Momentum

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Momentum

• Momentum
• Impulse
• Problems

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Definition The linear momentum p of a particle
is its mass times its velocity
p ? mv
Momentum is a vector, since velocity is a
vector. Units kg m/s
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Impulse
, or dp F dt
Newton 2
For a constant force, Dp F Dt . The vector
quantity F Dt is called the Impulse
J F?t ?p
(change in p) (total impulse from external
forces)
(Newtons Second Law again)
(Extra) In general (force not constant), we
integrate
where the integral gives the area under a curve
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Impulse is the area under the curve. The average
force is the constant force which would give the
same impulse.
Compare with work W F Dx so the work-energy
theorem (derived from Newton 2) is DK F Dx.
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Example

• A golf ball is launched with a velocity of 44
  m/s. The ball has a mass of 50g. Determine the
  average force on the ball during the collision
  with the club, if the collision lasted 0.01 s.

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Example

• Use the impulse-momentum theorem to find how long
  a falling object takes to increase its speed from
  5.5m/s to 10.4m/s.

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Example

• A 150 g baseball is thrown with a speed of 20m/s.
  It is hit straight back toward the pitcher at a
  speed of 40m/s. The interaction force is shown
  by the graphWhat is the maximum force
  Fmax that the bat exerts on the ball ?

Fmax
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Example the fire extinguisher
How can we calculate the backwards force a fire
extinguisher exerts on the operator?
Plan Calculate the momentum transferred to the
gas in an arbitrary time Dt this is equal to the
impulse the gas gets from the extinguisher
nozzle.
From Newtons Third Law, the nozzle gets an equal
but opposite impulse (somehow) from the gas.
Since impulse is FDt, divide by Dt to get the
force.
Result F (speed of gas) x (mass of gas ejected
per unit time)
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Concept Quiz

• A 100g rubber and a 100g clay ball are thrown at
  a wall with equal speed. The rubber ball bounces
  back while the clay ball sticks to the
  wall.Which ball exerts a larger impulse on the
  wall ?
• the clay bass b/c it sticks
• the rubber ball b/c it bounces
• they are equal because the have equal momenta
• neither exerts an impulse b/c the wall doesnt
  move