Gaya sentral fifsika mekanika

1. GAYA SENTRAL
Disusun oleh:
RUBEN CORNELIU SIAGIAN

2. The Birth of Modern Physics
• Mechanics - The Study of Motions and Forces
• Fundamental Concepts
• Mass - Amount of matter
• Inertia - Property of Matter Requiring a Force to Change
Motion
• Position - Location in space
- Absolute reference frame a Cartesian concept
• Velocity - Rate at which position changes
- Identified by both speed and direction
• Acceleration - Rate at which velocity changes
• Central Force

3. The Birth of Modern Physics
• Central Force
Fc = m v2 / R
R
m v

4. The Birth of Modern Physics
• Central Force
Fc = m v2 / R

5. Fig. 2.03

6. • Gravity is a Central Force interaction, that is, the force of
gravity attracts along a straight line between the center of
masses of the two bodies. The center of mass, CM, of a
body is the point where we can imagine all of the mass of
that body to be concentrated. Centripetal acceleration
ac=V2/R
• For objects in the solar system not moving directly
towards or away from the sun, the sun’s gravity causes
centripetal acceleration, a change in the velocity of that
object towards the sun.

7. Fig. 2.04

8. • Newton imagined a Cannon on a mountain top, fired a
ball with greater and greater velocity, eventually the ball
would go all the way around the world, that is it would
ORBIT the world. From the surface of the earth escape
velocity is 11 km/s or 24600 miles per hour

9. Fig. 2.04a

10. • The Apple and the Moon: Newton’s great insight was to
imagine the same force that caused an apple to fall on earth
also reaches out beyond earth, to the moon for example. He
was able to calculate with great accuracy the motion of the
moon. He calculated that the moon "falls" 1/20 of an inch
each second.
• Using Universal Gravity masses of planets and the sun and
even stars could be calculated.
• Halley used Newton’s Laws to predict the return of what is
now called Halley’s Comet.
• Perturbations or irregularities in the orbit of Uranus led
people to suspect another planet 1846, the discovery of the
Neptune was linked to Newton.
• Newton’s laws were incredibly successful
• Note, the law of gravity was not revised or even suspected to
be wrong, 150 years after Newton

11. Fig. 2.04b

12. The Birth of Modern Physics
• Central Force (also known as Centripetal Force)
• Central force required to keep object moving in a circle
Fc = m v2 / R

13. The Birth of Modern Physics
• Newton 1700 AD
1665-1666 plague was sweeping England … left Cambridge for home …
in next five years he developed his ideas on ….
Mechanics
Gravity
Calculus
Discovered Spectrum of Light
Theory of Light
Reflecting Telescope
Annus Mirablis

14. Newton’s Laws of Motion
1. A Body Remains at Rest or Moves at Uniform
Speed in a Straight Line unless acted Upon by
a Force.

15. The Birth of Modern Physics
• Central Force

16. Newton’s Laws of Motion
2. The Change of Motion is Proportional to the
Force Acting on it and in the Direction of the Force
F = m a

17. 4. Drop a ball … speed increases … acceleration … requires force
t (sec) d v a
0 0 0
1 490 cm 980 cm/sec 980 (cm/sec)/s
2 1960 cm 1960 cm/sec 980 (cm/sec)/
3 4410 cm 2940 cm/sec 980 (cm/sec)/

18. Change of direction … acceleration … requires force
10 km/hr
10 km/hr

19. Newton’s Laws of Motion
3. To Every Action there is an Equal and Opposite
Reaction

20. Newton’s Laws of Motion
3. To Every Action there is an Equal and Opposite
Reaction
• Recoil of a gun
• Collisions
• Rockets

21. Newton’s Law of Gravity
• Development of Law of Gravity -
It was insight of genius, not a miraculous revelation
Consider a falling apple …
1) Galileo’s experiment - at the surface of the Earth a wood ball and
a lead ball have the same acceleration due to gravity
From Newton’s Second Law
Fg,lead = mlead alead
Fg,wood = mwood awood
Since alead = awood, then the force of gravity must be proportional to
the mass of the falling object. So, the Law of Gravity must in part
look like …
Fg = mapple

22. Newton’s Law of Gravity
• Development of Law of Gravity -
2) Newton’s Third Law says that…
the force of gravity from the Earth on the apple
must equal
the force of gravity from the apple on the Earth
so the Law of Gravity must treat both the Earth and the
apple the same way …
Fg = mapplemEarth

23. Newton’s Law of Gravity
• Development of Law of Gravity -
3) How does the Law of Gravity depend on distance?

FG 
MappleMEarth
D?
=

24. Newton’s Law of Gravity
• Development of Law of Gravity -
3) How does the Law of Gravity depend on distance?

Fg,apple 
MappleMEarth
Dapple
?  Mapple • aapple

Fg,Moon 
MMoonMEarth
DMoon
?  MMoon • aMoon
=
=
DMoon
DApple

25. Newton’s Law of Gravity
• Development of Law of Gravity -
3) How does the Law of Gravity depend on distance?
DMoon
DApple








?

aapple
amoon

Fg,Moon 
MEarth
DMoon
?  aMoon

Fg,apple 
MEarth
Dapple
?
 aapple
DMoon
DApple

26. Newton’s Law of Gravity
• Development of Law of Gravity -
4) What are accelerations of apple and Moon?
• Acceleration of apple is 980 (cm/sec)/sec
• Acceleration of moon?
• For a circular orbit, must have a central force

Fcentral 
MMoon •VMoon
2
DMoon
 MMoon • aMoon
VMoon
2
DMoon
 aMoon
 aMoon
0.27 (cm/sec)/sec

27. Newton’s Law of Gravity
• Development of Law of Gravity -
4) What are accelerations of apple and Moon?

aapple
amoon

980(cm/sec) /sec
0.27(cm/sec) /sec
 3600

DMoon
Dapple

384000km
6378km
 60
DMoon
DApple








?

aapple
amoon
? = 2

28. Newton’s Law of Gravity
1 2
Fg
Fg
M1 = Mass of object 1 (grams)
M2 = Mass of object 2 (grams)
D = Distance between objects (cm)
G = 6.67x10-8 cm3/sec2/gm
D

Fg 
GM1M2
D2