Transcript Determining the acceleration of free-fall

Determining the
acceleration of free-fall
experimentally
Determining the acceleration of
free-fall experimentally
▪ Consider the multiflash image of an apple
and a feather falling in a vacuum:
▪ If we choose a convenient spot on the
apple, and mark its position, we get a
series of marks like so:
Determining the acceleration of
free-fall experimentally
▪ Now we SCALE our data. Given that the
apple is 8 cm in horizontal diameter we
can superimpose this scale on our
photograph.
0 cm
▪ Then we can estimate the position in
cm of each image.
-9 cm
-22 cm
-37 cm
-55 cm
Determining the acceleration of
free-fall experimentally
▪ Suppose we know that the time
between images is 0.056 s.
0 cm
▪ We make a table starting with the
raw data columns of t and y.
▪ We then make calculations columns
in t, y and v (processed data).
-9 cm
t(s)
.000
y(cm)
t
-22 cm
y
vv
0
cmt's. -161
-161
-9
-9
To.056
find t you-9
need to.056
subtract-37
TWO
Therefore
the
first
entry
for y
t is
BLANK.
-13
-232
-22
.056
-13
To
find
you
need
to
subtract
TWO
To.112
findvt
y
you
need
to
subtract
TWO
y's.-232
you
need
to
divide
by
t.t's.
CURRENT
PREVIOUS
CURRENT
MINUS
PREVIOUS
Same
for
y. t.y.-15
.168thingtyMINUS
-15
-268
-37the first
.056
-268
Since
t,
.224v = y /-55
-18
-321
.056
-18
-55
cm -321
the first v entry is also BLANK.
Determining the acceleration of free-fall experimentally
Now we plot v vs. t on a graph
VELOCITY / cm sec-1
v
0
-50
-100
-150
-200
-250
-300
.000
t(s)
y(cm)
t
y
v
.000
0
.056
-9
.056
-9
-161
.112
-22
.056
-13
-232
.168
-37
.056
-15
-268
.224
-55
.056
-18
-321
.056
TIME / sec
.112
.168
.224
t
Determining the acceleration of free-fall experimentally
0
-50
-100
-150
-200
-250
-300
.000
.056
.112
t = 0.224 s
TIME (sec)
.224
.168
t/s
v = -220 cm/s
VELOCITY (cm/sec)
v
Finally, the acceleration is the slope of the v vs. t graph:
𝑎=
∆𝑣 −220 𝑐𝑚/𝑠
𝑐𝑚
=
= −982 2 = −9.82 𝑚/𝑠 2
∆𝑡
0.224𝑠
𝑠
▪ The graph v vs. t is linear. Thus a is constant.
▪
The y-intercept (the initial velocity of the apple) is not zero. But this just
means we don’t have all of the images of the apple
Graphs of free fall motion
u = 0 m/s
x = 5 t2
distance
(m)
0
time
(s)
0
v = 10t
speed
(m/s)
0
1
10
5
2
20
20
3
4
30
40
45
80
Velocity vs. time
Distance vs. time
80
Distance (m)
velocity (m/s)
40
30
20
10
0
1
2
3
4
5
Time (s)
constant slope → constant acceleration
60
40
20
0
0
1
2
3
4
Time (s)
5
changing slope – changing speed → acceleration
Qualitatively describing the effect of fluid
resistance on falling objects or projectiles,
including reaching terminal speed
-Students should know what is meant by terminal speed.
-This is when the drag force exactly balances the weight
"A female Blue Whale weighing 190 metric tonnes
y
(418,877lb) and measuring 27.6m
At first,(90ft
v = 5in)
0. in
length suddenly materialized above the Southern
Ocean on 20 March 1947."
Guinness World Records.
Falkland Islands Philatelic Bureau. 2 March 2002.
▪ Suppose a blue whale suddenly
materializes high above the ground.
▪ The drag force D is proportional to the speed
squared for high speeds.
For low speeds it is proportional to speed.
W
Then, as v increases, so
y
does D.
D
▪ Thus, as the whale picks up speed, the
drag force increases
▪ Once the drag force equals the whale’s
weight, the whale will stop accelerating.
▪
v
W
v reaches a maximum
value, called terminal
speed.
D = W.
D
It has reached terminal speed.
vterminal
W
If air resistance can not be neglected, there is
additional force (drag force) acting on the body in
the direction opposite to velocity.
Comparison of free fall with no air resistance and with air resistance
In vacuum
displacement
displacement
In air
velocity
velocity
time
Acceleration is getting
smaller due to air resistance
time and eventually becomes
zero.
When the force of the air
resistance equals gravity, the
object will stop accelerating
and maintain the same
time speed.
It is different for different
bodies.
acceleration
acceleration
time
terminal velocity is maximum
velocity an object can reach
in air/any fluid.
time
time
Comparison of free fall with no air resistance and with air resistance
In vacuum
displacement
displacement
In air
velocity
velocity
time
Acceleration is getting
smaller due to air resistance
time and eventually becomes
zero.
When the force of the air
resistance equals gravity, the
object will stop accelerating
and maintain the same
time speed.
It is different for different
bodies.
acceleration
acceleration
time
terminal velocity is maximum
velocity an object can reach
in air/any fluid.
time
time
Air drag and terminal speed
If a raindrops start in a cloud at a height h = 1200m above the surface of the
earth they hit us at 340mi/h; serious damage would result if they did.
Luckily: there is an air resistance preventing the raindrops from accelerating
beyond certain speed called terminal speed….
How fast is a raindrop traveling when it hits the ground?
It travels at 7m/s (17 mi/h) after falling approximately only 6 m. This is a
much “kinder and gentler” speed and is far less damaging than the
340mi/h calculated without drag.
The terminal speed for a skydiver is about
60 m/s (pretty terminal if you hit the deck)