Acceleration due to Gravity We all know that any object dropped near the earth’s surface will fall downwards. The question is how do they fall? Do they fall at a constant speed? Or Do they increase speed as they fall? Do all objects fall at the same speed? (Do heavier objects fall “faster” than lighter objects?
Acceleration due to Gravity Historical Aspect: Aristotle’s View (~300 BC) Heavier objects fall faster All objects fall at a constant rate (speed) This notion was held to be correct for about ~1800 y
Acceleration due to Gravity Galileo Galilei (1564 – 1642) Began to question Aristotle’s views about falling objects. Do heavier objects fall faster? He imaged a combination object made up of a light object (ball) and heavy object (anvil) connected together by a rope. Would the combination object fall faster than the anvil because it is heavier or will the combination object fall slower because it has a lighter object attached to it?
Acceleration due to Gravity This situation ignited a lot of curiosity in Galileo about how objects actually fall. He also broke with traditional science of his day. Scientist of his day thought it was more important to search old text about science from people like Aristotle, Archimedes, Hero etc. Galileo did not trust some these old Master’s ideas. He thought that it would be more accurate to perform his own experiments to experience the answers himself. He is often called the “father of modern science”. This is the start of modern science as we know it Experimentation and proof for your ideas!
Acceleration due to Gravity Unfortunately for Galileo there were no accurate clocks available in his day to measure the speed of free-falling objects directly. He needed to slow down the objects motion and therefore used an inclined plane or ramp for his experiments The inclined plane has bells attached to it so Galileo could hear the balls at different times of their fall.
Acceleration due to Gravity So what did Galileo discover? Different size balls (different masses) rolled down the inclined plane at the same rate! The objects covers more distance during each successive second of its fall. The objects rolled down the inclined with an increase in speed … they accelerate as they move down the inclined plane. The acceleration however is constant!
Acceleration due to Gravity According to legend (it probable never happened) Galileo went to the top of the Leaning Tower of Pisa in Italy and dropped at the same time two equal sized balls. One was made of wood and the other of lead. Both balls hit the ground at the same time!
Acceleration due to Gravity Do “Picket Fence Lab” to determine the acceleration of gravity near the Earth’s surface.
Acceleration due to Gravity The acceleration due to gravity near the Earth’s surface has been determined to be: g = 9.80 m/s 2 A couple of qualifiers are needed here: 1) This is only true if there is no air is present! (Oops … I can’t breath) 2) The value for g actually depends on where you are on the Earth’s surface. The number fluctuates based on how far from the center of the Earth you are (between: 9.79 – 9.81 m/s 2 )
Falling Objects Falling Objects Problems Example 1: a) How high is the cliff if it takes the ball 4.5 s to hit the bottom? d = v o x t + ½ at 2 d = ½ at 2 But: v o = o d = ½ 9.80 x 4.5 2 d = 99 m b ) With what velocity will the ball hit the ground? v 2 = v o + at v 2 = 0 + 9.80 x 4.5v 2 = 44 m/s ? t = 4.5 v 2 = ?
Falling Objects Problems Example 2: a)How long does it take a dropped ball to fall 45 m? 45 m d = v o x t + ½ at 2 = 3.0 s t = 2d √ a Re-arrange the equation t = 2x 45 √ 9.80 d = ½ at 2 But: v o = o v o = o
Falling Objects Problems Example 3: a) A ball is thrown straight upwards at an initial velocity of 34 m/s. What maximum height does the ball reach? d = v 2 2 - v o 2 2a (This comes from: v 2 2 = v o 2 + 2ad) d = 0 2 - 34 2 2 x -9.80 d = -1156 -19.60 =59 m (v 2 = o at max. height) v 2 = o ? v 2 = 34 m/s
Falling Objects Problems b) How much time elapses for the ball to go up and come back down? time = ? v 2 = 34 m/s t = v 2 - v o a X 2 t = 0 - 34 -9.80 X 2 t = 3.469 x 2 t = 6.9 s Example 3: Time up =Time down
Falling Objects Problems 2) time for whole trip= ? 3) v f = ? 1) Maximum height above the cliff? Example #4 v 2 = 34 m/s 75 m Solutions on Overhead!!
Falling Objects Problems Go onto Worksheet on this Topic!