Download mass

Lecture 5
2012 Sept. 11
• The Law of Gravity
• Velocity and Acceleration
• Newton’s Laws: Force = mass acceleration (F=ma)
• Kepler’s 3rd Law: Newtonian Form
• Mass vs Weight
The Planets
Prof. Geoff Marcy
© 2005 Pearson
Education Inc.,
Isaac Newton
• Realized physical laws that operate
on Earth also operate in the heavens
 one universe
• Discovered laws of motion and
gravity
Sir Isaac Newton
(1642-1727)
• Experiments with light; first
reflecting telescope (using mirrors
rather than lenses)
• Invented calculus.
1. What determines the strength of
gravity?
The Universal Law of Gravitation
1. Every mass attracts every other mass.
2. Attraction is directly proportional to the product of their masses.
3. Attraction is inversely proportional to the square of the distance
between their centers.
Question:
You grab the moon, pulling it to 1/3 of its
current distance from Earth. (d  d/3)
The grav. force by the moon on the Earth is:
A.
B.
C.
D.
9x greater force than before
3x
1/3 of the force before.
1/9 of the force before.
Question:
You grab the moon, pulling it to 1/3 of its
current distance from Earth. (d  d/3)
The grav. force by the moon on the Earth is:
A.
B.
C.
D.
9x greater force than before
3x
1/3 of the force before.
1/9 of the force before.
Speed, Velocity, and Acceleration
• speed: rate at which object moves
ö
speed = distance æçèunits of m
s ÷ø
time
Example: speed of 10 m/s or 100 km/hr
• velocity is a “vector”: speed and direction
Example: 10 m/s, due east
• acceleration: rate of change of velocity.
units of speed/time (m/s per s)
Note: Acceleration occurs if
a) speed changes
b) direction of motion changes
c) or both change
Question:
An asteroid orbits the Sun at a = 4 AU.
How fast does it travel around Sun?
A.
B.
C.
D.
25% as fast as Earth
Half as fast as Earth
Twice as fast as Earth
4x Faster than Earth
Question:
An asteroid orbits the Sun at an average distance
a = 4 AU. How fast does it travel around Sun?
v EARTH
v ASTEROID
distance 2p a
=
=
time
1 year
distance 2p (4a) 1 2p a
=
=
=
time
8 years 2 year
To get Period, use Kepler’s 3rd Law:
P2 = a3 
P = Square Root( a3 ) = 8 years
Question:
An asteroid orbits the Sun at an average distance
a = 4 AU. How fast does it travel around Sun?
A.
B.
C.
D.
25% as fast as Earth
Half as fast as Earth
Same speed as our Earth
Twice as fast as Earth
v EARTH
v ASTEROID
distance 2p a
=
=
time
1 year
distance 2p (4a) 1 2p a
=
=
=
time
8 years 2 year
The Acceleration of Gravity
• On Earth, all falling
objects accelerate at the
same rate (ignoring air
resistance).
• On Earth, g = 9.8 m/s2 
Speed increases 9.8 m/s
each second of falling.
9.8 m/s
19.6 m/s
Using Calculus to Describe Motion
Position s
Differentiation
Integration
Example: Falling ball
s(t) (in meters)
s(t) = s0 +
ò v dt
h(t) = h0 - 12 gt 2
Velocity v
s2 - s1
v=
(in m/s)
t 2 - t1
v(t) = v 0 +
ò a dt
v(t)  v0  gt
Acceleration a
v 2 - v1 æ
çin m/s2 ö÷
a=
ø
t 2 - t1 è

a(t) = -g = const.
© 2005 Pearson Education Inc.,
publishing as Addison-Wesley
Newtonian Physics: Planets and
ordinary objects move by the same laws
Isaac Newton 1643-1727
The Acceleration of Gravity (g)
• Galileo showed that
g is the same for all
falling objects,
regardless of their
mass.
Apollo 15
Newton’s first law of motion
An object moves at constant velocity unless a net force acts
to change its speed or direction.
Object at rest: Won’t move unless a force acts on it
Object moving at constant velocity in straight
line: Won’t deflect or change velocity unless a
force acts on it
Newton’s second law of motion
Force = mass  acceleration
Units: Newton = kg 
m s-2
What is Force? Simple question, subtle answer.
however:
Pressure = force / area
Hook’s law: force of a spring
Newton’s third law of motion
For every force, there is always an equal and opposite reaction force.
How does Newton explain Keplerian orbits?
Newtons’s 2nd Law
F=ma
Universal law of Gravitation
How does Newton explain Keplerian orbits?
Newtons’s 2nd Law
Universal law of Gravitation
F=ma
Kepler had found
empirically:
P ~a
2
3
Newton derived the relation
from the two laws above.
Found a correction to
Kepler’s 3rd law:
2
4
p
P2 =
a3
G(M1 + M 2 )
Interactive Quiz
Where in the orbits does the largest force act on the planet?
B
A
C
D
(A) Point A
(B) Point B
(C) Point C
(D) Point D
Interactive Quiz
Where in the orbit does the largest acceleration occur?
B
A
C
D
(A) Point A
(B) Point B
(C) Point C
(D) Point D
Interactive Quiz
Where in the orbit does the planet move with lowest speed?
B
A
C
D
(A) Point A
(B) Point B
(C) Point C
(D) Point D
Quiz
Where in the orbit does the Sun get
jerked (accelerated) hardest?
most by the planet.
B
A
C
D
(A) Point A
(B) Point B
(C) Point C
(D) The same for all points
How is mass different from weight?
• mass – the amount of matter in an object
it relates force and acceleration (F=ma)
• weight – measures the gravitational force
that acts upon an object (F=mg)
Question
On the Moon:
A.
B.
C.
D.
My weight is the same, my mass is less.
My weight is less, my mass is the same.
My weight is more, my mass is the same.
My weight is more, my mass is less.
Question
On the Moon:
A.
B.
C.
D.
My weight is the same, my mass is less.
My weight is less, my mass is the same.
My weight is more, my mass is the same.
My weight is more, my mass is less.
How is mass different from weight?
• mass – the amount of matter in an object
• weight – the force that acts upon an object
You are weightless
in free-fall!
Why are astronauts weightless in space?
• There IS gravity in space…
• weightlessness is due to a constant state of free-fall:
Question: Is there a net force?
(A) YES
(B) NO
1.
2.
3.
4.
5.
A car coming to a stop.
A bus speeding up.
An elevator moving at constant speed.
A bicycle going around a curve.
A moon orbiting Jupiter.
Question: Is there a net force?
(A) YES
(B) NO
1.
2.
3.
4.
5.
A car coming to a stop. Y
A bus speeding up. Y
An elevator moving at constant speed. N
A bicycle going around a curve. Y
A moon orbiting Jupiter. Y
What have we learned?
•How do we describe motion?
•Speed = distance/time
•Speed + direction => velocity (v)
•Change in velocity => acceleration (a)
•Force causes a change in momentum, which means
acceleration.
What have we learned?
•
How did Newton change our view of the universe?
•
•
•
He discovered laws of motion & gravitation.
He realized these same laws of physics were identical in the
universe and on Earth.
What are Newton’s Three Laws of Motion?
1)
2)
3)
Object moves at constant velocity if no net force is acting.
Force = mass  acceleration
For every force there is an equal and opposite reaction force.
Next time . . .
• Conservation of energy and laziness
• Orbits
• Tides