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Astronomy 110 Announcements: • Reading quiz #5 today—first 5 min. of class • Reading assignment for tomorrow: pp. 85-90, 92-94 — Conservation Laws, Energy, Orbits • Homework #2 handed out in class yesterday—see me or the website if you need a copy. Goals for Today • How do we describe motion? • How is mass different from weight? • What are Newton’s three laws of motion and what applications do they have? • What is gravity, and how does it affect the things around us? • What causes the tides on Earth? http://www.ifa.hawaii.edu/~mcgrath/a110/ How do we describe motion? The Acceleration of Gravity Precise definitions to describe motion: • speed: rate at which object moves % speed = distance "$#units of m s '& time ! 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) • 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. Momentum and Force The Acceleration of Gravity (g) • Galileo showed that g is the same for all falling objects, regardless of their mass. • Momentum = mass ! velocity • A net force changes momentum, which generally means an acceleration (change in velocity) Apollo 15 demonstration Thought Question: Is there a net force? Y/N 1. 2. 3. 4. 5. 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. Is there a net force? Y/N 1. 2. 3. 4. 5. 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 How is mass different from weight? • mass – the amount of matter in an object • weight – the force that acts upon an object Why are astronauts weightless in space? • There IS gravity in space… • weightlessness is due to a constant state of free-fall: You are weightless in free-fall! Recap. How did Newton change our view of the Universe? •How do we describe motion? • Realized the same physical laws that operate on Earth also operate in the heavens " one universe • Studied the nature of light • Discovered laws of motion and gravity • Developed the first reflecting telescope • Invented calculus •Speed = distance/time •Speed + direction => velocity (v) •Change in velocity => acceleration (a) •Momentum = mass ! velocity •Force causes a change in momentum, which means acceleration. • How is mass different from weight? • Mass = quantity of matter • Weight = force acting on mass • Objects are weightless when in free-fall Sir Isaac Newton (1642-1727) “If I have seen farther than others, it is because I have stood on the shoulders of giants.” 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. An object in motion will continue to move in a straight line forever unless an external force acts on it. Aristotle claimed an object’s natural state was at rest. Instead we see that its natural state is to stay in motion, unless acted upon by some outside force. Newton’s third law of motion: For every force, there is always an equal and opposite reaction force. Example: When you’re standing on the Earth, you exert a force downwards on the Earth, and it exerts an equal force upwards so that you stay in the same place. Newton’s second law of motion: Force = mass ! acceleration When a force acts upon an object, it results in a change in that object’s acceleration. More massive objects have a smaller change in acceleration than less massive objects when acted upon by the same force. 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. 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 How does Newton’s law of gravity extend Kepler’s laws? 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.. Newton’s version of Kepler’s Third Law • 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 p2 = 4" 2 a3 G(M1+M2 ) ! p = orbital period a=average orbital distance (between centers) (M1 + M2) = sum of object masses