Free Fall - Ch 5.4

1. Free Fall - Ch 5.4 Does a falling object fall at constant speed or does it accelerate as it falls? How do you know? Aristotle, an ancient Greek philosopher, had argued that falling objects instantly acquire their final velocity after being released. Galileo, in the early 1600’s, argued that Aristotle was incorrect, and that objects do, indeed, accelerate as they fall. So, who was right?? ________ Galileo !

2. Certain objects seem to behave like Aristotle argued… such as a piece of flat paper, or a parachute. Other objects, like rocks dropped into water (the higher the drop, the bigger the splash!!), and pieces of crumpled paper, seem to behave like Galileo argued.

3. It took the genius of Galileo to realize that the ___________ through which objects were falling was “getting in the way” of our understanding. He realized that if we ignore the effects of air, all “freely falling” objects will _______________ at the _____________!! medium (air) accelerate same rate Legend has it that Galileo dropped a 1 pound and a 10 pound object off of the Leaning Tower of Pisa to show that they reach the ground in the same time. He likely never performed it, but instead performed a “thought experiment” involving 2 identical cannonballs – first dropped separately, and then dropped after being taped together. He argued that it was common sense that the rate at which they fall would NOT depend on their __________. weight

4. Demo: Drop paper below and then on top of a book…. evidence that if air were eliminated, a piece of paper would fall at the same rate as a heavy book! Demo: A feather and a coin fall in a vacuum at the same rate!! In Air Vacuum

5. 1971 - on the Apollo 15 mission, NASA astronauts drop a feather and a hammer on the moon, where there is NO atmosphere!

6. The Free Fall Acceleration, g If air resistance is either eliminated or is negligible, on earth, all falling objects accelerate at… 22 9.8 32 We use the symbol, g, because this acceleration is caused by a force we call _______. Gravity is a mysterious force (an attractive force that exists between any two masses!), but Isaac Newton showed that this acceleration depends on the _____ of earth (or any star, planet, etc.) and the ________ away from its center. gravity mass distance

7. A falling object’s speed will increase by _____ each ______ (___________) In this case, we typically define “down” as the positive direction and choose to use a = g = _______ in our “constant acceleration equations” that we derived previously. • An object that has been thrown up will decrease its speed by _______ each ______ (_____________) In this case, we typically define “up” as the positive direction and choose to use a = ___ = _________ in our equations. 9.8 second acceleration +9.8 9.8 second deceleration -g -9.8

8. Example 1: Aball is thrown up at 25 m/s. How long will it take the ball to reach its highest point? Use a = g = 10 m/s2. NOTE: Since 9.8 is so close to 10, we will sometimes round the acceleration of gravity to 10 m/s2 so we can do calculations in our heads! The Key to this Problem…. At the top of the ball’s path, v = ___, and a = _____!!! 0 -9.8 NOT ZERO!

9. Method 1: COUNTING _______________, beginning with the initial speed of 25 m/s! After 1 second, the ball is moving at ______, after 2 seconds, the ball is moving at ______, after ____ seconds, the ball is stopped at the top. backwards by 10 15 m/s 5 m/s 2.5 Method 2: A Shortcut…. ___________ Method 3: Using Physics Equations… Dividing OR

10. How long would it take for the ball to reach 25 m/s in the downward direction? __________ again! 2.5 sec

11. Example 2: Find the velocity and the distance fallen for a dropped object after 1 second, 2 seconds, and 3 seconds of free fall. Again, use a = g = 10 m/s2. 10 m/s 20 m/s 30 m/s

12. How much error is introduced because we rounded “g” to 10 m/s2? 0.1 m (2%) 0.4 m (2%) 0.9 m (2%)

13. An alternative way to find the distance fallen: For example: Calculate the free fall distance for t = 3 seconds.

14. Graph of Speed vs. Time for Free Fall From Paul Hewitt’s Conceptual Physics

15. Graph of Distance vs. Time for Free Fall Do you see a pattern in the data? The distances increase by +5, +15, +25, +35, etc. From Paul Hewitt’s Conceptual Physics

16. Example 3: Wile E. Coyote is “beep-beeped” off the cliff with an initial velocity of 10 m/sup and hits the bottom of the canyon floor 5 seconds later. How fast is he traveling when he hits bottom? Again, use a = g = 10 m/s2. Thinking… Using Equation…

17. Calculate the height of the cliff. The height of the cliff is equal to Wile E.’s ____________ during this time. displacement Wile E is 75 m below where he started, which means that height of cliff = 75 m Or…

18. Reaction Time Activity - # 2 on HW Dropping a ruler provides a simple and convenient method to measure your reaction time. Actually, you will measure the distance a ruler will fall before you can react and grab it. From the free fall distance, you can calculate the free fall time of the ruler, which is the same as your reaction time!! It’s impossible to catch a dropped dollar bill when held at George’s head, unless you’re anticipating!! The International Association of Athletics Federations (IAAF) says that a human takes at least a tenth of a second to react to the start line gun in a track race; They measure the reaction times of sprinters... any faster than 0.1 implies cheating…anticipating the gun!!!!