Newton

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					Isaac Newton
(1643 – 1727)

 Defining his
   3 Laws



                Newton at age 46
          Scalar vs. Vector
• Speed is scalar – (how fast something
  is going)

• Velocity is a vector so its direction
  matters! – (speed and direction)

• Acceleration is also a vector it has
  magnitude and direction
Speed and Direction

Speed is important
    (100 km/hr)

       But . . .

Direction can be even
  more important!!!
Uniform circular motion
How Many Accelerators Does
     Your Car Have?
      Newton’s First Law of Motion



• Every object in a state of uniform motion
  tends to remain in that state of motion
  unless an external force is applied to it
          Forces are Balanced
                 a = 0 m/s2


Object at rest                Object in Motion

  V = 0 m/s                      V ≠ 0 m/s




                           Stay in motion same
 Stay at rest             speed and direction in
                               straight line
Car in motion makes a left hand turn
               Acceleration in a car

Car starts from rest    Moving car brakes to stop
    Newton’s Second Law of Motion


• The relationship between an object’s
  mass (m), its acceleration (a), and the
  applied force (F) is F = ma

         In terms of acceleration:
                 a = F/m
      Forces are Unbalanced

              There is an acceleration


                     a = F/m


The acceleration                The acceleration
depends directly               depends inversely
   upon the                        upon the
  “net force”                    object’s mass
           Aristotle vs. Newton

• Aristotle  force maintains motion (s)
                     (F=ms)
             Common sense

• Newton  force causes change in velocity
•                 (F=ma)
          looks at all forces involved
           Baseball and Tennis Ball
       A. Drop in a vacuum from height of ~ 30 feet
       B. Drop from the roof of DeLaRoche
         Which hits the ground 1st?

Baseball
- mass 142 to 149 g
-circumference 22.9 to 23.5 cm



               Tennis ball
               - mass 57.7 to 58.5 g
               -circumference 19.95 to 20.95 cm
Drop a baseball and tennis ball (in vacuum)
• _____________________


• Baseball 2.5 times mass of tennis ball – Earth
  pulls 2.5 times as hard on baseball

                       But

• Baseball’s greater mass makes it 2.5 times as
  hard to accelerate

• ___________________________________
Drop a baseball and tennis ball (off DeLaRoche)

 • ________________ lands first

• must take into account air
  resistance

 • when air resistance = gravity
  terminal velocity

• ______________ reaches terminal velocity quicker
  than ______________

• ___________ falls longer before air resistance
  balances gravity – more time to fall more time to
  accelerate
             Terminal Velocity
           [Don’t try to memorize]
Vt is the terminal velocity

m is the mass of the falling object

g is gravitational acceleration at
the Earth's surface

Cd is the drag coefficient

ρ is the density of the fluid the
object is falling through

A is the object's cross-sectional
area
                Momentum
• Momentum – “mass in motion”

• All objects have mass so if moving object has
  momentum

• Newton’s statement of his second law
  involved the rate of change of “motion”
  (=momentum)

• can be restated in terms of momentum

                   ρ=m•v
         Stopping Momentum

• Any object with momentum is hard to stop

• Must apply a force against its motion over
  time

• The greater the momentum the greater the
  force or longer the time period to stop the
  object
Impulse = Force • Time = Change in Momentum
     Can be derived from Newton’s 2nd law

        F = ma              a = Δ v/t

        F = m(Δ v/t)        Ft = Δmv

To minimize the affect of the force on an object time
must be increased [Ft = Δmv]

To maximize the affect of the force on an object time
must be decreased [Ft = Δmv]
Combinations of Force and Time required
   to produce 100 units of Impulse
  Force         Time        Impulse
   100            1           100
   50             2           100
   25             4           100
   10            10           100
    4            25           100
    2            50           100
    1            100          100
   0.1          1000          100
Real Life Examples
Hitting the “Long Ball”
         Hitting the “Long Ball”
• You want the ball to have the largest
  possible velocity when it leaves the bat

• What does the impulse-momentum equation
  say about this?

