Falling (it can be free but often a drag)

Galileo's Pendulums Galileo Galilee once observed that pendulums of different masses swung back and forth at the same rate. Given a certain amount of time (i.e. 30 seconds) two pendulums of different masses will swing back and forth the same number of times. During this period of history it was well established that heavy (more massive) objects fall faster than light (Less massive) objects. Galileo's observations contradict this belief.

What force drives a pendulum? The pendulum swings because the gravitational force of the earth on the pendulum pulls it downward. The string’s tension force keeps the pendulum from falling straight down causing it to arc into a semicircular path, but it is the gravitational force that makes the pendulum move. FgFg F Tension

What force makes objects fall? Again it is the gravitational force, just like the pendulum Since both falling objects and pendulums are driven by the gravitational force they should then be affected by gravity in similar manners This means if heavy objects fall faster because the gravitational force is stronger, then a heavy pendulum should swing faster because a stronger gravitational force is driving it.

The great contradiction If heavy objects do fall faster than light objects, then heavy pendulums should swing faster than light ones. Light pendulums, however, swing just as fast as heavy ones. So, light objects should fall just as fast as a light one. All objects should fall at the same rate regardless of mass. But pendulums are not falling objects.

Ramping things up Galileo knew he had to examine other motion that is similar to the motion of falling objects. He then set up long ramps and rolled lead balls of different masses down the ramps, measured how far they traveled in a given time. The driving force on a ramp is gravity. So if a heavy object falls faster than a light one, a heavy object would roll down a greater distance on a ramp than a lighter one. This is when things got weird.

What society says should have happened. Objects once released fall at a constant speed Heavy objects reach a higher falling speed

What Galileo observed All objects rolled the same distance in a given time regardless of mass. As time passed the objects traveled greater distances per unit of time (They speed up)

The ramps both supported and expanded what the pendulums had indicated Supported: Light objects fall just as fast as heavy objects Expanded: The speed at which objects fall is not constant. Objects speed up as they fall. But neither case is a falling object

Pisa anyone? Galileo now dropped lead balls of different masses off the top of the tower of Pisa (It was not leaning yet.) and measured the time it took for the objects to hit the ground. All the objects hit the ground at the same time.

A gravity riddle. Let us assume that heavy objects fall faster than light ones. We drop two objects: Object A is a 10 pound ball Object B is a 10 pound ball that is tethered to a 2 pound ball Which of these two objects would fall fastest?

What about feathers Galileo suggested that just like the air pushes tree branches and other objects as wind, the air pushes on objects as they move through the air creating a drag. Feathers “want” to fall just as fast as rocks, but they are affected by the air more then the rocks are. If you could drop a feather and rock in a place where their was no air then they would both fall at the same rate. During the time of Galileo, the idea of a “vacuum” was at best sci-fi and at worst heresy.

Galileo’s rules of falling bodies (in the absence of air) If an object falls with only gravity affecting the object, it is said to be in Free Fall It is falling freely All objects in free fall travel at the same rate regardless of their mass As an object in free fall travels, it’s speed increases (it falls a greater distance per unit of time) The distance traveled per unit of time follow the rule of odd numbers

Visualizing a fall Distance = 1 unit Distance = 3 units Distance = 5 units Distance = 7 units t = 0 units t = 1 unit t = 2 units t = 3 units t = 4 units Displacementtime 0 units 1 unit 2 units 3 units 4 units 1 unit 4 units 9 units 16 units

Graphing a falling object Distance and time Speed and time Velocity and time Displacement and time

Problem solving Free Fall Free fall is solved just like any other accelerated motion problem. That is because free fall is simply accelerated motion The Big 3 equations still work The only new thing is we know automatically what the acceleration is if the object is on the planet Earth a g = 9.8 m/s/s downward (also known as g) a g = -9.8 m/s 2 (If we set the direction up to be positive)