Preview

1
Preview
Section 1 Circular Motion Section 2 Newtons
Law of Universal Gravitation Section 3 Motion
in Space Section 4 Torque 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 each example 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 each example 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
Newtons 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 Earths
  surface curves.
• Therefore, Earths gravitational pull extends to
  the moon.

15
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 Nm2/kg2

16
Law of Universal Gravitation
17
Gravitational Force

• If gravity is universal and exists between all
  masses, why isnt this force easily observed in
  everyday life? For example, why dont 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

• Newtons 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 gt Fin then MA gt 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 lt F1 so MA gt1 and d2 gt d1
• If the ramp is frictionless, the work is the same
  in both cases.
• F1d1 F2d2
• With friction, F2d2 gt 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 23.
• 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 23.
• 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 23.
• 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 cars
  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 23.
• 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 cars
  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 Nm2/kg2)
• F. 5.29 ? 1032 N
• G. 3.52 ? 1022 N
• H. 5.90 ? 102 N
• J. 1.77 ? 108 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 Nm2/kg2)
• F. 5.29 ? 1032 N
• G. 3.52 ? 1022 N
• H. 5.90 ? 102 N
• J. 1.77 ? 108 N

44
Multiple Choice, continued

• 5. Which of the following is a correct
  interpretation of the expression
  ?
• A. Gravitational field strength changes with an
  objects distance from Earth.
• B. Free-fall acceleration changes with an
  objects distance from Earth.
• C. Free-fall acceleration is independent of the
  falling objects 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
  objects distance from Earth.
• B. Free-fall acceleration changes with an
  objects distance from Earth.
• C. Free-fall acceleration is independent of the
  falling objects 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 89.

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.
51
Multiple Choice, continued

• Use the diagram to answer
• questions 89.

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.
52
Multiple Choice, continued

• Use the diagram to answer
• questions 89.

9. If each force is 6.0 N, the angle between F1
and F2 is 60.0, and the radius of the wheel
is 1.0 m, what is the resultant torque on the
wheel? A. 18 Nm C. 9.0 Nm B. 9.0 Nm D.
18 Nm
53
Multiple Choice, continued

• Use the diagram to answer
• questions 89.

9. If each force is 6.0 N, the angle between F1
and F2 is 60.0, and the radius of the wheel
is 1.0 m, what is the resultant torque on the
wheel? A. 18 Nm C. 9.0 Nm B. 9.0 Nm D.
18 Nm
54
Multiple Choice, continued

• 10. A force of 75 N is applied to a lever. This
  force lifts a load weighing 225 N. What is the
  mechanical advantage of the lever?
• F. 1/3
• G. 3
• H. 150
• J. 300

55
Multiple Choice, continued

• 10. A force of 75 N is applied to a lever. This
  force lifts a load weighing 225 N. What is the
  mechanical advantage of the lever?
• F. 1/3
• G. 3
• H. 150
• J. 300

56
Multiple Choice, continued

• 11. A pulley system has an efficiency of 87.5
  percent. How much work must you do to lift a
  desk weighing 1320 N to a height of 1.50 m?
• A. 1510 J
• B. 1730 J
• C. 1980 J
• D. 2260 J

57
Multiple Choice, continued

• 11. A pulley system has an efficiency of 87.5
  percent. How much work must you do to lift a
  desk weighing 1320 N to a height of 1.50 m?
• A. 1510 J
• B. 1730 J
• C. 1980 J
• D. 2260 J

58
Multiple Choice, continued

• 12. Which of the following statements is correct?
• F. Mass and weight both vary with location.
• G. Mass varies with location, but weight does
  not.
• H. Weight varies with location, but mass does
• not.
• J. Neither mass nor weight varies with location.

59
Multiple Choice, continued

• 12. Which of the following statements is correct?
• F. Mass and weight both vary with location.
• G. Mass varies with location, but weight does
  not.
• H. Weight varies with location, but mass does
• not.
• J. Neither mass nor weight varies with location.

60
Multiple Choice, continued

• 13. Which astronomer discovered that planets
  travel in elliptical rather than circular
  orbits?
• A. Johannes Kepler
• B. Nicolaus Copernicus
• C. Tycho Brahe
• D. Claudius Ptolemy

61
Multiple Choice, continued

• 13. Which astronomer discovered that planets
  travel in elliptical rather than circular
  orbits?
• A. Johannes Kepler
• B. Nicolaus Copernicus
• C. Tycho Brahe
• D. Claudius Ptolemy

62
Short Response

• 14. Explain how it is possible for all the water
  to remain in a pail that is whirled in a
  vertical path, as shown below.

63
Short Response

• 14. Explain how it is possible for all the water
  to remain in a pail that is whirled in a
  vertical path, as shown below.

Answer The water remains in the pail even
when the pail is upside down because the water
tends to move in a straight path due to inertia.
64
Short Response, continued

• 15. Explain why approximately two high tides take
  place every day at a given location on Earth.

65
Short Response, continued

• 15. Explain why approximately two high tides take
  place every day at a given location on
  Earth.
• Answer The moons tidal forces create two
  bulges on Earth. As Earth rotates on its axis
  once per day, any given point on Earth passes
  through both bulges.

66
Short Response, continued

• 16. If you used a machine to increase the output
  force, what factor would have to be sacrificed?
  Give an example.

67
Short Response, continued

• 16. If you used a machine to increase the output
  force, what factor would have to be sacrificed?
  Give an example.
• Answer You would have to apply the input
  force over a greater distance. Examples may
  include any machines that increase output force
  at the expense of input distance.

68
Extended Response

• 17. Mars orbits the sun (m 1.99 ? 1030 kg) at a
  mean distance of 2.28 ? 1011 m. Calculate the
  length of the Martian year in Earth days. Show
  all of your work. (G 6.673 ? 1011 Nm2/kg2)

69
Extended Response

• 17. Mars orbits the sun (m 1.99 ? 1030 kg) at a
  mean distance of 2.28 ? 1011 m. Calculate the
  length of the Martian year in Earth days. Show
  all of your work. (G 6.673 ? 1011 Nm2/kg2)

Answer 687 days