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Experiencing “g’s” Falling from a table (a = g down), feel 0 g’s Sitting on a table (a = 0) feel 1g Space shuttle launch: 20 m/s 2 up: (a = 2g), feel 3 g’s Extreme amusement park rides 20 to 50 m/s 2 (feel 3 to 6) g’s Fighter pilots: 40 to 80 m/s 2 5 to 9 g’s Your body feels what we call one “g” from not accelerating, just sitting or standing in earth’s gravitational force. The feeling of g’s comes from tension in your organs, and the need of the heart to push harder to get blood to your brain.

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Acceleration Position: where the object is. Displacement: change in position. Velocity: rate of change in position with time: instantaneous velocity is slope of x vs t graph. Acceleration: rate of change in velocity with time

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Some typical accelerations a due to gravity near earth’s surface: g = 9.8 m/s 2 (one “g”)

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among major cities: Lowest in Mexico City (g = 9.779 m/s²) and highest in Oslo and Helsinki (g = 9.819 m/s²). Provo g = 9.799 m/s 2

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Some typical accelerations Space shuttle launch: 20 m/s 2 Extreme amusement park rides 20 to 50 m/s 2 in turns Fighter pilots: 40 to 80 m/s 2 in turns

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Air Force’s Dr. John Stapp In 1954 he rode the "Sonic Wind" at 620 mph (280 m/s), to a dead stop in 1.4 seconds. Max a: 45 g’s.

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a is in the same direction as the force that causes v to change. Review What do we mean by +/- position? being on the + or - side of the origin What do we mean by +/- velocity? moving in the + or – direction. Change in position is +/- What do we mean by +/- acceleration? the change in velocity is in the + or – direction. New If a is in same direction as v, speeds up If a is in opposite direction as v, slows down

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Examples of acceleration direction or sign If a is in same direction as v, speeds up If a is in opposite direction as v, slows down a is in the same direction as the force that causes v to change. A car moves left at constant speed. a is ____ A car moving left is slowing down. a is ____ A car moving left speeds up. a is ____

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Paddle-bunji-ball P1. What is the direction of a of the ball while traveling to your right and slowing down because the elastic stretches? A.right B.left C.zero P2. What is the direction of a when the ball is coming back (to your left, and speeding up)? P3. What is the direction of a at the instant the ball is stopped by the elastic and about to start coming back?

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Paddle-bunji-ball Sketch a(t) for the ball being hit, going to right, and coming back.

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Ball thrown upward into air while throwing: while it’s traveling up: at the very top: while falling down: What is the direction of the acceleration…

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Ball thrown upward into air Sketch a(t) for the ball being thrown, going up, and coming back down.

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“Free-falling” motion acceleration is ______ with direction_________ …whenever object has only the force of gravity on it, whether going up or down (have to neglect air friction…OK when v is small )

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Whenever a is constant v(t) graph is a _______________ x(t) graph is a ________________

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“Kinematic equations” for constant a case Given on formula sheet for exams

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A boy runs 50 m, starting at rest, with a constant acceleration of 0.25 m/s 2. Find: a) the time it took b) his average velocity c) his final velocity ◦ Draw a diagram! ◦ Label with symbols, numbers for “initial” and “final” cases ◦ Look for connection with equations.

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Free-fall and kinematic equations Acceleration due to gravity choose positive direction, which determines whether g is + or – acceleration. A monkey drops from a tree and takes 2 sec to hit the ground. How far did the monkey drop? What was his average velocity?

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Given only the information in the diagram, which single kinematic equation can be used to answer the following in one calculation: P5) How long does it take to reach the top of its path? P6) What is the velocity when it was caught? P7) What was the average velocity for the motion? P8) How long does it take to hit the ground if you miss?

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milk drop demo

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Rocket Launch … a changes during trip Accelerates upward with a 1 by ejecting burning fuel for a time t 1 Engines stop and rocket continues up, then falls to earth “without air friction”. How long is the total time in the air? How high did it go?

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Lecture 3, acceleration Basic concepts: ◦ a as slope of v(t) ◦ directions and signs of a, including when objects stop and reverse Basic problems, skills: ◦ single step using a kinematic equation ◦ drawing good diagrams, using symbols Advanced problems, skills: ◦ more than one step using kinematic equations ◦ using quadratic equation to find t, or using two kin. eqns. ◦ using two different a’s in one problem

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L-4 constant acceleration and free fall (M-3)

L-4 constant acceleration and free fall (M-3)

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