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Newton – Three Laws of Motion
1. Inertia
2. F = ma
3. Action = Reaction
Newton’s Laws of Motion
• Law of Inertia: A body continues in state of
rest or motion unless acted on by an external
force; Mass is a measure of inertia
• Law of Acceleration: For a given mass m, the
acceleration is proportional to the force applied
F=ma
• Law of Action equals Reaction: For every
action there is an equal and opposite reaction;
momemtum (mass x velocity) is conserved
Velocity, Speed, Acceleration
• Velocity implies both speed and direction;
speed may be constant but direction could
be changing, and hence accelerating
• Acceleration implies change in speed or
direction or both
• For example, stone on a string being whirled
around at constant speed; direction is
constantly changing therefore requires force
Ball Swung around on a String:
Same Speed,
(in uniform circular motion)
Changing Direction
(swinging around the circle)
Donut Swung around on a String
Acceleration
Force
Conservation of momemtum:
action equal reaction
• The momemtum (mv) is conserved before and
after an event
• Rocket and ignited gases:
M(rocket) x V(rocket) = m(gases) x v(gases)
• Two billiard balls:
m1 v1 + m2 v2 = m1 v1’ + m2 v2’
v1,v2 – velocities before collision
v1’,v2’ – velocities after collision
• Example – you and your friend (twice as
heavy) on ice!
Action = Reaction
Equal and Opposite
Force from the Table
Net Force is Zero,
No Net Motion
Force = (apple’s mass)  (acceleration due to gravity)
Acceleration due to gravity
• Acceleration is rate of change of velocity, speed or
direction of motion, with time  a = v/t
• Acceleration due to Earth’s gravity : a  g
g = 9.8 m per second per second, or 32 ft/sec2
•
Speed in free-fall
T (sec)
v (m/sec)
v (ft/sec)
0
0
0
1
9.8
32
2
19.6
64
3
29.4
96
60 mi/hr = 88 ft/sec (between 2 and 3 seconds)
Galileo’s experiment revisited
• What is your weight and mass ?
• Weight W is the force of gravity acting
on a mass m causing acceleration g
• Using F = m a, and the Law of Gravitation
W = m g = G (m MEarth) /R2
(R – Radius of the Earth)
The mass m of the falling object cancels
out and does not matter; therefore all
objects fall at the same rate or acceleration
g = GM / R2
i.e. constant acceleration due to gravity 9.8
m/sec2
Galileo’s experiment on gravity
• Galileo surmised that time differences
between freely falling objects may be too
small for human eye to discern
• Therefore he used inclined planes to slow
down the acceleration due to gravity and
monitor the time more accurately
v
Changing the angle of the incline changes the velocity v
‘g’ on the Moon
g(Moon) = G M(Moon) / R(Moon)2
G = 6.67 x 10-11 newton-meter2/kg2
M(Moon) = 7.349 x 1022 Kg
R(Moon) = 1738 Km
g (Moon) = 1.62 m/sec/sec
About 1/6 of g(Earth); objects on the
Moon fall at a rate six times slower than on
the Earth
Escape Velocity and Energy
• To escape earth’s gravity an object must have
(kinetic) energy equal to the gravitational
(potential) energy of the earth
• Kinetic energy due to motion
K.E. = ½ m v2
• Potential energy due to position and force
P.E. = G m M(Earth) / R
(note the similarity with the Law of Gravitation)
• Minimum energy needed for escape: K.E. = P.E.
½ m v2 = G m M / R
Note that the mass m cancels out, and
• v (esc) = 11 km/sec = 7 mi/sec = 25000 mi/hr
The escape velocity is the same for all objects of
mass m
Object in orbit  Continuous fall !
Object falls towards the earth at the same rate as the earth curves away from it
Quiz 1
• Each quiz sheet has a different 5-digit
symmetric number which must be filled in
(as shown on the transparency, but NOT
the same one!!!!!)
• Please hand in both the exam and the
answer sheets with your name on both
• Question/answer sheets will be handed
back on Wednesday after class
• Please remain seated until we begin
collecting (20-25 minutes after start)
• Class after quiz