Transcript Lecture2_FreeFall

Falling objects accelerate down at
agravity  g  32 ft/sec2
9.8 m/sec2
more precisely:
at sea level
9.80621 m/sec2
32.1725 ft/sec2
16.0 km (10 miles) above earth’s surface
agravity drops to about 9.75 m/sec2
even skydivers experience a 9.8 m/sec2
32.5 km (20 miles) above earth’s surface
agravity drops to about 9.70 m/sec2
even commercial jet carriers experience
agravity only 1% under the value at sea level!
North Pole
San Francisco
Denver
agravity = 9.832
agravity = 9.800
agravity = 9.796
The gravitational force on an object
decreases by about a millionth for every
3 meter (~10 feet) gain in elevation.
An individual with a 50 kilogram mass
weighs 490 Newtons (110 pounds) in
New York City; but ~0.25 newton
(1 ounce) less in mile-high Denver.
If you drop an object (assuming air
resistance is negligible) it accelerates
down at g=9.8 m/sec2. If instead you
throw it upward, its acceleration the
moment after you release it is
A.
B.
C.
<g
=g
>g
If you drop an object (assuming air
resistance is negligible) it accelerates
down at g=9.8 m/sec2. If instead you
throw it downward, its acceleration
after release is
A.
B.
C.
<g
=g
>g
A ball is dropped from rest, and a
bullet shot out of a gun, straight
down. Neglecting air resistance,
which has the greater acceleration
just before hitting the ground?
A) the ball
B) the bullet
C) both have the same acceleration
The acceleration of gravity does not depend
on the mass or the speed of the object in free fall!
Inclined Plane
A ball rolling down an inclined plane has constant acceleration
12
22
32
42
52
Is the acceleration of the ball
down the ramp 9.8 m/s2?
A) yes
B) no
No! This ball is not in free fall.
Gravity alone does not act on it.
The inclined plane provides a force
of support which affects the motion!
A ball is thrown straight up and
falls back to the ground. Which of
the following is true about its
velocity v and its acceleration a at
the highest point in its path?
A)
v = 0 and a = 0
B)
v  0, but a = 0
C)
v = 0, but a  0
D)
v  0 and a  0
E) cannot be determined
At the highest point in its path, the ball momentarily
comes to a stop, and so its velocity is zero.
However, since the ball is in free fall,
its acceleration is g = 9.8 m/s2 (at every moment).
The maximum velocity, v, an object
reaches falling freely from rest, is
directly proportional to the time, t,
of its fall: v  t .
A) TRUE
B) FALSE
How fast is an object moving at the end
of a one second fall?
m
 1 sec = 9.8 m/sec
9.8
2
sec
How fast is an object moving at the end
of a three second fall?
m
 3 sec = 29.4 m/sec
9.8
2
sec
A ball is in free fall for 8 seconds.
Its speed after 4 seconds is half the
speed it will reach by 8 seconds.
A) TRUE
B) FALSE
The distance it travels in the first
4 seconds equals the distance it
will travel in the last 4 seconds.
A) TRUE
B) FALSE
For objects in freefall, the distance
fallen, d, is directly proportional to
the time, t, spent falling: d  t.
A) TRUE
B) FALSE
How far does an object in freefall drop
in one second? In 8 seconds?
Your grade
school
mnenomic
distance = rate  time
We qualify this slightly with
current
= starting point + rate  time
position
x  x0  v  t
position at t = 0
Since a falling object’s velocity is constantly
increasing, maybe we should use:
rate  time = (average velocity)  time
vmin + vmax
average velocity =
2
v0 + v
=
2
starting velocity
at time=0
current velocity
at the present time
x  x0  vavg  t
position at t = 0
average velocity =
starting velocity
at time=0
v0 + v
2
current velocity
at the present time
built up by accelerating
over the time t
v  v0  at
x  x0 
x  x0 
v0  ( v0  at )
2
2v0  at
2
t
x  x0  v0t  at
1
2
2
t
How far does an object in freefall drop
in one second? In 8 seconds?
x  x0  v0t  at
1
2
distance fallen
2
x  x0  v0t  at
1
2
0
from rest
In 1 second:
d  at   9.8m / s (1s )
1
2
2
2
1
2
= 4.9 m
In 8 seconds:
d   9.8m / s (8s)
1
2
2
= 313.6 m
2
2
2
We all saw:
150
100
3 sec
50
1 sec
downhill:
vavg=25 cm/sec
final speed:
v =150 cm/3sec
2 sec downhill:
1.5 sec
vavg=50 cm/sec
final speed:
v =100 cm/sec
3 sec
1 sec
downhill:
vavg=225 cm/3sec
final speed:
v =150 cm/sec
Which we can check out:
150
100
3 sec
50
1 sec
downhill:
vavg=25 cm/sec
25 is the average of 0+50.
final speed:
To build up to final speed of 50cm/sec
in 1 sec took an accleration = 50cm/sec2. v =150 cm/3sec
So along this ramp the ball accelerates this fast!
2 sec downhill:
1.5 sec
Accelerating for 2 seconds should allow
The ball to build to a speed of
(50cm/sec2)(2 sec) = 100 cm/sec…
exactly the final speed we observed!
vavg=50 cm/sec
final speed:
v =100 cm/sec
3 sec
1 sec
downhill:
vavg=225 cm/3sec
Accelerating for 3 seconds should
mean a final speed of
(50cm/sec2)(3 sec) = 150 cm/sec…
final speed:
Also note, the average speed down
v =150 cm/sec
the ramp now is (0 + 150)/2
= 75 cm/sec which equals our measured 225/3 = 75 cm/sec
Some Answers
Question 1
Question 3
B. = g
Question 2
B. = g
C) both have the same acceleration
Whenever an object is freed of constraints – a ball released from your grip, a bullet
escaping from its barrel, an arrow loosed from its bowstring – whatever forces
were supplied under those constraints (the driving push of your hand, the pressure
of expanding gases from exploding gunpowder, the tension of a bowstring) vanish.
In all the above cases, the ONLY force acting on the objects (after release) is gravity!
Question 4
Question 5
B) no
A ball on a ramp is not in free fall. Gravity alone
does not act on it. The inclined plane provides a
force of support which affects the motion!
C) v = 0, but a 
At the highest point in its path, the ball momentarily
comes to a stop, and so its velocity is zero.
0
However, since the ball is in free fall,
its acceleration is g = 9.8 m/s2 (at every moment).
Question 6
A) TRUE
vt.
Question 7
A) TRUE
vt.
Question 8
B) FALSE
Question 9
B) FALSE
Distance fallen is NOT proportional to time falling.
Initially, as you build speed from 0, your speeds
are modest (you may not get very far each second).
But as you build speed you travel greater distances
in the same interval of time!