Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

1. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

2. 4.1 Describing Motion Our goals for learning: • How do we describe motion? • How is mass different from weight?

3. How do we describe motion? Precise definitions to describe motion: • Speed: Rate at which object moves • example: speed of 10 m/s • Velocity: Speed and direction • example: 10 m/s, due east • Acceleration: Any change in velocity units of speed/time (m/s2)

4. Free Fall • Free fall is the condition of an object that is only acted upon by gravity. • A stone dropped off the side of a cliff is in the state of free fall once it is released. • All falling objects accelerate at the same rate (not counting friction of air resistance). • Apollo 15 Demonstration

5. a Uniform Acceleration • All objects in free fall experience uniform, or a constant rate of acceleration. • Near the surface of the Earth, the rate of acceleration is close to 10 m/s2 in the downward direction. • At 10 m/s2 the speed of an object would increase by 10 m/s for every second the object is in free fall. a

6. a Uniform Acceleration • How does the speed change over time when a = 10 m/s2? • Speed increases ≈ 10 m/s with each second of falling.

7. a Uniform Acceleration • How far would an object travel if a = 10 m/s2?

8. The Acceleration of Gravity (g) • Galileo showed that g is the same for all falling objects, regardless of their mass. Apollo 15 demonstration

9. How did Newton change our view of the universe? • Realized the same physical laws that operate on Earth also operate in the heavens • one universe • Discovered laws of motion and gravity • Much more: Experiments with light; first reflecting telescope, calculus… Sir Isaac Newton (1642-1727)

10. The Motion of Objects • Before Newton: during the 17th Century, Galileo was the first to suggest that objects have a natural tendency to resist a change in motion. • The reason that objects do not continue to move is because of the force of friction. • Without friction, an object would continue to move in a straight line at a constant speed indefinitely.

11. What is Inertia? • Galileo coined the term inertia. He said that: • All matter consists of inertia. • Inertia is a measure of an object’s resistance to change in motion. • An object’s mass is a measure of an object’s inertia: the more massive the more inertia. • More massive objects are more resistant to changes in motion.

12. Definition: The Law of Inertia • The Law of Inertia and Newton’s 1st Law of Motion are one and the same. • An object in motion will remain in motion (in a straight line at constant speed), and • An object at rest will remain at rest. Unless acted upon by an unbalanced external force.

13. Newton’s First Law of Motion Describe the command module’s motion in terms of Newton’s 1st Law of Motion. • The command module will continue in a straight path unless an external force acts on it. • What forces? • From the engine • Gravity from Earth or the moon

14. How do Forces Act on Objects? • A force can cause an object to speed up (accelerate). • A force can cause an object to slow down (accelerate negatively). • A force can cause an object to change direction.

15. Thought Question#1Is there a net force? Y/N • A car coming to a stop. • A bus speeding up. • An elevator moving at constant speed. • A bicycle going around a curve. • A moon orbiting Jupiter. Y Y N Y Y

16. Thought Question#2 • Is a force required to keep an object in motion? • No • While a force is required to put an object into motion, any additional force may cause it to speed up or slow down, or change direction.

17. Newton’s 2nd LawThe Relationship Between Force and Mass • Newton determined that the acceleration of an object is directly proportional to the force applied to move it and inversely proportional to the mass of the object. • What does this mean? • As mass increases and the force is held constant, the rate of acceleration will decrease. • As the amount of force is increased while keeping the mass constant, the acceleration will increase.

18. Slope = mass Mass Force Acceleration Acceleration Newton’s 2nd Law • Newton’s 2nd Law in relation to the acceleration of objects a = F/m Inverse Relationship Direct Relationship More Force = More Acceleration More Mass = Less Acceleration

19. What have we learned? • How do we describe motion? • Speed = distance / time • Speed & direction => velocity • Change in velocity => acceleration • Force causes change in velocity, producing acceleration

20. How is mass different from weight? • Mass – the amount of matter in an object • Weight – the force that acts upon an object due to gravity Note: You are weightless in free-fall!

21. Thought Question #3On the Moon: • My weight is the same, my mass is less. • My weight is less, my mass is the same. • My weight is more, my mass is the same. • My weight is more, my mass is less.

22. Why are astronauts weightless in space? • Does gravity exist in space? • Yes • Then why does an astronaut experience weightlessness? • It is because they are in a constant state of free-fall

23. What have we learned? • How is mass different from weight? • Mass = quantity of matter • Weight = force acting on mass • Objects are weightless in free-fall

24. Newton’s Third Law of Motion: For every force, there is always an equal and opposite reaction force.

25. Interaction Pairs • All forces exist in pairs (no isolated forces) that are opposite in direction and equal in magnitude (size). • When you kick a ball, you exert a force on the ball while the ball exerts a force on you. • You pull on a door to open it while the door exerts a force on you. • A hammer exerts a force on a nail while the nail exerts a force on the hammer. • When you pull on a rope, it pulls on you.

26. Force of floor on person. Force of person on floor. Do the forces cancel each other out? • No. • Since the forces act on different objects, it is not possible for them to cancel each other out. Ff = mfaf Fp = mpap

27. F2 F1 Newton’s 3rd Law of Motion & Acceleration • Newton’s 3rd Law of Motion says that -F1 = F2 • And Newton’s 2nd Law of Motion says that m1a1 = m2a2 • While the forces may be equal but opposite in direction, the accelerations of each object may be different.

