Gravity and Free Fall 2012b

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```					                                    Acceleration
A car travelling at an initial speed of 30 m/s [North]
brakes to a stop in 3 s.
The magnitude of its acceleration is:
A. 0 m/s2         B. 0.1 m/s2         C. 10 m/s2
The direction of its acceleration is:
A. North          B. South            C. 0
The direction of its displacement is:
A. North          B. South            C. 0
Acceleration
A car travelling at an initial speed of 30 m/s [North]
brakes to a stop in 3 s.
The magnitude of its acceleration is:
A. 0 m/s2         B. 0.1 m/s2         C. 10 m/s2
The direction of its acceleration is:
A. North          B. South            C. 0
The direction of its displacement is:
A. North          B. South            C. 0
Gravity and Free-Fall:
Student Learning Goals

Students will describe the characteristics of
and use kinematics equations to solve
problems related to the motion of a
projectile in one dimension. (B3.3, B2.8)

They will also conduct an
inquiry into the motion of a
projectile in one dimension.
(B2.6)
Gravity and Free-Fall

SPH3U
g

The acceleration due to the Earth’s gravity is
9.8 m/s2 [down].
32  1
The magnitude of this acceleration is denoted
by the letter g.
Up, then Down
An object feels this acceleration when travelling up
(when it slows them down) and when travelling
down (when it speeds them up).
Mass doesn’t matter

Note that all objects, regardless of mass,
experience the same acceleration.
Galileo

This discovery is attributed to Galileo.
yAfk
Drag

However, some objects are slowed by
atmospheric drag more than others.
An equation for drag

Fd  v ACd
1
2
2

Fd  drag force
  density of the atmosphere
v  relative speed of the object
A  reference area
Cd  drag coefficient
Terminal velocity

At a given speed, the drag will equal the
gravity, and the object will stop
accelerating, i.e. reach “terminal velocity.”
Terminal velocities

Typical terminal velocities:

Human                          53 m/s (190 km/h)
Human with parachute           5 m/s (18 km/h)
Dandelion seed                 0.5 m/s (1.8 km/h)
The fastest man

On August 16th, 1960 U.S. Air Force Captain
Joe Kittinger broke the sound barrier (1240
km/h) during a free-fall from the high
altitude balloon Excelsior III, at an altitude
of approximately 31 km.
Highest fall survived
(without a parachute)

Flight attendant Vesna Vulovič fell 10,000 m
on January 26, 1972 when she was aboard a
plane that was brought down by explosives
over the Czech Republic.
She suffered a broken skull, three broken
vertebrae (one crushed completely), and
was in a coma for 27 days, but she
survived!
g’s

Accelerations are often given in terms of g.
For example,

 1g 
49   m
s2
          5g
 9.8 s2 
m
Blackout

A typical person can handle about 5 g
before loss of consciousness,
“blackout,” occurs.
The record for the most g forces on a
roller coaster belongs to Mindbender
at Galaxyland Amusement Park in
Edmonton, Alberta, at 5.2 g.
Greyout
Through the combination of special g-
suits and efforts to strain muscles —
both of force blood back into the
brain— modern pilots can typically
handle 9 g or more.
They may experience a “greyout”
(temporary loss of colour vision,
tunnel vision, or an inability to
interpret verbal commands) between
6 and 9 g.
Negative g’s

Resistance to "negative" or upward g’s, which
drive blood to the head, is much less
(typically in the -2 to -3 g range).
During “redout,” vision goes red, probably
due to capillaries in the eyes bursting under
the increased blood pressure.
“g-Force”

Acceleration perpendicular to the spine is
more tolerable.
Acceleration pushing the body backwards
(“eyeballs in”) is tolerable up to 17g, and
pushing the body forwards (“eyeballs out”)
up to 12g.
Strongest g-forces survived

Voluntarily: Colonel John Stapp in 1954
sustained 46.2 g in a rocket sled, while
conducting research on the effects of human
deceleration
Strongest g-forces survived

Involuntarily: Formula One racing car driver
David Purley survived an estimated 178 g in
1977 when he decelerated from 173 km/h to
0 in a distance of 66 cm after his throttle got
stuck wide open and he hit a wall
Everyday g-forces

Coughing: 3.5 g
Sneezing: 2.9 g
Free fall

Objects in free-fall feel
0 g, or “weightlessness.”

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