Preview

1. Preview Section 1 Circular Motion Section 2 Newton’s Law of Universal Gravitation Section 3 Motion in Space Section 4Torque and Simple Machines

2. What do you think? • Consider the following objects moving in circles: • A car traveling around a circular ramp on the highway • A ball tied to a string being swung in a circle • The moon as it travels around Earth • A child riding rapidly on a playground merry-go-round • For eachexample above, answer the following: • Is the circular motion caused by a force? • If so, in what direction is that force acting? • What is the source of the force acting on each object?

3. Tangential Speed (vt) • Speed in a direction tangent to the circle • Uniform circular motion: vt has a constant value • Only the direction changes • Example shown to the right • How would the tangential speed of a horse near the center of a carousel compare to one near the edge? Why?

4. Centripetal Acceleration (ac) • Acceleration is a change in velocity (size or direction). • Direction of velocity changes continuously for uniform circular motion. • What direction is the acceleration? • the same direction as v • toward the center of the circle • Centripetal means “center seeking”

5. Centripetal Acceleration (magnitude) • How do you think the magnitude of the acceleration depends on the speed? • How do you think the magnitude of the acceleration depends on the radius of the circle?

6. Tangential Acceleration • Occurs if the speed increases • Directed tangent to the circle • Example: a car traveling in a circle • Centripetal acceleration maintains the circular motion. • directed toward center of circle • Tangential acceleration produces an increase or decrease in the speed of the car. • directed tangent to the circle

7. Centripetal Acceleration Click below to watch the Visual Concept. Visual Concept

8. Centripetal Force (Fc)

9. Centripetal Force • Maintains motion in a circle • Can be produced in different ways, such as • Gravity • A string • Friction • Which way will an object move if the centripetal force is removed? • In a straight line, as shown on the right

10. Describing a Rotating System • Imagine yourself as a passenger in a car turning quickly to the left, and assume you are free to move without the constraint of a seat belt. • How does it “feel” to you during the turn? • How would you describe the forces acting on you during this turn? • There is not a force “away from the center” or “throwing you toward the door.” • Sometimes called “centrifugal force” • Instead, your inertia causes you to continue in a straight line until the door, which is turning left, hits you.

11. Classroom Practice Problems • A 35.0 kg child travels in a circular path with a radius of 2.50 m as she spins around on a playground merry-go-round. She makes one complete revolution every 2.25 s. • What is her speed or tangential velocity? (Hint: Find the circumference to get the distance traveled.) • What is her centripetal acceleration? • What centripetal force is required? • Answers: 6.98 m/s, 19.5 m/s2, 682 N

12. Now what do you think? • Consider the following objects moving in circles: • A car traveling around a circular ramp on the highway • A ball tied to a string being swung in a circle • The moon as it travels around Earth • A child riding rapidly on a playground merry-go-round • For eachexample above, answer the following: • Is the circular motion caused by a force? • If so, in what direction is that force acting? • What is the source of the force acting on each object?

13. What do you think? Imagine an object hanging from a spring scale. The scale measures the force acting on the object. • What is the source of this force? What is pulling or pushing the object downward? • Could this force be diminished? If so, how? • Would the force change in any way if the object was placed in a vacuum? • Would the force change in any way if Earth stopped rotating?

14. Newton’s Thought Experiment • What happens if you fire a cannonball horizontally at greater and greater speeds? • Conclusion: 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.

15. Law of Universal Gravitation • Fg is proportional to the product of the masses (m1m2). • Fgis 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

16. Law of Universal Gravitation

17. Gravitational Force • If gravity is universal and exists between all masses, why isn’t this force easily observed in everyday life? For example, why don’t we feel a force pulling us toward large buildings? • The value for G is so small that, unless at least one of the masses is very large, the force of gravity is negligible.

18. Ocean Tides • What causes the tides? • How often do they occur? • Why do they occur at certain times? • Are they at the same time each day?

