Acceleration Due To Gravity

FREE-FALL

• You awake inside an airplane. You are somewhat groggy and disoriented, but comfortable with Northwest Airline’s finest pillow keeping your head from banging against the unforgiving window. You can’t help but get slightly annoyed at the child repeatedly kicking, punching, and head butting the back of your seat, but you drift off to sleep again, knowing full well that there are still many hours of flight left.

• You are violently awoken by a strong and sudden urge to use the Airline’s restroom. By instinct, you bolt upright and charge down the aisle. The airplane is poorly lit and most of the passengers are sleeping. The urge to relieve yourself is building, so you quickly increase your velocity.

• (Increasing your velocity is also known as what?)

Accelerating!

• At this point you are racing down the aisle. You quickly turn left, savagely rip the door from its hinges, and take the longest step of your life…

• You wonder why they would make a bathroom without a floor as you keep trying to step on something solid. And why is the bathroom so windy? Did someone leave the fan on or something?

• Wait a second! That wasn’t the bathroom door, it was the emergency exit! As the wind is rushing through your hair, you feel calmed by your understanding of the physics occurring all around you and you start to contemplate your interesting situation…

We know that objects have a speed or velocity when they fall,

but do they also accelerate?

1 2

50%50%

1. Yes

2. No

Objectives

• To find your acceleration at any time during your fall.

• To find your velocity at any time during your fall.

• To find how far you’ve fallen at any given time during your fall

Acceleration Due to Gravity

• So this means that as you fall, you are speeding up or falling faster and faster.

• All objects falling towards earth Accelerate at a rate of 9.8 m/s2 (neglecting air resistance)

Feather and Moon Video Clip

After falling for one second, what is your acceleration?

1 2 3 4

25% 25%25%25%1. 0 m/s2

2. 4.9 m/s2

3. 9.8 m/s2

4. 19.6 m/s2

After falling for two seconds, what is your acceleration?

1 2 3 4

25% 25%25%25%1. 0 m/s2

2. 4.9 m/s2

3. 9.8 m/s2

4. 19.6 m/s2

After falling for three seconds, what is your acceleration?

1 2 3 4

25% 25%25%25%1. 0 m/s2

2. 9.8 m/s2

3. 19.6 m/s2

4. 29.4 m/s2

Objectives

• To find your acceleration at any time during your fall. Done

• To find your velocity at any time during your fall.

• To find how far you’ve fallen at any given time during your fall.

Velocity of a Falling Object

• Since the acceleration is 9.8 m/s2 of an object in free-fall and your velocity is in the same direction as the acceleration, you gain 9.8 m/s of speed every second!

v a

vf = vi + gt

Final velocity

Initial velocity0 m/s

Acceleration due to gravity (9.8 m/s2)

time

Example

t = 2 s

v = 0 m/st = 0 s

t = 1 s

t = 3 s

v = 9.8 m/s

v = 19.6 m/s

v = 29.4 m/s

v= 29.4 m/sv= 29.4 m/s

v= 19.6 m/sv= 19.6 m/s

v= 9.8 m/sv= 9.8 m/s

v= 0 m/sv= 0 m/s

v= 9.8 m/sv= 9.8 m/s

v= 19.6 m/sv= 19.6 m/s

v= 29.4 m/sv= 29.4 m/sv a

a

a

a

a

a

a

v

v

v

v

v

v

Objectives

• To find your acceleration at any time during your fall. Done

• To find your velocity at any time during your fall. Done

• To find how far you’ve fallen at any given time during your fall.

Distance

• Because you are going faster as you fall, the distance you have fallen per second is greater.

• To find the distance fallen, use the following formula:

d = ½ gt2distanceAcceleration due to gravity (9.8 m/s2)

time

Example

t = 2 s

v = 0 m/st = 0 s

t = 1 s

t = 3 s

v = 9.8 m/s

v = 19.6 m/s

v = 29.4 m/s

d = ½ gt2

d = ½ (9.8)(1)2

d = ½ (9.8)(2)2

d = ½ (9.8)(3)2

d = 0 m

d = 4.9 m

d = 19.6 m

d = 44.1 m

Objectives

• To find your acceleration at any time during your fall. Done

• To find your velocity at any time during your fall. Done

• To find how far you’ve fallen at any given time during your fall. Done

Rearrange distance equation