• You want the largest possible momentum
  for the ball as it leaves the bat. Ball has
  essentially zero momentum when you hit it
  (i.e., zero velocity)
              Hitting the “Long Ball”

• You want the largest possible change in
  momentum for the ball

• The change in momentum of the ball equals the
  impulse that you apply (with the bat) to the ball

• To get the largest possible change in momentum,
  apply the largest possible impulse to the ball
              Hitting the “Long Ball”

• Impulse depends directly on force applied and
  time the force is applied. (Impulse = (force)(time)

• To get the largest possible impulse you should
  either:

   apply the largest possible force

   apply the force for the longest possible time

   or both
               Hitting the “Long Ball”


• You want to apply maximum force by hitting the
  ball hard. If you hit the ball with twice the force,
  you will impart twice the impulse to the ball
• Impulse = change in momentum - this will double
  the ball's change in momentum
• Momentum equals mass times velocity - doubling
  the ball's momentum will double its velocity
• However, if you try to apply too much force your
  coordination and timing will suffer, and your swing
  will not be accurate - you may even miss the ball!
          Hitting the “Long Ball”


• You can also increase the impulse on the ball
  by increasing the time that the bat exerts its
  force on the ball - "following through"

• If you hit the ball for twice as much time, you
  will impart twice the impulse to the ball, which
  means twice the change in momentum for the
  ball. So, following through is important
         Golf – Tennis - Soccer
• To get largest possible velocity for the ball:

   want the largest possible momentum for the ball

• To get the largest possible momentum for the ball:

   want to apply the largest possible impulse to the
  ball

• To apply the largest possible impulse to the ball:
  want to apply the largest possible force
  apply a force for the longest possible time
  or both
   Newton’s Third
   Law of Motion



• For every action
  there is an equal
    and opposite
      reaction
             Balanced Forces
      The forces on the person are balanced




                                  Gravity pulls
The floor pushes                downward on the
upward on the person                person
      Conservation of Momentum


• Product of mass x velocity

• In isolated system momentum must
remain constant

 • Adult pushing child away on ice

• Angular momentum and a spinning ice
  skater
   [Don’t try to memorize following slides!!]
 Is the force the car exerts on the truck?
A. greater than the force the truck exerts on the car
B. less than the force the truck exerts on the car
C. equal to the force the truck exerts on the car
          mass-car (m1) = 1500kg
          mass-truck (m2) = 20,000kg

          Velocity-car (u1) = 8m/s,
          Velocity-truck (u2) = 5 m/s




solution for final velocity can be derived from
         conservation of momentum
ρ 0 = ρf
ρ1 + ρ2 = (m1 + m2)*V
(m1u1) – (m2u2) = (m1 + m2)*V
V = (m1u1 – m2u2)/(m1 + m2)
V= [(1500 kg)(8 m/s) – (20,000 kg)(5 m/s)]/)1500 kg + 20,000 kg)
V = -4.09 m/s
We can find the forces acting on the driver in each
vehicle by noting that the change in velocity of the
car or truck is the same as the change in velocity of
the driver

Let's assume the crash takes place over a time
period of about 0.2 s. The acceleration of the truck
is a2 = vf - v0/tcrash = (V - u2)/ tcrash = (-4.09 m/s – (-5)
m/s)/0.2 s = +4.6 m/s2
The car driver experiences an acceleration of
(V - u1)/tcrash = (-4.09 m/s - 8 m/s)/0.2 s = -60.5
m/s2

The magnitude of the forces are equal since,
Ftruck = (20,000 kg)(4.6 m/s2) = 92,000 Nt and
Fcar = (1500 kg) (60.5 m/s2) = 91,000 Nt with the
difference being round off error

Since the accelerations of the car and truck are
opposite signed, the directions of the forces on
both are in opposite directions just as Newton's
Third Law demands
If the truck driver and car driver are about the
same mass, then the force on the car driver is
about 13 times as great as the force on the truck
driver!

F = ma if mass = 70 kg = 154 lbs
Ftruck driver = 70kg * 4.6 m/s2 = 322 Nt
Fcar driver = 70kg * 60.5 m/s2 = 4235 Nt

				
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posted:8/8/2011
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