sign in sign up
<<
Home , Conservation of energy

Astro 110-01 Lecture 11 Newton’s laws

Twin Sun- grazing comets

11/02/09 Habbal Astro110-01 Lecture 11 1 http://umbra.nascom.nasa.gov/comets/movies/SOHO_LASCO_C2.mpg Understanding Newton’s 3rd law Weight = 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(elev) = ma F = mg

R = 0 R = ma R = -ma R = -mg F = mg F = mg + ma F = mg - ma F = mg – mg = 0 11/02/09 Habbal Astro110-01 Lecture 11 2 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 ?

11/02/09 Habbal Astro110-01 Lecture 11 3 1. Conservation of : 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 .

11/02/09 Habbal Astro110-01 Lecture 11 4 1. Conservation of Momentum: Linear momentum (cont’d)

• Newton’s 2nd law: – Object 1 exerts a force that will change the momentum of object 2 • Newton’s 3rd 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 Astro110-01 Lecture 11 5 Conservation of Angular Momentum m x v x r = constant or What keeps a planet rotating and orbiting the Sun?

r greater so r smaller so v is smaller v is greater

v = v r = average distance from the Sun 11/02/09 Habbal Astro110-01 Lecture 11 6 Angular momentum conservation also explains why objects rotate faster as they shrink in radius

Extending arms means Bringing arms in reduces larger radius, so smaller the radius, so increases velocity of rotation rotational velocity 11/02/09 Habbal Astro110-01 Lecture 11 7 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 , spinning disks orbiting young stars: They will start to spin faster as gravity makes them shrink in size

11/02/09 Habbal Astro110-01 Lecture 11 8 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 Astro110-01 Lecture 11 9 Basic Types of Energy

• Kinetic (motion): – Moving objects – • Radiative energy: – carried by • Potential or Stored energy: – Gravitational – energy –

11/02/09 Habbal Astro110-01 Lecture 11 10 Thermal Energy, a form of 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 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 Astro110-01 Lecture 11 11 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 Air in oven at density 400 F is hotter than the boiling water (212 F) in the pot

11/02/09 Habbal Astro110-01 Lecture 11 12 Common Temperature Scales

 Absolute zero Kelvin is when all motion stops

11/02/09 Habbal Astro110-01 Lecture 11 13 Energy due to movement of object • Example of kinetic energy due to motion

2 Ek = ½ m v

11/02/09 Habbal Astro110-01 Lecture 11 14 Exercise

Compare kinetic energy of a car traveling at 100 km/hr with one traveling at 50 km/hr

11/02/09 Habbal Astro110-01 Lecture 11 15 Gravitational Potential Energy

Eg = 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 Astro110-01 Lecture 11 16 Gravitational Potential Energy

Eg = 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.

h h’ o

11/02/09 Habbal Astro110-01 Lecture 11 17 Mass-Energy • Mass itself is a form of potential energy. EE == mcmc22

• 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 Astro110-01 Lecture 11 18 Energy comparisons

Energy of sunlight at Earth (per square meter per second) 1.3 x 103 Energy from metabolism of 1 candy bar 1 x 106 Energy needed to walk for 1 hour 1 x 106 Daily food energy need of average adult 1 x 107 Energy released by fission of 1 kg of U235 5.6 x 1013 Energy released by 1 megaton H-bomb 5 x 1015 Energy released by major (magnitude 8) earthquake 2.5 1016 Energy released by a supernova 1044 - 1046

11/02/09 Habbal Astro110-01 Lecture 11 19 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 Astro110-01 Lecture 11 20 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 Astro110-01 Lecture 11 21 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 . 3. Attraction is inversely proportional to the square of the distance between their centers.

11/02/09 Habbal Astro110-01 Lecture 11 22 Exercise

• Compare the strength of gravity between Earth and Sun to that between Earth and Moon M(Sun) = 1.99 1030 kg M(Moon) = 7.35 1022 kg d(Earth-Sun) = 1.5x108 km d(Earth-Moon) = 3.84 105 km G = 6.67 10-11 m3/kg s2 179

11/02/09 Habbal Astro110-01 Lecture 11 23 g = 9.8 m/s2

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

11/02/09 Habbal Astro110-01 Lecture 11 24