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```PHYSICS 103: Lecture 11
Agenda for Today:
• Circular Motion (continued)
• Gravity and orbital motion
• Example Problems
HW (due Tuesday)
CENTRIPETAL FORCE: EXAMPLE
•ROTATING SPACE SHIP: MOVIE 2001
FORCE OF GRAVITY
• Attractive force between all massive objects
• Increases with increasing masses
F  m1  m2
• Increases as the two objects get closer by r-2
1
F  2
r
m1  m 2
FG
r2
G = 6.67  10-11 N m2/kg2
Gravitational Force Between People
•Calculate the gravitational force between you and your
neighbor. Assume your masses are 100 kg and the distance
between you is 50 cm. Compare this to the gravitational force
between you and the Earth. The radius of the Earth is 6370 km
and its mass is 5.981024 kg.
m1  m 2
F G
r2
ORBITAL SPEEDS
Example: What is the speed of the Moon?
1) Newton’s Law of Motion
2) Newton’s Law of Gravitation
3) Circular motion
F = ma
F = (GmM) / r2
a = v2 / r
Steps ...acceleration of mass is
a = v2/r
therefore force acting on object is
f = ma =
mv2/r
If object (m) is circling another massive object (M), then
f = GmM/r2
i.e.,
i.e.,
mv2/r = GmM/r2
v2 = GM/r
M
v G
r
Orbital velocity
How fast does the moon orbit?
v  1000 m/s
How fast does a satellite orbit?
v  7800m/s (17,400 miles/hr!)
Problem: Speed of moon?
r
Data:
r = 3.84  108 m
G = 6.67  10-11 N
Me = 5.98  1024 kg
M
v G
r
V = 1020 m/s
Problem: Speed of moon?
Data:
r = 3.84  108 m
Steps: speed = distance / time period
total dist. = 2 p r = 2  p  3.84  108 (m)
time period = 27.3  24  60  60 (s)
\
speed = (2.4  109) / (2.4  106)
= ~ 1  103 m/s
Main Points from Today’s Lecture
• Gravity
You should understand that gravity is a force that exists between all
objects and that it is proportional to the masses of the objects and
inversely proportional to the distance squared.
• Gravity and Orbital Motion
You should understand that gravity is a force that exists between all
objects. It is the force that is responsible for the moon orbiting the earth,
the earth orbiting the sun, etc. The orbital velocity of anything is
v
GM
r
where M is the mass of the central body being orbited.
```