19. Ocean Tides • Newton’s law of universal gravitation is used to explain the tides. • Since the water directly below the moon is closer than Earth as a whole, it accelerates more rapidly toward the moon than Earth, and the water rises. • Similarly, Earth accelerates more rapidly toward the moon than the water on the far side. Earth moves away from the water, leaving a bulge there as well. • As Earth rotates, each location on Earth passes through the two bulges each day. • Link to web

20. 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.

21. 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 ag (9.81 m/s2) • The value for g (on Earth) can be calculated as shown below.

22. Classroom Practice Problems • Find the gravitational force that Earth (mE= 5.97  1024 kg) exerts on the moon (mm= 7.35  1022 kg) when the distance between them is 3.84 x 108 m. • Answer: 1.99 x 1020 N • Find the strength of the gravitational field at a point 3.84 x 108 m from the center of Earth. • Answer: 0.00270 N/m or 0.00270 m/s2

23. Now what do you think? Imagine an object hanging from a spring scale. The scale measures the force acting on the object. • What is the source of this force? What is pulling or pushing the object downward? • Could this force be diminished? If so, how? • Would the force change in any way if the object was placed in a vacuum? • Would the force change in any way if Earth stopped rotating?

24. What do you think? • Make a sketch showing the path of Earth as it orbits the sun. • Describe the motion of Earth as it follows this path. • Describe the similarities and differences between the path and motion of Earth and that of other planets.

25. What do you think? • What does the term weightless mean to you? • Have you ever observed someone in a weightless environment? If so, when? • How did their weightless environment differ from a normal environment?

26. Weight and Weightlessness • Bathroom scale • A scale measures the downward force exerted on it. • Readings change if someone pushes down or lifts up on you. • Your scale reads the normal force acting on you.

27. Apparent Weightlessness • Elevator at rest: the scale reads the weight (600 N). • Elevator accelerates downward: the scale reads less. • Elevator in free fall: the scale reads zero because it no longer needs to support the weight.

28. Apparent Weightlessness • You are falling at the same rate as your surroundings. • No support force from the floor is needed. • Astronauts are in orbit, so they fall at the same rate as their capsule. • True weightlessness only occurs at great distances from any masses. • Even then, there is a weak gravitational force.

29. Now what do you think? • Make a sketch showing the path of Earth as it orbits the sun. • Describe the motion of Earth as it follows this path. • Describe the similarities and differences between the path and motion of Earth and that of other planets.

30. Now what do you think? • What does the term weightless mean to you? • Have you ever observed someone in a weightless environment? If so, when? • How did their weightless environment differ from a normal environment?

31. Simple Machines • Change the size or direction of the input force • Mechanical advantage (MA) compares the input force to the output force. • When Fout > Fin then MA > 1 • MA can also be determined from the distances the input and output forces move.

32. Overview of Simple Machines Click below to watch the Visual Concept. Visual Concept

33. Simple Machines • Simple machines alter the force and the distance moved. • For the inclined plane shown: • F2 < F1 so MA >1 andd2 > d1 • If the ramp is frictionless, the work is the same in both cases. • F1d1 = F2d2 • With friction, F2d2 > F1d1. • The force is reduced but the work done is greater.

34. Efficiency of Simple Machines • Efficiency measures work output compared to work input. • In the absence of friction, they are equal. • Real machines always have efficiencies less than 1, but they make work easier by changing the force required to do the work.

35. Preview • Multiple Choice • Short Response • Extended Response

36. Multiple Choice 1. An object moves in a circle at a constant speed. Which of the following is not true of the object? A. Its acceleration is constant. B. Its tangential speed is constant. C. Its velocity is constant. D. A centripetal force acts on the object.

37. Multiple Choice 1. An object moves in a circle at a constant speed. Which of the following is not true of the object? A. Its acceleration is constant. B. Its tangential speed is constant. C. Its velocity is constant. D. A centripetal force acts on the object.

