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

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

2 How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves sp e e d = d ista n c e tim e u n its o f ms 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)

3 The Acceleration of Gravity All falling objects accelerate at the same rate (not counting friction of air resistance). On Earth, g 10 m/s2: speed increases 10 m/s with each second of falling.

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

5 Momentum and Force Momentum = mass velocity A net force changes momentum, which generally means an acceleration (change in velocity) Rotational momentum of a spinning or orbiting object is known as angular momentum

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

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

8 How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon an object You are weightless in free-fall!

9 Thought Question On the Moon: A. B. C. D. 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.

10 Thought Question On 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.

11 Why are astronauts weightless in space? There is gravity in space Weightlessness is due to a constant state of free-fall

12 QUIZ Which of the following is true? 1. You can have acceleration not equal zero, but velocity equal to zero 2. You can have acceleration equal to zero, but velocity not equal to zero 3. You can accelerate without changing your speed 4. 1 and , 2, and 3

13 If a planet travels in a circular orbit without speeding up or slowing down, is it accelerating? 1. No 2. Yes QUIZ

14 If a planet travels in a circular orbit without speeding up or slowing down, does it have a force on it? 1. No 2. Yes QUIZ

15 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 ( )

16 What are Newton s three laws of motion? Newton s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction.

17 Newton s second law of motion Force = mass acceleration

18 Newton s third law of motion: For every force, there is always an equal and opposite reaction force.

19 Thought Question: Is the force the Earth exerts on you larger, smaller, or the same as the force you exert on it? A. Earth exerts a larger force on you. B. I exert a larger force on Earth. C. Earth and I exert equal and opposite forces on each other.

20 Newton s third law says that for every force there is an equal and opposite reaction force. For rockets, this means: 1. If a rocket shoots gas out the back, the rocket moves forward 2. #1 is only true if there is air to push against. It is not always true QUIZ

21 4.3 Conservation Laws in Astronomy: Our goals for learning: Why do objects move at constant velocity if no force acts on them? What keeps a planet rotating and orbiting the Sun? Where do objects get their energy?

22 Conservation of Momentum The total momentum of interacting objects cannot change unless an external force is acting on them Interacting objects exchange momentum through equal and opposite forces

23 What keeps a planet rotating and orbiting the Sun?

24 Conservation of Angular Momentum angular momentum = mass x velocity x radius The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely

25 Angular momentum conservation also explains why objects rotate faster as they shrink in radius:

26 Where do objects get their energy? Energy makes matter move. Energy is conserved, but it can: Transfer from one object to another Change in form

27 Basic Types of Energy Kinetic (motion) Radiative (light) Stored or potential Energy can change type but cannot be destroyed.

28 Thermal Energy: the collective kinetic energy of many particles (for example, in a rock, in air, in water) Thermal energy is related to temperature but it is NOT the same. Temperature is the average kinetic energy of the many particles in a substance.

29 Temperature Scales

30 Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends both on temperature AND density Example:

31 Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall

32 Gravitational Potential Energy In space, an object or gas cloud has more gravitational energy when it is spread out than when it contracts. A contracting cloud converts gravitational potential energy to thermal energy.

33 Mass-Energy Mass itself is a form of potential energy E = mc 2 A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators)

34 Conservation of Energy Energy can be neither created nor destroyed. It can change form or be exchanged between objects. The total energy content of the Universe was determined in the Big Bang and remains the same today.

35 A cake is baking at 400 degrees. If you briefly touch the cake you will not be burned. If you touch the metal pan for the same length of time you will be burned. Why? 1. The metal is hotter than the cake 2. The metal is denser than the cake there are more atoms per unit volume 3. The metal is a better conductor 4. 2 and 3 QUIZ 5. All of the above

36 Which of the basic types of energy is illustrated when you stand on a ladder? kinetic potential radiative heat None of the above QUIZ

37 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?

38 What determines the strength of gravity? The Universal Law of Gravitation: 4 Every mass attracts every other mass. 4 Attraction is directly proportional to the product of their masses. 4 Attraction is inversely proportional to the square of the distance between their centers.

39 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) Unbound Parabola Hyperbola

40 Center of Mass Because of momentum conservation, orbiting objects orbit around their center of mass

41 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.

42 Newton s Version of Kepler s Third Law p2 = 4π2 G (M 1+M 2 ) a3 OR 2 a3 4 π M 1+M 2 = G p2 p = orbital period a=average orbital distance (between centers) (M1 + M2) = sum of object masses

43 Newton s version of Kepler s third law allows us to calculate the mass of Saturn from orbital characteristics of its moon Titan. 1. Yes, but we can measure Saturn s mass more precisely by measuring how long it takes to orbit the Sun. 2. Yes, knowing Titan s period and semi-major axis allows us to calculate Saturn s mass. 3. No, we can only measure Titan s mass this way, not Saturn s. 4. No, we have to measure all of Saturn s moons orbits, not just Titan s. 5. No, this can be done for other planets but not Saturn because of its rings. QUIZ

44 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?

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

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

47 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)

48 How does gravity cause tides? Moon s gravity pulls harder on near side of Earth than on far side Difference in Moon s gravitational pull stretches Earth

49 Tides and Phases Size of tides depends on phase of Moon

50 Tidal Friction Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). Moon once orbited faster (or slower); tidal friction caused it to lock in synchronous rotation.

51 Why do all objects fall at the same rate? a ro ck = Fg M ro ck a ro c k M E arth M ro ck F g =G R E2 arth M E arth M ro ck M E a rth =G 2 =G 2 R E a rth M ro ck R E a rth 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.

52 Newton s law of gravity is F = G m1 m2 / d2 Can this be used to find the force between the Earth and YOU? If so, what is d? No Yes, d is the diameter of the Earth Yes, d is the distance from you to the ground Yes, d is the distance from you to the center of the Earth QUIZ

53 How does the gravitational force between two objects change if the distance between them triples? The force increases by a factor of three. The force increases by a factor of nine. The force remains the same. The force decreases by a factor of three. The force decreases by a factor of nine. QUIZ

54 At any given time, how many high tides are there on the Earth? 1. One 2. Two 3. There may be none or one, depending on what time of day 4. None, one, or two depending on the time of day QUIZ

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