Transcript Universal Gravity

How fast would a bowling ball have to be
moving for it to clear the gap in the elevated alley
and continue moving on the other side?
A body in free fall falls 4.9m in the
first second of fall.
1 2
d  vot  at
2
1
2
d  0  (9.8)(1 )
2
16 ft

1 sec
8 km
4.9 m
How fast would a bowling ball have to be
moving for it to clear the gap in the elevated alley
and continue moving on the other side?
8 km/sec. In fact,
you could remove
the whole alley!
Ball launched horizontally
from a cannon with no
gravity
Add in gravity…
Now with a slightly larger
velocity…
V = 8 km/s
V > 8 km/s
Would a cannon
fired
upward
No!ball
It would
simply
act as at
a 8
projectile
andorbit?
crash back into the
km/s go into
Earth
Earth at 8 km/s. To circle the Earth it
must have a tangential speed of 8 km/s
Law of Universal Gravitation
Every body in the universe attracts
every other body with a mutual force that is
directly proportional to the product of their
masses and inversely proportional to the
square of the distance between their
centers.
Where:
GM 1 M 2
Fgravity 
2
R
G = 6.67x10-11 N m2/kg2
The Universal Gravitation Constant
He is obviously
attracted to her. But,
how much force of
attraction is there?
GM 1 M 2
Fgravity 
2
R
Assume: His mass = 80. kg
Her mass = 52 kg.

0.75m
He is obviously
attracted to her. But,
how much force of
attraction is there?
GM 1 M 2
Fgravity 
2
R
Assume: His mass = 80 kg
Her mass = 52 kg.

(6.67 1011 )(80kg)(52kg)

(0.75m) 2
= 4.9x10-7N
Example: A satellite is orbit around the Earth
makes one complete revolution every 3 days. At
what altitude is the orbit? (Mass of Earth = 6.0 E
24 kg, Radius of Earth = 6.4 E 6 m)
T  3days 
24hr 60min 60sec


 2.5910 5 sec
1day
1hr
1min
Fc  Fg
m s 4 d GM s M E

2
2
T
d
2
GM
T
3
E
R 
4 2
2


R  8.8010 m
7
The altitude of the distance above the
surface of the Earth.

Altitude = 8.80x107 - 6.4x106
Altitude = 8.16x107m
How do the Tides work?
But what about the bulge on
the other side?
What we already know: The water under the
moon is closer to the moon then the center
of the Earth is. So the moon’s gravity pulls
harder on the water and the water “heaps
up” under the moon.
The New Part: The center of the Earth
is closer to the moon then the water on
the OPPOSITE side of the Earth. The
moon pulls the Earth away from the water,
and it appears to “heap up” too.