Linear Kinematics - Free Fall Contents: Graph Definition of and Terminal velocity Handy Truths Examples and demos Whiteboards

Problem Solving tips for free fall 1. Acceleration is always -9.81 m/s/s 2. Even at the top 3. v at the top is zero Iff start and end at same elevation 4. 1/2 time up, 1/2 time down 5. v = -u Make a v vs. time graph for an object thrown straight up from leaving my hand, to landing back in my hand (draw axes, endpoints) TOC

Bottom (start) Velocity v time + V Top 0 m/s Bottom (end) - V Time Slope unbroken, top: a != 0

Example 1 An object is launched straight up with a velocity of +33.0 m/s, and strikes the ground at the same elevation from which it is launched. Use the acceleration of gravity to be -9.81 m/s/s, and neglect air friction When is it at the top? How high does it go at the highest? What total time is it in the air? What is its velocity at an elevation of 45.0 m? What is its velocity and displacement at 5.20 s?

An object is launched straight up with a velocity of +33 m/s An object is launched straight up with a velocity of +33 m/s. Use the acceleration of gravity to be -9.81 m/s/s, and neglect air friction When is it at the top? How high does it go at the highest? launch to top: s u = +33 m/s v = 0 (at the top) a = -9.8 m/s/s t use v = u + at, 0 = 33 + (-9.81)t, t = 3.364 ≈ 3.4 s use v2 = u2 + 2as, (0)2 = (33)2 + 2(-9.81)s, s = 55.504 ≈ 56 m What total time is it in the air? This would be twice the time to the top since up is presumably the same distance as down: total time = 3.364 + 3.364 = 6.728 ≈ 6.7 s What is its velocity at an elevation of 45 m? launch to 45 m elevation: s = 45 m v = ? a = -9.81 m/s/s use v2 = u2 + 2as, v2 = (33)2 + 2(-9.81)(45), |v| = 14.356 ≈ (+14 m/s OR -14 m/s) It is + 14 m/s on the way up, and -14 m/s on the way down, as it passes 45 m twice on the way to 56 m

Example 2 A piece falls off a rocket that is 27.0 m above the ground when the rocket is moving upwards at 21.0 m/s. Neglect air friction. Describe to your neighbor what the piece will do To what height does the piece rise above its release point before coming down? What is the velocity of impact of the piece with the ground? What time does the piece take to reach the ground?

Whiteboards: Free Fall 1 | 2 TOC

s = -43 m, u = 0 m/s, v = ??, a = -9.81 m/s/s, t = ?? s = ut + 1/2at2 A steel marble falls from the roof of a building that is 43 m tall. In what time does it reach the ground, and what is its velocity of impact? ignore air friction. Use 9.81 as g, and make down negative. s = -43 m, u = 0 m/s, v = ??, a = -9.81 m/s/s, t = ?? s = ut + 1/2at2 .:. t = 2.9608 s 3.0 s v = u + at .:. v = -29.0458 m/s -29 m/s W 3.0 s -29 m/s

What is the initial upward velocity the ball has? A baseball is popped up and lands on top of a light tower that is 23.8 m above the elevation of the bat after having been in the air for 4.75 seconds. What is the initial upward velocity the ball has? With what velocity does it strike the tower? What is the greatest height the ball reaches? Use 9.81 as g, and neglect air friction, down is - s = +23.8 m, u = ??, v = ??, a = -9.81 m/s/s, t = 4.75 s s = ut + 1/2at2 .:. u = 28.309 m/s 28.3 m/s v = u + at .:. v = -18.2882 m/s -18.3 m/s s = ??, u = 28.309 m/s, v = 0, a = -9.81 m/s/s, t = ?? v2 = u2 + 2as .:. s = 40.8468 m 40.8 m W 28.3 m/s, -18.3 m/s, 40.8 m

Feather, Ping pong ball, Steel marble Demos: Feather, Ping pong ball, Steel marble vertical wind tunnel terminal velocity definition of Free Fall Zero Gravity gravity detector Drop Fling DC-9 filming Apollo 13 YouTube(NASA Water Balloons in Zero G (High Quality)) YouTube(Symphony of Spheres in Microgravity)

PSU: http://ddt.pdx.edu/node/605

Extra slides I don’t have time for

Try this problem A pop fly remains airborne for 8.42 seconds and is caught at bat level. Ignore air friction. What time did it spend going up? What was its initial velocity? Its final? What maximum height does the ball reach? What was the velocity at an elevation of 60. m? Why are there two answers to the previous? What is the ball’s velocity and displacement at 5.05 s? +41.3 m/s, final is -41.3 m/s, 86.9 m, ±23.0 m/s, going up/down, 83.5 m

A pop fly remains airborne for 8.42 seconds and is caught at bat level. Ignore air friction. What time did it spend going up? half the time: 4.21 s What was its initial velocity? Its final? use v = u + at: going up v = 0; u = 41.3001 initial is +41.3 m/s, final is -41.3 m/s (going down) What maximum height does the ball reach? use v2 = u2 + 2as? v = 0 at the top s = 86.9367… m s = 86.9 m What was the velocity at an elevation of 60. m? v2 = u2 + 2as: |v| = 22.989 m/s, so v = +23.0 m/s on the way up v = -23.0 m/s on the way down Why are there two answers to the previous? going up and going down What is the ball’s velocity and displacement at 5.05 s? v = u + at: v = -8.24 m/s s = ut + 1/2 at2 : s = 83.5 m above bat.

A B C 0 m/s Velocity Time Copy this velocity vs time graph into your notes and answer these questions: What is the object doing? (describe with words) What is happening to the acceleration in regions A, B, and C? Why might a dropped object undergo this motion on earth?

A B C A - Free Fall - only gravity acts (a = -9.8 m/s/s) Velocity Time A - Free Fall - only gravity acts (a = -9.8 m/s/s) B - Transition from free fall to terminal velocity (a goes to zero) C - Terminal velocity (a = 0) (forces, vertical wind tunnels, type of object) (Demo - feather in vacuum, ping pong ball in vacuum, race twixt steel ball and pp ball)

A B C Objects in free fall (region A) experience a zero g situation 0 m/s Velocity Time Objects in free fall (region A) experience a zero g situation Demo - water bottle