PHY 102 1st Edition Outline of Last Lecture I Bullet Problem a Kinematics b Conservation of Energy II Bullet in block of wood a Conservation of Energy III Newton s Apple a Derivations of formulas b Acceleration toward earth IV Newton Derives Kepler s Third Law V Dark Matter VI Relationship of Weight v Mass Outline of Current Lecture I Gravity a Equations II Orbital Velocity III Escape Velocity IV Examples V Sample Problems Current Lecture These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute I II III IV Gravity a Weight m force due to gravity b F GMm r2 i Force Universal Gravitational Constant Mass of the earth mass of the object pulled by earth distance between the two objects 2 c G does not equal g force due to gravity d g GM r2 because masses cancel out in the equation e acceleration due to gravity is independent of the mass Orbital Velocity a Fg GMm r2 b Fc mv2 r c In orbital motion the Force due to gravity forcec which is mv2 r i So GM r2 v2 r ii When reduced vorbit GM r Escape Velocity a Kinetic energy potential energy i This is equal to mv2 GMm r ii Etotal 0 for v 0 at infinity iii mv2 GMm r b Vescape 2GM r Examples a Force between two objects Fg GMm r2 GM b Orbital Velocity vorbit r 2 GM c Escape velocity vescape r 11 2 2 d G 6 67x10 Nm kg e M 5 97x1024kg f r 6 371 000m Samples a What is the gravitational force between a proton and a n electron in a Hydrogen atom mp 1 673x10 27kg me 9 109x10 31kg ro 5 29x10 11m G 6 67x10 11Nm2 kg2 F Gmemp ro2 Plug Chug from this point b What is the orbital velocity of the International Space Station ISS whose altitude is 330km Take the radius of Earth to be 6378 1km The mass of Earth is 5 97x1024kg c V
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