Impulse and Linear Momentum

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Impulse and Linear Momentum
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Definition of Impulse

• Impulse Force x Elapsed Time F(?t)
• The abbreviation for Impulse is I or J but there
  is no commonly accepted abbreviation so it is
  often abbreviated, F(?t).
• The SI Unit for Impulse is Newton?second (N?s).
  There is no shortened form for this unit.
• Impulse is a vector. (More to follow)

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Calculating Impulse (1 dimensional situations)

• An eastward force of 8.0 newtons is applied to a
  stone for 3.0 seconds. What is the impulse
  applied by the force to the stone?
• F(?t) (8.0 N)(3.0 s) 24 N?s (eastward)
• A westward force of 12 newtons is applied to a
  wagon for 2.0 seconds. What is the impulse
  applied by the force to the wagon?
• F(?t) (-12 N)(2.0 s) -24 N?s (westward)
• Note that although the magnitudes of the forces
  in the two examples are different, the magnitudes
  of the impulses are the same. Why is this so?

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Definition of Linear Momentum

• Linear Momentum mass x velocity mv
• The abbreviation for linear momentum is p, so p
  mv.
• The SI Unit for linear momentum is kg?m/s.
• N?s (kg?m/s2)?s kg?m/s, so the SI Unit for
  linear momentum is the same as the SI Unit for
  impulse.
• Linear Momentum is a vector just as impulse is.

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Calculating Linear Momentum (1 dimensional
situations)

• A 1200 kg car travels northward at a speed of 15
  m/s. What is the linear momentum of the car?
• p mv (1200 kg)(15 m/s) 1.8 x104 kg?m/s
  (northward)
• A 1800 kg car travels southward at a speed of 10
  m/s. What is the linear momentum of the car?
• p mv (1800 kg)(-10 m/s) -1.8 x104 kg?m/s
  (southward)
• Note that although the magnitudes of the
  velocities in the two examples are different, the
  magnitudes of the linear momenta are the same.
  Why is this so?

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The Impulse-Momentum Theorem

• Derivation
• F ma m(?v/?t)
• THUS F(?t) m(?v) ?p
• SO..
• Impulse change in linear momentum

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Application of the Impulse-Momentum Theorem

• A 50 kg grocery cart is rolling along the floor
  at a speed 4.0 m/s. What force must be applied
  to the cart to slow it down to 1.5 m/s in 5.0
  seconds?
• Solution
• pi mvi (50 kg)(4.0 m/s) 200 kg?m/s
• pf mvf (50 kg)(1.5 m/s) 75 kg?m/s
• ?p pf pi 75 kg?m/s - 200 kg?m/s -125
  kg?m/s
• F(?t) ?p thus F(5.0 s) -125 kg?m/s
• F -25 kg?m/s2 -25 N

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Another Example of the Impulse-Momentum Theorem

• A 2.0 kg stone slides eastward along the ice
  initially at 15 m/s. A westward force of 10 N
  acts on the stone for 4.0 seconds. What is the
  velocity of the stone after the force is applied?
• Solution
• F(?t) (-10 N)(4.0 s) -40 N?s ?p
• pi mvi (2.0 kg)(15 m/s) 30 kg?m/s
• ?p pf pi thus -40 N?s pf - 30 kg?m/s
• So pf -10 kg?m/s
• vf pf / m (-10 kg?m/s) / 2.0 kg -5.0 m/s
  (westward)