38. Multiple Choice, continued Use the passage below to answer questions 2–3. A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m. 2. What is the centripetal acceleration of the car? F. 2.4  10-2 m/s2 G. 0.60 m/s2 H. 9.0 m/s2 J. zero

39. Multiple Choice, continued Use the passage below to answer questions 2–3. A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m. 2. What is the centripetal acceleration of the car? F. 2.4  10-2 m/s2 G. 0.60 m/s2 H. 9.0 m/s2 J. zero

40. Multiple Choice, continued Use the passage below to answer questions 2–3. A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m. 3. What is the most direct cause of the car’s centripetal acceleration? A. the torque on the steering wheel B. the torque on the tires of the car C. the force of friction between the tires and the road D. the normal force between the tires and the road

41. Multiple Choice, continued Use the passage below to answer questions 2–3. A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m. 3. What is the most direct cause of the car’s centripetal acceleration? A. the torque on the steering wheel B. the torque on the tires of the car C. the force of friction between the tires and the road D. the normal force between the tires and the road

42. Multiple Choice, continued 4. Earth (m = 5.97  1024 kg) orbits the sun (m = 1.99  1030 kg) at a mean distance of 1.50  1011 m. What is the gravitational force of the sun on Earth? (G = 6.673  10-11 N•m2/kg2) F. 5.29  1032 N G. 3.52  1022 N H. 5.90  10–2 N J. 1.77  10–8 N

43. Multiple Choice, continued 4. Earth (m = 5.97  1024 kg) orbits the sun (m = 1.99  1030 kg) at a mean distance of 1.50  1011 m. What is the gravitational force of the sun on Earth? (G = 6.673  10-11 N•m2/kg2) F. 5.29  1032 N G. 3.52  1022 N H. 5.90  10–2 N J. 1.77  10–8 N

44. Multiple Choice, continued 5. Which of the following is a correct interpretation of the expression ? A. Gravitational field strength changes with an object’s distance from Earth. B. Free-fall acceleration changes with an object’s distance from Earth. C. Free-fall acceleration is independent of the falling object’s mass. D. All of the above are correct interpretations.

45. Multiple Choice, continued 5. Which of the following is a correct interpretation of the expression ? A. Gravitational field strength changes with an object’s distance from Earth. B. Free-fall acceleration changes with an object’s distance from Earth. C. Free-fall acceleration is independent of the falling object’s mass. D. All of the above are correct interpretations.

46. Multiple Choice, continued 6. What data do you need to calculate the orbital speed of a satellite? F. mass of satellite, mass of planet, radius of orbit G. mass of satellite, radius of planet, area of orbit H. mass of satellite and radius of orbit only J. mass of planet and radius of orbit only

47. Multiple Choice, continued 6. What data do you need to calculate the orbital speed of a satellite? F. mass of satellite, mass of planet, radius of orbit G. mass of satellite, radius of planet, area of orbit H. mass of satellite and radius of orbit only J. mass of planet and radius of orbit only

48. Multiple Choice, continued 7. Which of the following choices correctly describes the orbital relationship between Earth and the sun? A. The sun orbits Earth in a perfect circle. B. Earth orbits the sun in a perfect circle. C. The sun orbits Earth in an ellipse, with Earth at one focus. D. Earth orbits the sun in an ellipse, with the sun at one focus.

49. Multiple Choice, continued 7. Which of the following choices correctly describes the orbital relationship between Earth and the sun? A. The sun orbits Earth in a perfect circle. B. Earth orbits the sun in a perfect circle. C. The sun orbits Earth in an ellipse, with Earth at one focus. D. Earth orbits the sun in an ellipse, with the sun at one focus.

50. Multiple Choice, continued Use the diagram to answer questions 8–9. 8. The three forces acting on the wheel have equal magnitudes. Which force will produce the greatest torque on the wheel? F.F1 G.F2 H.F3 J. Each force will produce the same torque.