newton believed that every object ___attracts_____ every other object. the force of the attraction...
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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:
Fg = Fg
mg = G m1 m2 one of the masses cancels
r2
g = G m r2
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 105 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 = G m 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:GPScell phone satellitesTV 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 = v 2 r
g = the acceleration due to gravity in m/s2
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 rWe need g at that altitude: Fg = Fg
mg = G m1 m2
r2
g = G m 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!)