Astro Lecture 11 Newton s laws
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1 Astro Lecture 11 Newton s laws Twin Sungrazing comets 11/02/09 Habbal Astro Lecture
2 Understanding Newton s 3 rd law Weight = force that acts upon an object due to acceleration of gravity Let R = reaction force = - ma (a= acceleration of elevator) F = force on scale inside elevator F = mg + R F = mg F(elev) = ma R = 0 F = mg R = ma R = -ma R = -mg F = mg + ma F = mg - ma F = mg mg = 0 11/02/09 Habbal Astro Lecture 11 2
3 Conservation Laws in Astronomy [Section 4.3] Our goals for learning: What keeps a planet rotating and orbiting the Sun? Where do objects get their energy? 11/02/09 Habbal Astro Lecture 11 3
4 1. Conservation of Momentum: Linear 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. 11/02/09 Habbal Astro Lecture 11 4
5 1. Conservation of Momentum: Linear momentum (cont d) Newton s 2 nd law: Object 1 exerts a force that will change the momentum of object 2 Newton s 3 rd law: Object 2 exerts an equal and opposite force on object 1 momentum(1) = - momentum(2) Total momentum of colliding objects is conserved 11/02/09 Habbal Astro Lecture 11 5
6 Conservation of Angular Momentum m x v x r = constant or What keeps a planet rotating and orbiting the Sun? r greater so v is smaller r smaller so v is greater v = velocity v r = average distance from the Sun 11/02/09 Habbal Astro Lecture 11 6
7 Angular momentum conservation also explains why objects rotate faster as they shrink in radius Extending arms means larger radius, so smaller velocity of rotation Bringing arms in reduces the radius, so increases rotational velocity 11/02/09 Habbal Astro Lecture 11 7
8 Conservation of Angular Momentum 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 rate and orbit must stay about the same But Earth is very gradually transferring some of its rotational angular momentum to the Moon, and is gradually slowing down Clouds of gas, spinning disks orbiting young stars: They will start to spin faster as gravity makes them shrink in size 11/02/09 Habbal Astro Lecture 11 8
9 2. Conservation of Energy Energy cannot appear out of nowhere or disappear into nothingness. Objects can gain or lose energy only by exchanging energy with other objects All actions in the universe involve exchanges of energy or the conversion of energy from one form to another The total energy content of the universe was determined in the Big Bang and remains the same today. Energy can change type but cannot be destroyed. 11/02/09 Habbal Astro Lecture 11 9
10 Kinetic (motion): Moving objects Thermal energy Radiative energy: carried by light Potential or Stored energy: Basic Types of Energy Gravitational potential energy Mass energy Chemical energy 11/02/09 Habbal Astro Lecture 11 10
11 Thermal Energy, a form of Kinetic Energy the collective/total kinetic energy of many particles moving randomly within a substance, like a rock, the air or the gas within a distant star Thermal energy is related to temperature but it is NOT the same. Temperature is a measure of the average kinetic energy of the many particles in a substance. particles, on average have a higher kinetic energy, move faster 11/02/09 Habbal Astro Lecture 11 11
12 Thermal energy is a measure of the total kinetic energy of all the particles in a substance. It therefore depends on both temperature AND density. But water in the pot contains more thermal energy because of its much higher density Air in oven at 400 F is hotter than the boiling water (212 F) in the pot 11/02/09 Habbal Astro Lecture 11 12
13 Common Temperature Scales Absolute zero Kelvin is when all motion stops 11/02/09 Habbal Astro Lecture 11 13
14 Energy due to movement of object Example of kinetic energy due to motion E k = ½ m v 2 11/02/09 Habbal Astro Lecture 11 14
15 Exercise Compare kinetic energy of a car traveling at 100 km/hr with one traveling at 50 km/hr 11/02/09 Habbal Astro Lecture 11 15
16 Gravitational Potential Energy E g = m g h On Earth, it depends on an object s mass (m). the strength of gravity (g). the distance an object could potentially fall. 11/02/09 Habbal Astro Lecture 11 16
17 Gravitational Potential Energy E g = m g h In space, an object or gas cloud has more gravitational potential energy when it is spread out than when it contracts. A contracting cloud converts gravitational potential energy to thermal energy. o h h 11/02/09 Habbal Astro Lecture 11 17
18 Mass-Energy Mass itself is a form of potential energy. E = 2 mc A small amount of mass can release a great deal of energy. Concentrated energy can spontaneously turn into particles (for example, in particle accelerators). 11/02/09 Habbal Astro Lecture 11 18
19 Energy comparisons Energy of sunlight at Earth (per square meter per second) Energy from metabolism of 1 candy bar 1 x 10 6 Energy needed to walk for 1 hour 1 x 10 6 Daily food energy need of average adult 1 x x 10 3 joules Energy released by fission of 1 kg of U x Energy released by 1 megaton H-bomb 5 x Energy released by major (magnitude 8) earthquake Energy released by a supernova /02/09 Habbal Astro Lecture 11 19
20 What have we learned? What keeps a planet rotating and orbiting the Sun? Conservation of angular momentum Where do objects get their energy? Conservation of energy: Energy cannot be created or destroyed but only transformed from one type to another. Energy comes in three basic types: kinetic, potential, radiative. 11/02/09 Habbal Astro Lecture 11 20
21 The Force of Gravity [Section 4.4 ] Our goals for learning: What determines the strength of gravity? How does Newton s law of gravity extend Kepler s laws? How do gravity and energy together allow us to understand orbits? How does gravity cause tides? 11/02/09 Habbal Astro Lecture 11 21
22 What determines the strength of gravity? The Universal Law of Gravitation: 1. Every mass attracts every other mass. 2. Attraction is directly proportional to the product of their masses. 3. Attraction is inversely proportional to the square of the distance between their centers. 11/02/09 Habbal Astro Lecture 11 22
23 Exercise Compare the strength of gravity between Earth and Sun to that between Earth and Moon M(Sun) = kg M(Moon) = kg d(earth-sun) = 1.5x10 8 km d(earth-moon) = km G = m 3 /kg s /02/09 Habbal Astro Lecture 11 23
24 g = 9.8 m/s /02/09 Habbal Astro Lecture 11 24
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