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exam02_f10

# exam02_f10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 Fall Term 2010 Exam 2: Equation Summary One-Dimensional Kinematics: ( ) ( ) ,0 0 0 0 ( ) , ( ) t t t t x x x x t t v t v a t dt x t x v t dt ! ! = = ! ! = = ! ! ! ! " = " = # # Newton’s Second Law sys ext d dt = p F ! ! Center of Mass: cm total total 1 body 1 1 i N i i i m dm m m = = = ! " # R r r ! ! ! ; Velocity of Center of Mass: cm total total 1 body 1 1 i N i i i m dm m m = = = ! " # V v v ! ! ! Momentum: m = ! ! p v , sys 1 i N i i i m = = = ! p v ! ! Impulse: 0 ( ) f t t t t dt = = ! = " # I F p ! ! ! Translational Kinetic Energy: 2 1 2 K mv = ; 2 2 0 1 1 2 2 f K mv mv ! = " Work- Kinetic Energy: f 0 r r W d = ! " ! ! F r total W K = ! Power: P = ! F v ! ! Potential Energy: conservative B c A U W d ! = " = " # \$ F r ! ! Potential Energy Functions with Zero Points: Constant Gravity: ( ) U y mgy = with 0 ( 0) 0 U y = = . Inverse Square Gravity: U gravity (r) = ! Gm 1 m 2 r with U gravity (r 0 = ! ) = 0 . Hooke’s Law: U spring ( x ) = 1 2 kx 2 with U spring ( x = 0) = 0 . Work- Mechanical Energy : W nc = ! K + ! U total = ! E mech = K f + U f total ( ) " K 0 + U 0 total ( ) Simple Harmonic Oscillator: 0 0 ( ) cos( ) sin( ) x t A t B t ! ! = + Period: 0 2 T ! " = Frequency: 0 1 2 f T ! " = =

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2010 Exam 2 Name Section Table and Group With the exception of Problem 1, answers without work shown will not be given any credit. Comments on how you are approaching the problem and what you are doing at any given point will be helpful to the grader in awarding partial credit, as will carefully drawn free body diagrams when appropriate. Problem 1 (20 points) Problem 2 (25 points) Problem 3 (30 points) Problem 4 (25 points) Total (100 points) 1
Problem 1a (5 points) Consider a rocket with speed v and maximum relative exhaust speed u . What is always true about the motion of the rocket in free space (that is, no gravity)? 1. It can not go faster than u (at which point the exhaust would be moving forward in the rest frame).

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exam02_f10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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