Newton

1
Newton Three Laws of Motion

• Inertia
• F ma
• Action Reaction

2
Newtons 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 m a
• Law of Action equals Reaction For every action
  there is an equal and opposite reaction momemtum
  (mass x velocity) is conserved

3
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

4
Ball Swung around on a String
Same Speed, (in uniform circular motion) Changing
Direction (swinging around the circle)
5
Donut Swung around on a String
6
Conservation of momemtumaction 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!

7
Action Reaction
Equal and Opposite Force from the Table
Net Force is Zero, No Net Motion
8
Acceleration due to gravity

• Acceleration is rate of change of speed or
  direction of motion with time
• Acceleration due to Earths gravity
• 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)

9
Galileos 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

10
Galileos 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
11
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

12
Escape Velocity and Energy

• To escape earths 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

13
Object in orbit ? Continuous fall !
Object falls towards the earth at the same rate
as the earth curves away from it
14
(No Transcript)