28. Example: Newton’s 3rd Law of Motion A physics student is pulling on a rope, which in both cases causes the scale to read 500 Newtons. The physics student is pulling a. with more force when the rope is attached to the wall. b. with more force when the rope is attached to the elephant. c. the same force in each case.

29. Thought Question #4Is the force the Earth exerts on you larger, smaller, or the same force you exert on it? • Earth exerts a larger force on you. • I exert a larger force on Earth. • Earth and I exert equal and opposite forces on each other.

30. Thought Question #5 • The Earth and moon are attracted to one another by a gravitational force. Which one attracts with a greater force? Why? • Neither. They both exert a force on each other that is equal and opposite in accordance with Newton’s 3rd Law of Motion. Fmoon on Earth FEarth on moon

31. Thought Question #6A compact car and a Mack truck have a head-on collision. Are the following true or false? • The force of the car on the truck is equal and opposite to the force of the truck on the car. • The change of velocity of the car is the same as the change of velocity of the truck. T F

32. What have we learned? • How did Newton change our view of the universe? • He discovered laws of motion & gravitation • He realized these same laws of physics were identical in the universe and on Earth • What are Newton’s Three Laws of Motion? • 1. Object moves at constant velocity if no net force is acting. • 2. Force = mass  acceleration • 3. For every force there is an equal and opposite reaction force

33. 4.4 The Universal Law of Gravitation • Our goals for learning: • What determines the strength of gravity? • How does Newton’s law of gravity extend Kepler’s laws?

34. Gravity • What is it? • The force of attraction between all masses in the universe.

35. What determines the strength of gravity? The Universal Law of Gravitation: • Every mass attracts every other mass. • Attraction is directly proportional to the product of their masses. • Attraction is inversely proportional to the square of the distance between their centers.

36. The Effects of Mass and Distance on Fg

37. The Inverse Square Relationship • As the distance between two objects increases, the gravitational force decreases by 1/r2. • If the distance between two objects is doubled, the gravitational force will decrease by 4 x. • If the distance between two objects is halved, the gravitational force will increase by 4 x.

38. The Inverse Square RelationshipWhat it Looks Like rE = 6380 km Shuttle orbit (400 km) g = 8.65 Geosynchronous Orbit (36,000 km) g = 0.23

39. The Cavendish Experiment https://video.search.yahoo.com/video/play;_ylt=A2KLqIEGEDFVzlsA1RosnIlQ;_ylu=X3oDMTByZWc0dGJtBHNlYwNzcgRzbGsDdmlkBHZ0aWQDBGdwb3MDMQ--?p=youtube+cavendish+experiment&vid=ceffb99e10a7de8282dd343f188c360e&l=1%3A59&turl=http%3A%2F%2Fts1.mm.bing.net%2Fth%3Fid%3DWN.UX5sc%252bcC6tcV5sLBvVqkFQ%26pid%3D15.1&rurl=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DdyLYbvZIYoU&tit=Cavendish+Experiment&c=0&sigr=11bulhojq&sigt=10k9bc3d1&sigi=121e0bcmj&age=1381239063&fr2=p%3As%2Cv%3Av&hsimp=yhs-001&hspart=mozilla&tt=b

40. How does Newton’s law of gravity extend Kepler’s laws? • Kepler’s first two laws apply to all orbiting objects, not just planets • Ellipses are not the only orbital paths. Orbits can be: • Bound (ellipses) • Not enough speed to escape • Unbound • Parabola • Just enough speed to escape • Hyperbola • More than enough speed to escape

41. Why do all objects fall at the same rate? • The gravitational acceleration of an object like a rock does not depend on its mass because Mrock in the equation for acceleration cancels Mrock in the equation for gravitational force • This “coincidence” was not understood until Einstein’s general theory of relativity.

42. Newton and Kepler’s Third Law His laws of gravity and motion showed that the relationship between the orbital period and average orbital distance of a system tells us the total mass of the system. • Examples: • Earth’s orbital period (1 year) and average distance (1 AU) tell us the Sun’s mass. • Orbital period and distance of a satellite from Earth tell us Earth’s mass. • Orbital period and distance of a moon of Jupiter tell us Jupiter’s mass.

43. Newton’s Version of Kepler’s Third Law p = orbital period a=average orbital distance (between centers) (M1 + M2) = sum of object masses

44. What have we learned? • What determines the strength of gravity? • Directly proportional to the product of the masses (M x m) • Inversely proportional to the square of the separation • How does Newton’s law of gravity allow us to extend Kepler’s laws? • Applies to other objects, not just planets. • Includes unbound orbit shapes: parabola, hyperbola • Can be used to measure mass of orbiting systems.

45. 4.5 Orbits, Tides, and the Acceleration of Gravity • Our goals for learning: • How do gravity and energy together allow us to understand orbits? • How does gravity cause tides? • Why do all objects fall at the same rate?

46. More gravitational energy; Less kinetic energy How do gravity and energy together allow us to understand orbits? • Total orbital energy (gravitational + kinetic) stays constant if there is no external force • Orbits cannot change spontaneously. Less gravitational energy; More kinetic energy Total orbital energy stays constant

47. Changing an Orbit • So what can make an object gain or lose orbital energy? • Friction or atmospheric drag • A gravitational encounter.

48. Escape Velocity • If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit) • Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr)

50. Escape and orbital velocities don’t depend on the mass of the cannonball