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FREELY FALLING OBJECTS• - we will consider the case where

objects move in a gravity field –

•namely free-fall motion. • We will neglect [for now!] air

resistance on an object.

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Galileo's Observation• Galileo did more than just observe that spheres of

different mass struck the ground at the same time when dropped from rest, at the same time, from a balcony of the Leaning Tower of Pisa.

• This observation, alone, allowed him to conclude that the spheres fell with the same acceleration, independent ofthe mass they had.

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Free FallOn Earth, when an object falls under the

influence of gravity, it speeds up, or accelerates.

Thus, an object doesn’t fall at a constant speed. Its speed increases at a constant rate though.

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FREELY FALLING OBJECTS• All objects feel a force acting on them

directed toward the center of the earth.• This force causes the object to

accelerate at a constant or uniform manner. The symbol [g] will be used for this acceleration and the magnitude of this acceleration is

»32 ft/s2

»9.8 m/s2

»10 m/s2

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DivingYou jump off a very high diving board into

a pool. How do you speed up?

t = 0 sec v = 0m/s

t = 1 sec v = 10 m/s

t = 2 sec v = 20 m/s

t = 3 sec v = 30 m/s

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Direction?? & How Far???Upward is usually considered the positive direction.

Downward is usually considered the negative direction.

Thus, the acceleration from gravity is sometimes given a negative sign.

g = -10 m/s2 or –32 ft/s2

How fast you speed up doesn’t necessarily indicate how much farther you will go.

The distance you cover is proportional to the square of the time.

d = ½ gt2

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The ball begins with a positive upward velocity as you let it go.

Due to the (-) acceleration from gravity, the velocity is gradually

reduced to zero at the top – it slows down.

The ball continues down from the apex, with an increasing negative

velocity.

Free Fall Animation

Free Fall 2

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Ex 1: If a stone falls off a cliff for 1 sec, how fast is it going? For 2 sec?

GIVEN: vi = 0 m/s; g= 10 m/s2; t = 1 s vy= (10m/s2)(1s)

vy = 10m/s

vy= 0 + (10m/s2)(2s)vy = 20 m/s

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Ex 2: If a stone falls off a cliff for 1 sec, how far does it fall? For 2 sec?

GIVEN: vi = 0 m/s; g= 10 m/s2; t = 1 s dy = .5(10m/s2)(1s)2

dy = -5m

dy = .5(10m/s2)(2s)2

dy = 20m

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SOME EXAMPLES

• 1. Bart drops a pumpkin from the top of his school. The time it takes for the pumpkin to hit the ground is 3 seconds. At what speed does it hit the ground?

GIVEN: vi = 0 m/s; g= 10 m/s2; t = 3 s

UNKNOWN: vy = ?

vy = (10m/s2 )(3s) = 30 m/s

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• 2. Bart drops a pumpkin from the top of his school. The time it takes for the pumpkin to hit the ground is 3 seconds. How tall is the school at that point?

GIVEN: vi = 0 m/s; g= 10 m/s2; t = 3 s UNKNOWN: d = ?

dy = .5 (10m/s2)(3s)2

dy = 45m

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• 3. Bart is at home and launches a spitwad straight up into the air with an initial velocity of + 40 m/s. What is the “final” velocity of the spitwad on the way up?

GIVEN: vi = +40 m/s; a= -10 m/s2;vtop = 0 UNKNOWN: d = ?

EQUATION : vf2= vi

2 + 2ad

SOLVE : d = vf2 - vi

2 / 2a

SUBS: d = (02)-((+40 m/s)2 )/ 2(-9.8 m/s2)

d = 81.6 m

Velocity @ the top = O!

Acc @ the top Still –10 m/s2!

•What is the distance the spitwad travels on the way up?

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• What is the “final” velocity of the spitwad on the way down?

GIVEN: vi = +40 m/s; a= -9.8 m/s2;vtop = 0 UNKNOWN: t= ?

EQUATION : vf = vi + at

SOLVE : vf = vi + at

SUBS: 0 = (+40m/s) + (-9.8m/s2 )(t) = 4.08 s

Velocity @ the bottom = -40 m/s!Acc the entire trip Still –9.8 m/s2!

•How long did it take the spitwad to travel to the top?

•How long will it take the spitwad to travel from the top back to Bart?

4.08 s Total Time in the Air = 8.16 s

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• 4. Homer is working at home, smashes his thumb. In an angry rage, he throws the hammer straight up into the air with an initial velocity of + 26 m/s.

• What is the “final” velocity of the hammer on the way up?

•What is the distance the hammer travels on the way up?•How long did it take the hammer to travel the top?•How long will it take the hammer to travel from the top back to Homer?

•How long total does Homer have to get out of the way of the hammer?

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Free FallYou might notice that some objects don’t seem to fall as fast as others in real life. Ex: rock, feather

The feather is more susceptible to resistance from air molecules, so it is slowed more.

In the absence of air, a rock and a feather would fall at exactly the same rate. Where

could you accomplish this?