Lecture3 - Kinematic equations of motion (1D) x = x0 + v0 t...

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Kinematic equations of motion (1D) x = x 0 + v 0 t + at 2 1 2 v 2 = v 2 0 + 2a (x – x 0 ) v = v + v 0 2 v = v 0 + at x, t v, t v, x Mathematically equivalent a= constant Valid only if
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Free falling objects Aristotele -> heavier objects fall faster Galileo (17 th century) - > challenge Aristotele’s view and conclude that 2 objects in free fall, have same acceleration Which one will fall faster? Show Demo “Falling feather and coin” g = -9.80 m/s 2 • All objects fall being subject to the same constant acceleration, known as acceleration of gravity g
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x = x 0 + v 0 t + at 2 1 2 v x 2 = v 2 0x + 2a x (x – x 0 ) v x = v x + v 0x 2 v x = v 0x + a x t Freely falling objects: This is a motion with constant acceleration a= - g We can apply the kinematic equations… with some small change y = y 0 + v 0 t - g t 2 1 2 v y 2 = v 2 0y - 2g (y – y 0 ) v y = v y + v 0y 2 v y = v 0y - gt This equation does not depend on mass. Galileo’s idea that two free falling objects arrive at the bottom at the same time is correct (BUT in absence of air resistance)
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How to solve problems- equations 1. Choose your reference frame 2. Write down known quantities and what you need to find 3. Put in the correct initial conditions 4. Choose equations from list of kinematics equation
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v fA v fA = 0 How to solve problems- equations Example A cannonball is shot straight up in the air with an initial speed of v 0 . Neglect air resistance. How high does it go? How long does it take to reach the top? What is the velocity when it hits the ground? Part A 2. Known and not known quantities y 0A = 0 1. Choose reference frame y y 0A y fA y fA = ? v 0A = v 0 t 0A = 0 a = -g t fA = ? Part B y y 0B y fB y 0B = y fA v 0B = 0 t 0B = 0 y fB = 0 v fB = ? t fB = ? Solved in class
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While standing in an elevator, you see a screw fall from the ceiling. The ceiling is 3m above the floor. How long does it take for the screw to hit the floor if the elevator is moving upward and gaining speed at a constant rate of a f = 4.0m/s 2 ? y
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This note was uploaded on 04/03/2008 for the course PHYSICS 7A taught by Professor Lanzara during the Spring '08 term at University of California, Berkeley.

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Lecture3 - Kinematic equations of motion (1D) x = x0 + v0 t...

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