Newton s Laws of Motion 2008 Feb 26 Brian Jackson PtyS 206 Section 2 Essay Instructions Essay Research You should have 3 sources Using only 1 source gets a failing grade However don t use too many sources it s only a 3 page report Reference your sources properly The reader needs enough info to find the source themselves Be careful with Web Sources Read all most of your sources before you start writing Homework 3 Please staple multiple pages If you collaborate with others don t use the exact same wording in your answers Homework 3 Question 1 Briefly state the arguments for the Copernican model for the solar system Arguments for a model are different from arguments of a model Arguments for Copernican model Galilei s observations of Venus phases Galilei s observations that moon is not a perfect sphere etc Arguments of Copernican model Planets orbit the sun not the Earth orbits are circular etc Homework 3 Question 2 Draw one diagram illustrating Ptolemy s model for solar system and another diagram illustrating Copernicus model for the solar system Ptolemy s Copernicus Homework 3 Question 3 What drove Kepler to use elliptical orbits to describe planetary motion when earlier astronomers could get by with circles Kepler analyzed Brahe s observations which were more precise than any previous observations Brahe s observations of Mars motion in the sky were inconsistent with a circular orbit Homework 3 Question 4 Consider the imaginary planet X orbiting the Sun in an elliptical orbit with a semi major axes of 3 Astronomical Units i e 3 times the distance of the Earth from the Sun How long is a year on planet X Kepler s Third Law P years 2 a AU 3 P2 3 AU 3 27 P sqrt 27 5 2 years 2 significant figures Kepler s Third Law says that the period of an orbit does not depend on the shape of the orbit Homework 3 Question 4 5 AU 5 AU Which orbit has a longer period Homework 3 Question 4 5 AU 5 AU Which orbit has a longer period They both have the SAME period Homework 3 Question 5 The orbit of planet X is highly elliptical At perihelion planet X is 2 A U form the sun and at aphelion it is 4 A U from the sun How does the velocity of planet X at perihelion compare with its velocity at aphelion Be quantitative if you can Planet closer to sun so moves faster Farther from sun so moves slower Homework 3 Question 5 How to be quantitative If you used Kepler s Third Law you got credit but solution is wrong Kepler s Second Law The line joining a planet to the Sun sweeps over equal areas in equal intervals of time What does that mean Homework 3 Question 5 Homework 3 Question 5 Aa b aha ta Homework 3 Question 5 Ap b php tp Homework 3 Question 5 Equal areas in equal times Aa Ap ta tp b a h a v a ta r a b p h p v p tp r p rp ra va vp So if planet is twice as far its velocity is twice as small Describing Motion Position x The distance from one place to another Units meters miles Velocity v Change in position with time Units meters second miles hour Acceleration a Change in velocity with time Units meters second2 miles hours second Position and Velocity Vectors Velocity v Planetary position vector r Velocity and Acceleration Vectors Velocity v Acceleration a Definition of Velocity and Acceleration Vectors Velocity vector magnitude length is the change of distance with time in meters per second Points in the direction in which position is changing Acceleration vector magnitude length is the change of velocity with time in meters per second per second Points in the direction in which velocity is changing Acceleration vector Change in speed and or direction of motion For circular motion a 2 v r Magnitude of vector a Let s pause for a minute Position tells us where things are Velocity tells us where things are going and how fast they re going there Acceleration tells us how fast and in what direction things will be going shortly How do we use these to describe and predict motion Sir Isaac Newton 1642 1727 First to derive basic laws of motion Invented calculus Life long virgin Newton s Laws of Motion 1 An object remains at rest or in constant velocity unless acted on by a force 2 Force equals mass times acceleration F ma 3 Each action has an equal and opposite reaction 1 An object remains at rest or in constant velocity unless acted on by a force 2 Force equals mass times acceleration F ma Force mass x acceleration What does this mean If you push hard on something that has little mass it will accelerate a lot If you push the same on something with a lot of mass it won t accelerate as much Units of force Newtons kilogram meters per second per second 3 Each action has an equal and opposite reaction If you push on something it pushes back with an equal force but does not necessarily induce the same acceleration For example you are pushing down on your chair with a force equal to your weight but your chair is pushing back on you with the same force As a result you don t move 3 Each action has an equal and opposite reaction Newton s Law of Gravity All bodies with mass exert a gravitational force on each other The force of gravity depends directly on the product of their masses i e bigger masses bigger force The force of gravity gets weaker the farther two bodies are from one another Newton s Law of Gravity Gravitational Force F is given by F G M m r2 M and m are the masses of the two bodies kg r is distance between the centers of the bodies m and G is a constant number called Newton s Gravitational Constant N kg 2 m2 Gravity on Earth F m a G m ME r2 a G ME r2 where G 6 7x10 11 m3kg 1s 2 ME 6 0x1024 kg On Earth s surface r RE 6400 km Thus a G ME RE2 9 8 m s 2 a Newton Explains Galileo Newton s 2nd Law F ma Newton s law of gravity F GMm R2 Set them equal ma GMm R2 Cancel m on both sides a GM R2 of the equation The acceleration does not depend on m Bodies fall at the same rate regardless of mass The Gravity of all things The acceleration that we feel just sitting in the class room From the Earth g G ME RE2 9 8 ms 2 Note If you don t move too far from Earth g is constant From the Moon a G MM RM2 ms 2 From the person sitting next to you a G MP DP2 ms 2 This is a homework problem for next week Constant Acceleration From what we just learned …
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