Lecture 9 + 10 Fall 2005 Astronomy 110 1
Isaac Newton and the birth of Physics If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (1642 1727) Nature and Nature's laws lay hid in night; God said, Let Newton be! And all was light. Alexander Pope (1688-1744) (Newton s epitaph) Fall 2005 Astronomy 110 2
Sir Isaac Newton (1642-1727) Realized the same physical laws that operate on Earth also operate in the heavens one universe Discovered laws of motion Discovered gravity Co-invented Calculus First reflecting telescope Many experiments with light and color. Fall 2005 Astronomy 110 3
How did Newton describe the motion of a particle? Position is a description of the location of an object Velocity is the rate of change of position. It is made up of two pieces of information: speed: rate of motion speed = distance units of time m s and example: speed of 10 m/s Direction example: 10 m/s, due east Acceleration: any change in velocity units of speed/time (m/s 2 ) Fall 2005 Astronomy 110 4
Newton s first law of motion: An object moves at constant velocity unless a net force acts to change its speed or direction. When your car hits a wall - you go through the windshield. Isaac says: Wear your seatbelt! Fall 2005 Astronomy 110 5
Newton s second law of motion: Force = mass acceleration Defines Mass Defines the effect of forces Includes first law (Force = 0) Hitting the wall causes a large deceleration hence a large force on the car. Isaac says: Drive carefully Fall 2005 Astronomy 110 6
Newton s third law of motion: For every force, there is an equal and opposite reaction force. Putting a large force on the car results in a large reactive force on the wall the wall breaks. Isaac says: Fix my wall! Fall 2005 Astronomy 110 7
Momentum and Force Momentum = mass velocity Has direction and magnitude A force is a change in momentum. It can be: an acceleration (change in velocity) Change in speed Change in direction or a change in mass (rocket) Fall 2005 Astronomy 110 8
Newton s Law of Universal 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.. Fall 2005 Astronomy 110 9
The Acceleration of Gravity All falling objects accelerate at the same rate (not counting friction of air resistance). On Earth, g 10 m/s 2 : speed increases 10 m/s with each second of falling. Fall 2005 Astronomy 110 10
The Acceleration of Gravity (g) Galileo showed that g is the same for all falling objects, regardless of their mass. Fall 2005 Astronomy 110 11
Thought Question: Is there a net force? Y/N 1. A car coming to a stop. 2. A bus speeding up. 3. An elevator moving up at constant speed. 4. A bicycle going around a curve. 5. A moon orbiting Jupiter. Fall 2005 Astronomy 110 12
Is there a net force? Y/N 1. A car coming to a stop. Y 2. A bus speeding up. Y 3. An elevator moving at constant speed. N 4. A bicycle going around a curve. Y 5. A moon orbiting Jupiter. Y Fall 2005 Astronomy 110 13
What is the force between You and the Earth? F YE YE = G MassYouMass ( D ) You Earth G Mass FYE Radius F = g Mass Earth 2 Earth = Earth You Mass You Fall 2005 Astronomy 110 14
How is mass different from weight? mass an intrinsic property of an object its resistance to being accelerated. weight the force caused by gravity acting on an object. Weight is an extrinsic property! It depends on where you are. You are weightless in free-fall! Fall 2005 Astronomy 110 15
Thought Question On the Moon: A. My weight is the same, my mass is less. B. My weight is less, my mass is the same. C. My weight is more, my mass is the same. D. My weight is more, my mass is less. Fall 2005 Astronomy 110 16
On the Moon A. My weight is the same, my mass is less. B. My weight is less, my mass is the same. C. My weight is more, my mass is the same. D. My weight is more, my mass is less. Fall 2005 Astronomy 110 17
Why are astronauts weightless in space? There IS gravity in space weightlessness is due to a constant state of free-fall: Fall 2005 Astronomy 110 18
Thought Question: A compact car and a Mack truck have a head-on collision. Are the following true or false? 1. The force of the car on the truck is equal and opposite to the force of the truck on the car. 2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. 3. The change of velocity of the car is the same as the change of velocity of the truck. Fall 2005 Astronomy 110 19
Thought Question: A compact car and a Mack truck have a head-on collision. Are the following true or false? 1. The force of the car on the truck is equal and opposite to the force of the truck on the car. T 2. The momentum transferred from the truck to the car is equal and opposite to the momentum transferred from the car to the truck. T 3. The change of velocity of the car is the same as the change of velocity of the truck. F Fall 2005 Astronomy 110 20
Three important conservation laws: Conservation of momentum Conservation of angular momentum Conservation of energy These laws are embodied in Newton s laws, but offer a different and sometimes more powerful way to consider motion. Fall 2005 Astronomy 110 21
What keeps a planet rotating and orbiting the Sun? Conservation of Angular Momentum As long as Earth doesn t transfer angular momentum to other objects, its rotation and orbit cannot change. Fall 2005 Astronomy 110 22
Angular momentum conservation also explains why objects rotate faster as they shrink in radius: Fall 2005 Astronomy 110 23
Where do objects get their energy? Energy is either associated with motion (Kinetic energy, heat etc) Or The ability to do work. (chemical potential energy, gravitational potential energy) Energy is conserved, but it can: Transfer from one object to another Change in form Fall 2005 Astronomy 110 24
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Fall 2005 Astronomy 110 25
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 grav. potential energy to thermal energy. Fall 2005 Astronomy 110 26
Newton s law of gravity derives 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 Fall 2005 Astronomy 110 27
Fall 2005 Astronomy 110 28 Newton generalized Kepler s Third Law: Planet orbits balance Gravity with Centripetal acceleration 2 2 2 3 2 2 4 p p p p p p p p V GM R R R V P GM P R π π = = =
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) Fall 2005 Astronomy 110 29
How does gravity cause tides? Fall 2005 Astronomy 110 30
Tides vary with the phase of the Moon: Fall 2005 Astronomy 110 31
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. Fall 2005 Astronomy 110 32
Mass-Energy Mass itself is a form of potential energy A small amount of mass can release a great deal of energy Concentrated energy can spontaneously turn into particles (for example, in particle accelerators) E = mc 2 Fall 2005 Astronomy 110 33