Transcript gravity ppt - District 196

Newton believed that
every object
___attracts_____
every other object.
The force of the
attraction depends
on the __mass___
and _distance__ of
the two objects.
Fg = G (m1m2)
r2
Fg = gravitational force in (N)
m1 = mass object 1 (kg)
m2 = mass object 2 (kg)
r = the distance between the masses
(m)
(measured from their centers)
G = 6.67 x 10-11 N m2/kg2
(a constant everywhere!)
Ex. 1 Are you attracted to the person sitting next to you?
Calculate the gravitational force between you
(mass 70kg) and the person next to you (mass 65kg)
if you are 1.2 m apart.
Given: m1 = 70 kg
m2 = 65 kg
r = 1.2 m
G = 6.67 x 10-11 N m2/kg2
Unknown: Fg
Equation: Fg = G (m1m2)
r2
= (6.67 x 10-11 N m2/kg2)(70 kg)(65 kg)
(1.2 m)2
= 2.11 x 10-7 N
= 0.000000211 N
(tiny!)
As you go further away from the earth’s surface the
acceleration due to gravity _decreases____.
 Two equations for gravitational force
F = ma becomes Fg = mg
and Fg = G (m1m2)
r2
We can set them equal to each other:

cancels
Fg = Fg
mg = G m1 m2
r2
g=Gm
r2
one of the masses





g = the acceleration due to gravity (m/s2)
G = 6.67 x 10-11 N m2/kg2
m = the mass of the planet in kg
r = the distance from the center of the
planet in (m)
Remember- r measures from CENTER of
planet, not the surface.

Ex. 2 Find the gravity if you are 2.1 x 10 5 m above the earth’s
surface.
Given: r = 2.1 x 105 m + 6.37 x 106 m
= 6.58 x 106 m
mearth = 5.98 x 1024 kg
Unknown: Fg
Equation: F = ma, now Fg = mg
(We need g at that altitude.)
Fg = Fg
mg = G m1 m2
r2
g=Gm
r2
= (6.67 x 10-11 N m2/kg2)(5.98 x 1024 kg)
(6.58 x 106 m)2
= 9.21 m/s2
So you would weigh Fg = mg
= (60kg) (9.21 m/s2)
Fg = 553 N
A geosynchronous
satellite orbits above
the same point on
the equator of the
earth at all times.
Examples:
GPS
cell phone satellites
TV satellites
Satellites are _____projectiles_____. In order
to not fall back to earth, they need to
maintain a certain velocity…
In order for a satellite to stay in a consistent
orbit gravitational force = centripetal force
Fg= Fc
mg = m v2
r
(The mass of the satellite cancels out!)
g= v2
r
g = the acceleration due to gravity in m/s 2
v = the speed of the satellite in m/s
r = the distance from the center of the planet
in meters

Ex. 3 Calculate the speed needed for one of the Direct TV satellites to
orbit at an altitude of 320,000 m above the earth’s surface.
Given: r = 320,000 m + 6.37 x 106 m = 6,690,000 m or 6.69 x 106
m
Unknown: v
Equation: Fg = Fc
mg = mv2
r
g = v2
r
We need g at that altitude:
Fg = F g
mg = G m1 m2
r2
g=Gm
r2
= (6.67 x 10-11 N m2/kg2)(5.98 x 1024 kg)
(6.69 x 106 m)2
g = 8.91 m/s2
8.91 m/s2 = ___v2__
(6.69 x 106 m)
v = 7,721 m/s
(that’s about 17,000 mph!)