3. Galileo Galilei 1564-1642

4. Aristotle said that a heavy body falls faster than a light body. A feather, for example, clearly falls more slowly than a gold coin. But Galileo considered the following paradox. Suppose that one drops two gold coins. They fall at the same rate, according to Aristotle, because they are equally heavy. But now suppose that the coins are connected with a very light thread. This, according to Aristotle, should make them fall faster, because they are now one object that is twice as heavy. But why? How do they know that the thread is there? Since the coins are falling at the same rate when unconnected, neither can pull on the other through the thread to make it fall faster. Galileo carefully analyzed this paradox and concluded that Aristotle must be wrong. In the absence of air resistance (which slows the feather more than the coin) all bodies must fall the same, whether they are heavy or light. Free Fall

6. A legend says that Galileo dropped cannonballs of unequal weights from the Leaning Tower of Pisa to show that both objects reach ground at the same time.

9. This story is probably not true. In fact, Galileo experimented with balls rolling down a ramp. Galileo experimentally proved that objects fall with the same acceleration independently on their masses.

11. Freely Falling Objects  In a vacuum (absence of air resistance) all objects fall at the same rate  Freely falling bodies undergo constant acceleration

14.  Gravity is the force of attraction between 2 particles of matter due to their masses  If gravity is the only force acting, then the object is said to be in free fall (g)  The acceleration of a freely falling object is also called acceleration due to gravity

16. In a Vacuum

18. Acceleration Due to Gravity  Denoted by symbol g  a (acceleration) = g = 9.8 m/s 2 = 32.2 ft/s 2  This means that when an object is dropped the speed of the object increases by 9.8 m/s during each second

30. Free Falling Time in s Velocity in m/s Displacement in m Acceleration In m/s/s 0009.8 1 4.99.8 219.6 9.8 329.444.29.8 439.278.49.8

31. Is this true? If acceleration due to gravity is 32ft/sec per sec how fast is it going after 3 seconds? 32ft per sec for 3 seconds means 96 ft/s at 3 seconds.

32. Free Fall on the Moon   The acceleration due to gravity on the moon is much less than it is on the Earth.   g = 1.6 m/s/s

33. Time in s Velocity in m/s Displacement in m Acceleration In m/s/s 0001.6 1.81.6 23.2 1.6 34.87.21.6 46.412.81.6 The moon

34. Free Fall (continued)  When object is thrown vertically upward, gravity slows object down at same rate it speeds falling objects (9.8 m/s 2 )  Object continues rising until speed drops to zero, then falls back toward Earth (accelerated by gravity)  Can find how high object travels, how long it is in air, velocity as it hits the ground

35. Terminal Velocity  Terminal speed: air resistance of falling object equals object's weight, the net force is zero and no further acceleration occurs  Terminal Velocity: terminal speed with direction  Sky diver without parachute, terminal velocity = 150 km/h to 200 km/h  With a parachute, terminal velocity =15-25 km/h  Terminal velocity depends on weight and aerodynamic features:  Shape of object (symmetrical more aerodynamic)  Orientation object is travelling (sky diver spreads body out, slows fall)  Smoothness of surface (smoother= less resistance)