Galileo Galilei

1564-1642

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

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.

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.

Freely Falling ObjectsFreely Falling Objects

In a vacuum (absence In a vacuum (absence of air resistance) all of air resistance) all objects fall at the same objects fall at the same raterate

Freely falling bodies Freely falling bodies undergo constant undergo constant accelerationacceleration

Gravity is the force of attraction between 2 Gravity is the force of attraction between 2 particles of matter due to their massesparticles of matter due to their masses

If gravity is the only force acting, then the If gravity is the only force acting, then the object is said to be in free fall (g)object is said to be in free fall (g)

The acceleration of a freely falling object is The acceleration of a freely falling object is also called acceleration due to gravity also called acceleration due to gravity

In a Vacuum

Acceleration Due to GravityAcceleration Due to Gravity Denoted by symbol Denoted by symbol gg

aa (acceleration) = (acceleration) = gg = 9.8 m/s = 9.8 m/s22

= 32.2 ft/s= 32.2 ft/s22

This means that when an object is This means that when an object is dropped the speed of the object dropped the speed of the object increases by 9.8 m/s during each secondincreases by 9.8 m/s during each second

Free FallingTime in

sVelocity

in m/s

Displacement in m

Acceleration

In m/s/s

0 0 0 9.8

1 9.8 4.9 9.8

2 19.6 19.6 9.8

3 29.4 44.2 9.8

4 39.2 78.4 9.8

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.

? 96 1 360065.5 /

sec 5280 1

mi ft mi smi hr

hr ft hr

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

Time in s

Velocity

in m/s

Displacement in m

Acceleration

In m/s/s

0 0 0 1.6

1 1.6 .8 1.6

2 3.2 3.2 1.6

3 4.8 7.2 1.6

4 6.4 12.8 1.6

The moon

Free Fall (continued)Free Fall (continued) When object is thrown vertically upward, When object is thrown vertically upward,

gravity slows object down at same rate it gravity slows object down at same rate it speeds falling objects (9.8 m/sspeeds falling objects (9.8 m/s22))

Object continues rising until speed drops to Object continues rising until speed drops to zero, then falls back toward Earth zero, then falls back toward Earth (accelerated by gravity) (accelerated by gravity)

Can find how high object travels, how long it Can find how high object travels, how long it is in air, velocity as it hits the groundis in air, velocity as it hits the ground

Terminal VelocityTerminal Velocity Terminal speedTerminal speed: air resistance of falling object equals : air resistance of falling object equals

object's weight, the net force is zero and no further object's weight, the net force is zero and no further acceleration occursacceleration occurs

Terminal Velocity:Terminal Velocity: terminal speed with direction terminal speed with direction Sky diver without parachute, terminal velocity = 150 km/h to Sky diver without parachute, terminal velocity = 150 km/h to

200 km/h200 km/h With a parachute, terminal velocity =15-25 km/hWith a parachute, terminal velocity =15-25 km/h

Terminal velocity depends on weight and aerodynamic Terminal velocity depends on weight and aerodynamic features:features: Shape of object (symmetrical more aerodynamic)Shape of object (symmetrical more aerodynamic) Orientation object is travelling (sky diver spreads body out, Orientation object is travelling (sky diver spreads body out,

slows fall)slows fall) Smoothness of surface (smoother= less resistance)Smoothness of surface (smoother= less resistance)