Momentum

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Momentum Newton's 2nd Law
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THE CHANGE OF NEWTON'S SECOND LAW

• Isaac Newton first delineated what is now known
  as Newtons second law in 1686. During the
  interceding centuries, Newtons original version
  of this rule has been rewritten.
• For purposes of education, textbooks and teachers
  have expressed this law as the familiar Fnet
  ma. This is a useful statement, since it relates
  acceleration to force and mass.
• However, when Newton originally explained the
  relation between force and motion he explained it
  in terms of what he called quantity of motion.

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• NEWTONS 2nd LAW AS WE NOW USE IT Fnetma
• The net force acting on a body is equal to the
  product of the bodys mass and its acceleration.
• NEWTONS 2nd LAW AS NEWTON ORIGINALLY REVEALED
  IT Fnet?p/?t
• The net force acting on a body is equal to the
  rate at which the body's quantity of motion is
  changing. (p quantity of motion, the word
  rate implies division by time.)

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HOW ARE THESE EQUIVALENT?

• Newtons quantity of motion is what we now call
  momentum. Momentum is the product of an
  objects mass and its velocity (velocity, not
  speed).
• In symbols, p mv. The momentum of a body is a
  vector whose direction is the direction of the
  bodys velocity.
• The magnitude of momentum is the product of mass
  and speed p mv.
• The SI unit of momentum is the kilogram-meter per
  second (kgm/s) which is equivalent to the
  newton-second (Ns).

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WHAT?

• ??? F ma ?p/?t ???
• First how is acceleration defined?
• Substitute into OUR version of Newtons 2nd Law
  and voila!

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So what is this momentum thing quantity of
motion?

• TRUCK STOP
• Conceptually, think of momentum as inertia in
  motion. Newtons first law explains that objects
  in motion want to stay in motion.
• But just how much do moving objects wish to stay
  in motion?
• Does a 1 kg skate moving at 10 m/s want to stay
  in motion as much as a 10,000 kg truck moving at
  the same speed?
• To answer, think about which one would be harder
  to stop.
• Better yet, which one would you rather have
  approaching you?

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Other NEW things!

• Impact the force that causes a change in
  momentum
• When a golf club hits a golf ball the club
  exerts a force on the ball (and by Newtons ___
  Law the ball exerts an equal and opposite force
  on the golf club). This force of IMPACT changes
  the balls momentum takes it from a state of
  rest to a state of motion.
• Impulse the change in momentum
• How can momentum change?
• Change mass (pulling a wagon full of sand (with
  a hole) at a constant velocity
• Change velocity throwing a football (the most
  likely situation)
• Change both mass and velocity pulling a wagon
  full of sand (with a hole) while changing
  velocity
• What must happen for momentum to change?
• There must be force time!
• Recall the ORIGINAL VERSION of Newtons 2nd Law
• Dont confuse the Is!

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So what have you learned?

• Which has more momentum?
• A railroad car at rest
• A sprinter running the 100 m dash
• Suppose you punch the wall. Which experiences
  the greater impact?
• Your fist
• The wall
• How could you reduce the impact? In other words,
  why is it better for your hand to punch a
  mattress instead of the wall?
• Suppose while playing pool you hit the stationary
  eight ball with the cue ball. Which ball
  experiences the greater impulse?
• The eight ball
• The cue ball
• Not enough information what happens after they
  collide
• Which requires more impulse?
• A ball that is dropped and stays on the floor
• A ball with the same mass that is dropped (from
  the same height) and bounces

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Examples with numbers

• Bernie, whose mass is 70.0 kg, leaves a ski jump
  with a velocity of 21.0 m/s. What is the
  magnitude of Bernies momentum as he leaves the
  ski jump?
• Tiger Woods hits a 0.050 kg golf ball, giving it
  a speed of 75 m/s. What impulse does he impart
  to the ball?
• A tennis ball traveling at 10.0 m/s is returned
  by Venus Williams. It leaves her racket with a
  speed of 36.0 m/s in the opposite direction from
  which it came.
• What is the change in momentum of the 0.060 kg
  ball?
• If the ball is in contact with the racket for
  0.020 s, with what average force has Venus hit
  the ball?