Free Fall PDF

FREE FALL Aristotle’s Theory of Motion Galileo’s Theory of Motion  Which is safer to catch, a stone dropped from the tip of a two-meter pole or from the th 5 floor of a building?  FALLING OBJECTS What goes up must come down. It is a common observation that when you toss a coin up, it will come...

FREE FALL Aristotle’s Theory of Motion Galileo’s Theory of Motion  Which is safer to catch, a stone dropped from the tip of a two-meter pole or from the th 5 floor of a building?  FALLING OBJECTS What goes up must come down. It is a common observation that when you toss a coin up, it will come down after some time.  When we say, “something is falling down,” we mean, it is falling toward the ground.  We know that, if an object is held above the ground and released, it would fall toward the ground due to the gravitational attraction between the earth and the object.  https://uplo ad.wikimed ia.org/wikip edia/com mons/thum b/a/ae/Aris totle_Altem https://stati ps_Inv8575.j c01.nyt.co pg/1200px- m/images/ Aristotle_Alt 2016/05/27/ emps_Inv85 world/27ARI 75.jpg STOTLE/27A RISTOTLE- superJumb o.jpg  Aristotle’s Theory of Motion Aristotle was born in 384 B.C. in Macedonia, Greece. He completed his education in Athens where he spent twenty years as a student. He was a colleague of Plato and became the tutor of Alexander the Great. He is known as “The Philosopher.”  The results of the study of motion by Aristotle are summarized below: 1. The fall of a heavy object toward the center of the earth is a natural motion because the object is just returning to its natural place. 2. Heavy objects fall faster than lighter ones. He explained that the increase in the rate of motion is proportional to the weight of the object. 3. Objects fall faster in air than in water. He assumed that the decrease in the rate of motion is in proportion to the resisting force of the medium ( air or water). 4. Objects sometimes move away from their natural place. He called this type of motion “violent motion” which he explained was caused by an outside force. In spite of certain limitations, Aristotle’s theory of motion survived for 2000 years because of the ff. reasons: 1. The theory was consistent with common sense and observation. 2. No other theories about motion were known during that time. 3. The quantitative method of observation to prove the validity of the theory was not yet developed. https://upload.wikime dia.org/wikipedia/co mmons/thumb/d/d4/J ustus_Sustermans_- _Portrait_of_Galileo_G alilei%2C_1636.jpg/120 0px- Justus_Sustermans_- _Portrait_of_Galileo_G alilei%2C_1636.jpg Galileo’s Theory of Motion 1. The two objects (light and heavy), dropped simultaneously from the tower of Pisa, fell and struck the earth at the same time. 2. When a ball was rolled down an incline at a fixed angle θ, the ratio of the distance covered to the square of the corresponding time was always the same. (d/t2 = constant) Galileo’s Theory of Motion 1. The two objects (light and heavy), dropped simultaneously from the tower of Pisa, fell and struck the earth at the same time. (See video) 2. When a ball was rolled down an incline at a fixed angle θ, the ratio of the distance covered to the square of the corresponding time was always the same. (d/t2 = constant)  In the first case, the notebook fell faster than the sheet of paper. The second case shows that in the absence of (or with negligible) air resistance, the two objects would fall at the same rate regardless of their weights. Galileo’s Theory of Motion 3. When the angle of inclination is changed, the constant also changes. For example, if θ = 30 , then d/t = constant 0 2 A; if θ = 60 , then d/t = constant B. 0 2 The constant however remains the same for the same angle. Galilieo extended his third experimental result to large angles like a 900. At this angle of inclination, the motion of the ball is the same as freely falling object. Galileo’s Theory of Motion 4. The constant d/t2 is also the constant for a falling object. Galileo considered that the ratio 2 d/t is a constant for all freely falling objects and that this constant refers to the acceleration due to gravity. (See video)- Free fall- Base Jumping  FREE FALL When an object is dropped, the object starts from rest and gains speed as it falls. This gain in speed indicates that the object accelerates as it falls because of gravity. https://www.u niversetoday. com/wp- content/uplo ads/2009/12/ Christiaan_Hu ygens- e14465006257 69.jpg  In general, the magnitude of the acceleration due to gravity decreases as you move farther from the center of the earth: 9.7804 m/s at the equator and 9.8321 2 m/s at the North and South poles. 2 Assuming no air resistance, all problems involving motion of falling objects can be solved by using the equations for accelerated motion. 2 𝑔𝑡 d = 𝑣𝑖𝑡 + *The displacement of falling objects in a given period of time. 2 vf = 2 vi+ 2gd 2 *The final velocity of falling objects can be calculated by that equations. vf = vi + gt Sample Problem The time a male bungee jumper is freely falling is 1.5 s. a. What is the velocity of the https://blog.airpaz.com/en/the-unique-and-excitement-of-reverse- jumper at the end of bungee-jumping-in-pattaya/ 1.5 seconds? b. How far does he fall? a. What is the velocity of the jumper at the end of 1.5 seconds? b. How far does he fall? Although we speak of falling objects, objects in upward motion experience the same free fall https://images.s acceleration. lideplayer.com /13/4171877/sli des/slide_2.jpg  Activity: Solve the following problems. A boy threw a ball upward with an initial velocity of 10.5 m/s and was able to catch it before it reached the ground on its return. a. What was its velocity after 1.0 second? b. What was its displacement in the first second? c. How long did it take the ball to reach its maximum height? d. How far was the maximum height from the starting point?