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Chapter 2 completion...
Thursday, January 31
Spring 2008
Momentum
•
•
•
•
Motion depends on mass and speed
Linear momentum: p = mv
Law of conservation of linear momentum
Angular momentum
– the right-hand rule
Universal Gravitation
“...the power of gravity (which brought an apple from a tree to the
ground) was not limited to a certain distance from earth, but that
this power must extend much further than was usually thought.
Why not as high as the Moon...?”
Newton’s illustration from
Mathematical Principles of Natural Philosophy
Launching Into Orbit
Universal Gravitation
F=
Gm1m2
d2
The universal gravitational constant: G = 6.67 × 10-11 N·m2/kg2
The gravitational force between two objects is proportional to the mass
(m) of each object and inversely proportional to the square of the
distance (d) between the centers of the masses:
The direction of the force is attractive and lies along the line joining the
centers of the two masses.
Universal Gravitation
Gm1m2
F=
d2
Newton’s law of universal gravitation
obeys his 3rd law of motion:
d
F1 = F2 = F
Universal Gravitation
• The gravitational force
between two objects is
exerted by each object
on the other
(ME)
(mass)
• It demonstrates a 3rd
law action-reaction pair
of forces
RE
F=
Gm1m2
d2
• The two objects may
react differently,
depending on their
masses and the size of
the force
Weight and Gravity
• Weight
– Force of gravity acting on an object’s mass:
W = mg
• Weight depends on acceleration due to
gravity (g = 9.8 m/s2 on Earth)
– Different on Earth, Moon, Mars, etc.
• Mass is constant
– Amount of matter comprising an object
– Independent of location in universe
Mass and Weight
Mass is a measure of the amount of
matter in an object, and it determines
an object’s inertia, or resistance to a
change in its motion.
The gravitational force acting on an
object is the weight of the object.
W = mg
1 N ≈ 0.225 lb; 1 lb ≈ 4.448 N
Big G and Little g
• Closely related:
Force of Earth’s gravity on a mass at its surface:
F = (G × mass × ME) / RE2
F = mass × g
• Setting equations equal:
mass × g = (G × mass × ME) / RE2
• Divide by mass
g = (G × ME) / RE2
• Plug in values of g and G
9.8 m/s2 = 9.8 N·kg
For Tuesday 02/05:
Complete HW #2, Chapter 2 Mallard quiz (due by
midnight on Monday 02/04)
In-class quiz on Chapter 2