Download Lecture2_Freefall

Interlude:
Here’s a fairly
common trait
sought after
in the personals:
“Seeking…
“Weight proportional to height.”
What’s that supposed to mean?
Is that a desirable trait?
Proportionalities
A
B
D
C
A
= ?
z
1.A/w
2.A/x
3.B/x
4.C/x
5.D/x
6.D/w
y
w
x
z
A and z are bases of their respective
(isosceles) triangles, i.e, they are
“corresponding sides.” D is an
“altitude” and so corresponds to x.
s
a
r
The ratio of surface areas
A
= ?
a
1.R/r2
2. R2/r2
3. R2/r
4. R/r
5. r/R
R
A
S
The ratio of the sides of
the square areas S/s = R/r
since S is to R as s is to r.
However the areas A = S2
and a = s2.
Consider this block weighing “W”
height, h
weight, W
This stack
of 2 blocks height, 2h
weighs
how much?
Are these blocks
in proportion?
2W
To scale proportionally
height, h
weight, W
And this double-sized block weighs
1. 2W
2. 4W
3. 6W
4. 8W
5. 10W
6. 12W
More generally,
2L
2w
h
L
w
2h
original
=hwL
volume
new
=(2h)(2w)(2L)
volume
= ( 8 )hwL
=(8
original
)( volume )
Is weight meant to be proportional to height?
Weight  (Height)3
Each 1% increase in height should
correspond to a (1.01)3 = 1.03
3% increase in weight
5% increase in height
(5’4”  5’7”) 15.2% gain in weight
10% increase in height
(5’10”  6’5”) 30% gain in weight
Easy to
push
Hard to
push
To produce the same amount of acceleration,
need to push the car much harder!
How much?
Twice as much mass requires twice the force!
100 as much mass requires 100 the force!
Fm
If a lot of others join in, each contributing
an additional force, the net force will
be greater, and the acceleration greater.
Fa
together with F
m
can be combined consistently to give
Newton’s 2nd Law
F = ma
Unveiled at yesterday’s
International Auto Show in Detroit:
The Toyota FT-HS is a
400-horsepower hybrid sports car
its 3.5-liter V6 engine
provide an acceleration of
0-to-60-miles-an-hour in 4 seconds
v
acceleration, a =
t
+60 miles/hour
4 seconds
= 15 miles/hour
sec
+60 miles/hour
4 seconds
miles/hour
= 15
sec
Notice 60 miles/hour is the same as
miles 5280 feet
feet
60

= 316800
hour
1 mile
hour
feet
316800
hour
1
hour
feet

= 88
3600 seconds
sec
So alternately
+60 miles/hour
4 seconds
= 22 feet/sec
sec
or 22 ft/sec2
14 lb. medicine ball
Tennis ball Softball
2 ounces 6.5-7.0 oz.
(57 grams)
112 times
heavier
than a
tennis
ball!
32 times
heavier
than a
softball!
If all 3 balls were released simultaneously,
from the same height, they would reach ground
1. tennis ball first, medicine ball last.
2. medicine ball first, tennis ball last.
3. together at about the same time.
A large boat whose maximum speed
in still water is v1, tows a smaller boat
whose maximum speed is the smaller
v2.
across the lake. If both outboard motors
run together at full bore, the speed that
they travel together with will be
1. the smaller value v1.
2. the larger value v2.
3. somewhere between v1 and v2.
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 500 Newtons (110 pounds) in
New York City; but ~0.25 newton
(1 ounce) less in mile-high Denver.
If you drop an object (assuming its
air resistance is negligible) it accelerates
downward at g=9.8 m/sec2. If instead
you throw it downward, its downward
acceleration after release is
A.
B.
C.
<g
=g
>g
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).
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!
The maximum velocity, v, an object
reaches falling freely from rest, is
directly proportional to the time, t,
of its fall: v  t .
1) TRUE
2) FALSE
How fast is an object moving at the end
of a one second fall?
How far does an object in freefall drop
in one second?