Gravity
 Free
falling bodies undergo a constant
acceleration.
 This
constant downward acceleration is
gravity.
Earth’s gravity = (g) = - 9.81 m/s²
1 TON
Gravity (cont.)
 When
CRASH
an object is
moving at a
downward
(-) v
velocity, it is
moving in the
direction of
gravitational
(-) g
acceleration.
More Gravity
 When
an object is
moving at an
upward velocity, it
(+) v is moving in the
opposite direction
of gravitational
(-) g acceleration.
Question
What will fall faster when
released at the same height and
at the same time…………a text
book or a pencil???
Even More Gravity
 The
rate at which an object falls is
independent of its mass.
Sample Problem #1
A robot probe drops a camera off the
rim of a 239 m high cliff on Mars
where the free-fall acceleration is
-3.70 m/s².
a.
b.
What is the velocity of the camera
when it hits the ground?
How long does it take for the camera
to hit the ground?
a. Find vf !
a = -3.70 m/s² vi = 0.00 m/s
vf² = vi² + 2aΔy
vf² = 2aΔy
vf = √2aΔy
vf = √2(-3.70 m/s²)(-239 m)
Δ y = - 239 m
vf = 42.1 m/s down
b. Find Δt ! a = -3.70 m/s² vi = 0.00 m/s
vf = - 42.1 m/s Δ y = - 239 m
Vf = Vi + a(Δt)
Δt = Vf / a
Δt = - 42.1 m/s / -3.70 m/s²
Δt = 11.4 s
Sample Problem #2
Jason hits a volleyball so that it moves
with an initial velocity of 6.00 m/s
straight upward. If the ball starts from
2.00 m above the floor, how long will it
be in the air before it strikes the floor?
Step 1: Find out how
high the ball reaches.
Vf ² = Vi ² + 2aΔy
Δy = (Vf ²- Vi ²)
2a
Vf = 0.00
m/s
a = -9.81 m/s²
Δy = -(6.00 m/s)²
2(-9.81 m/s²)
Δy = -36.0 m²/s²
-19.6 m/s²
Δy= 1.84 m
y tot= 1.84m + 2.00m = 3.84
Vi = 6.00 m/s
2.00 m
m
Step 2: Find out the
time of the ball
traveling up!
Vf = 0.00 m/s
Vf = Vi + a(Δt)
Δt = (Vf – Vi) / a
g = -9.81 m/s²
Δt = – 6.00 m/s / -9.81 m/s²
Vi = 6.00 m/s
Δt up = 0.612 s
Step 3: Find time traveling
down.
Δy = Vi (Δt) + ½(a)(Δt)²
Vi = 0.00 m/s
g = - 9.81 m/s²
Δt = √(2Δy)/a
Δy = -3.84 m
Δt = √2( -3.84 m) /-9.81 m/s²
0.885 s = Δt down
Step 4: Solve for the total time of
ball before it hits the floor.
Total time = Δt up + Δt down
Total time = 0.612 s + 0.885 s
Total time = 1.50 s