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Test1ReviewNotes - Physics I Review 1 Review Notes Exam 1...

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R1-1 Physics I Review 1 Review Notes Exam 1 Rev. 26-Sep-04 GB
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R1-2 Definitions Scalar: A number – positive, negative, or 0. Magnitude: Absolute value – positive or 0. Vector: Magnitude (or length) and direction in space. Time: t (scalar) Position: x (vector) Displacement: 0 x x x - = Time interval: 0 t t t - =
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R1-3 Definitions (Continued) Average or mean velocity is defined as follows: t x t t x x v 0 0 avg - - Instantaneous velocity or just “velocity”: t d x d t x lim v 0 t
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R1-4 Definitions (Continued) Average acceleration is defined as follows: t v t t v v a 0 0 avg - - Instantaneous acceleration or just “acceleration”: 2 2 0 t t d x d t d v d t v lim a
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R1-5 Class #1 Take-Away Concepts 1D Equations of Motion for Constant Acceleration Basic Equations 1. ( 29 0 0 t t a v v - + = 2. 2 0 2 1 0 0 0 ) t t ( a ) t t ( v x x - + - + = Derived Equations 3. ) t t )( v v ( x x 0 0 2 1 0 - + + = 4. 2 0 2 1 0 0 ) t t ( a ) t t ( v x x - - - + = (compare with 2.) 5. ( 29 0 2 0 2 x x a 2 v v - + =
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R1-6 Problem Solving Strategy for Projectile Motion Make a table, see what you know and what you need to find. X Y a v 0 x 0 or y 0 v f x f or y f t-t 0 SAME SAME The common factor in both the X and Y equations is the time at which something happens (last row).
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R1-7 Hit the Falling Target Diagram d h θ The target will drop at the instant the ball leaves the launcher. The objective is to adjust the angle θ so that the ball hits the falling target.
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R1-8 Hit the Falling Target Table of Kinematic Quantities X ball Y ball Y target a 0 -g -g v 0 v 0 cos( θ ) v 0 sin( θ ) 0 x 0 or y 0 0 0 h v f v 0 cos( θ ) ? ? x f or y f d ? Same as ball. t-t 0 ? SAME SAME We have all data in the “X ball” column except time. Solve for that first.
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R1-9 Hit the Falling Target Solving for Time ) cos( v d ) t t ( ) t t ( ) cos( v x x 0 0 0 0 0 f θ = - - θ + = We don’t care what v f is for the ball or target (Y). X ball Y ball Y target a 0 -g -g v 0 v 0 cos( θ ) v 0 sin( θ ) 0 x 0 or y 0 0 0 h v f v 0 cos( θ ) (don’t care) (don’t care) x f or y f d ? Same as ball. t-t 0 d/[v 0 cos( θ )] SAME SAME Next, use the kinematics equation to find y f .
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R1-10 Hit the Falling Target Solving for Final Y Position Y ball: 2 0 0 0 f ) cos( v d g 2 1 ) cos( v d ) sin( v 0 y θ - θ θ + = Y target: 2 0 f ) cos( v d g 2 1 0 h y θ - + = Setting the two expressions equal, the “g” terms cancel and we are left with h ) cos( d ) sin( = θ θ OR d h ) tan( = θ
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R1-11 Class #2 Take-Away Concepts 1. X and Y motions are independent.
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