Acceleration due to Gravity

CCHS Physics

Historical Background

Hypothesis:Objects fall at

speeds proportionalto their weights

Natural Motion-Results from the "nature" of objects

Objects strive to get to their proper placeEX- clay vs. smoke vs. feather

Summary-All motion results from the

nature of the moving object or froma sustained push or pull

Violent Motion-Results from pushing or pulling forces

Externally caused- outside force requiredEX- pushing a cart, tugging a rope

Aristotle (Greek philosopher/scientist)divided motion into two main classes:

Galileo attempts to prove Aristotle’s hypothesis

wrong…• He drops objects of various weights

from the Leaning Tower of Pisa and compares the falls.

• He thinks that light and heavy objects will fall at the same rate.

• We’ll find out who is correct with a demonstration…

Let’s See The Real Thing

QuickTime™ and aSorenson Video decompressorare needed to see this picture.

So who’s right?• Both- why?• In the absence of air resistance, all objects

accelerate towards Earth at the same rate.• We call this “free-fall” acceleration- meaning

gravity is the only force acting on an object.• Because we use this value so often we’ll give

it a name- g• What do you think g depends on?

For an object in free-fall, g depends on…

• Mass of the planet object is near• Distance from object to the center of the

planet

• (G = universal gravitational constant) • Near the surface of the Earth, g = -9.8 m/s2

g =GMr2

Free Fall

• Motion of a body when only the force of gravity is acting on the body

• The acceleration of an object in free fall is called the acceleration due to gravity, or free fall accleration

• Free fall acceleration is denoted by the symbol g

Free Fall Movie

Handy Chart

Velocity and Acceleration Movie

Let’s try some examplesEstimate the following:

• A stone is dropped off a cliff. What is its velocity 5 seconds later?

• A ball is tossed straight up at 30 m/s. How long will it take to land? (It returns to same height.)

a =vf −vi

t−10 =

v f − 05

⇒ v f = −50 m/s

a =vf −vi

t−10 =

−30 − 30t

⇒ t = 6 s

Let’s try some more … a little harder though

• Ms. Clark throws a ball straight down off a building with an initial speed of 10 m/s. It lands 3 seconds later. How high was the building?d =

12at2 +vit

d =12

−10( )32 + −10( )3

d =−75 m

h=75 m

One More Example• Jason hits a volleyball so that it moves with an initial

velocity of 6 m/s straight upward. If the volleyball starts from 2 m above the floor, how long will it be in the air before it strikes the floor?– Choose origin to be initial position of ball– The displacement of the ball is -2 m

d =12at2 +vit

−2 =12

−9.8( )t 2 + 6t

t = 1.5s or t = −0.27s