opposite forces on each other

  39. Problems with more than two masses in one axis • You need to know your frame of reference • At what point are you determining the overall gravitational force

  40. Ex. C • The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are mA = 363 kg, mB = 517 kg, and mC = 154 kg. Find the magnitude and direction of the net gravitational force acting on (a) particle A, (b) particle B, and (c) particle C.

  41. Ex. C • The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are mA = 363 kg, mB = 517 kg, and mC = 154 kg. Find the magnitude and direction of the net gravitational force acting on (a) particle A, (b) particle B, and (c) particle C.

  42. Ex. C • The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are mA = 363 kg, mB = 517 kg, and mC = 154 kg. Find the magnitude and direction of the net gravitational force acting on (a) particle A, (b) particle B, and (c) particle C.

  43. Ex. C • The drawing shows three particles far away from any other objects and located on a straight line. The masses of these particles are mA = 363 kg, mB = 517 kg, and mC = 154 kg. Find the magnitude and direction of the net gravitational force acting on (a) particle A, (b) particle B, and (c) particle C.

  44. Problems with more than two masses in 2D • Figure out the individual forces and set them up head to tail

  45. Ex D. The drawing shows one alignment on the sun, earth, and moon. The gravitational force FSM that the sun exerts on the moon is perpendicular to the force FEM that the earth exerts on the moon. The masses are: mass of sun = 1.99 x 1030 kg, mass of earth = 5.98 x 1024 kg, and mass of moon = 7.35 x 1022 kg. The distances shown in the drawing are: rSM = 1.5 x 1011 m and rEM = 3.85 x 108 m. Determine the magnitude of gravitational force on the moon.

  46. 1.5 x 1011 m mM= 7.35 x 1022 kg • Ex. D Determine the magnitude of gravitational force on the moon. mS= 1.99 x 1030 kg 3.85 x 108 m mE= 5.98 x 1024 kg

  47. Part 2: Kepler’s Law’s of Planetary Motion

  48. Kepler's First Law: All planets move about the sun in an elliptical orbit with the sun at one foci. Sun distance varies elliptical orbit

  49. Kepler’s Laws of Planetary Motion • Kepler's Second Law: Motion is not constant but equal areas of the elliptical orbit are covered in equal times

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