Momentum : Real World Examples

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Momentum Real World Examples
Book Reference Pages 4-17
Learning Objectives

• To Summarise what has been learnt about momentum
  by looking at real world examples.
• Rebound impacts including oblique impacts
• Dropped balls
• Explosions Guns
• Rockets Water jets

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Rebound Impacts 1
We have seen that momentum is a vector quantity
since its related to velocity which is a vector
quantity. ? direction is important and therefore
we need a sign convention to take this into
account. If we consider a ball with mass m
hitting a wall and rebounding normally, (i.e. at
90)
Towards the wall we can take as positive Away
from the wall we can take as negative
Initial velocity u Initial momentum mu
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Rebound Impacts 2
Final velocity -u Final momentum -mu
If we assume there is no loss of speed after the
impact then considering the change in
momentum... Ft final momentum initial
momentum Ft -mu (mu) F -2mu /t
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Rebound Impacts 3
When the impact is oblique, (i.e. At an angle,
not normally at 90)
?
?
Initial velocity u Initial momentum mu
In this case we use the normal components of the
velocity. Initially, this is (u cos ?).
Similarly this will give an overall change in
momentum of Ft -2mu cos ?
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Dropped Bouncing balls 1
If we drop a perfectly bouncy ball onto a hard
surface it should rebound to almost the original
height it was dropped from. Kinetic energy just
prior to impact will equal kinetic energy just
after impact if it is a perfect elastic
collision In this way we can make a connection
between elastic and a perfectly bouncy ball
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Dropped Bouncing balls 2
When approaching dropped ball calculations one
applies our SUVAT equations in a manner similar
to the way we approached projectiles
v u at (1) s (u v)t (2) 2 s ut
½at2 (3) v2 u2 2as (4)
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Explosions 1
Explosion problems are categorised by all the
components initially being at rest. Then after
some event, two or more objects move apart. Since
initially all objects are at rest, the total
initial momentum is zero We use the signed
nature of direction to again equate the total
final momentum to zero Common examples include,
trolleys or air track vehicles pushed part by
springs or by repelling magnets The recoil in gun
barrels is also a good example
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Explosions 2
Explosion problems can be tested with either
sprung trolleys or air track vehicles
Spring loaded bolt
Block
Block
B
Trolley A
Trolley B
A
When the sprung bolt is released the two trolleys
move apart in opposite directions. The blocks A
and B are positioned such that the trolleys
strike them at the same moment. From sd/t, since
the time is identical, the ratio of the distances
to the blocks is the same as the ratio of the
speeds of the trolleys which is turn is the
inverse of the mass ratios.
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Rockets
When a rocket fires its engines the rocket gains
momentum equal and opposite to the momentum of
the hot exhaust gases. For example we could be
told that a 20,000kg rocket at rest fires its
rocket for 10s. The exhaust gases leave at
100kgs-1 at a speed of 1kms-1. Show that the
final velocity of the rocket is 53ms-1
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Water jets

• Water of density 1000 kg m-3 flows out of a hose
  pipe with cross sectional area 7.2x10-4 m2 at a
  rate of 2.0 x 10-4 m3 per second. How much
  momentum is carried by the water each second?
• First we need to consider the mass each second.
  Knowing the volume and density we can find the
  mass
• m/v ?m ?v
• Mass each second 1000 x 2x10-4 0.2kg per
  second
• Next we need to consider the velocity. We know
  the volume leaving each second and also the area.
  We effectively have a cylinder of length 2x10-4 /
  7.2 x10-4 0.278 m. Hence the velocity is 0.278
  ms-1
• Momentum each second 0.2 x 0.278 0.056 kgms-1

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Problems 1...
A squash ball is released from rest above a flat
surface. Describe how the energy changes if i) it
rebounds to the same height, ii) It rebounds to a
lesser height If the ball is released from a
height of 1.20m and rebounds to a height of 0.9m
show that 25 of the kinetic energy is lost upon
impact
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Problems 2...

• A shell of mass 2kg is fired at a speed of
  140ms-1 from a gun with mass 800kg. Calculate the
  recoil velocity of the gun
• A molecule of mass 5.0 x 10-26 kg moving at a
  speed of 420ms-1 hits a surface at right angles
  and rebounds at the opposite direction at the
  same speed. The impact lasted 0.22ns. Calculate
• The change in momentum
• The force on the molecule
• Repeat the last question. This time the molecule
  strikes the surface at 60 to the normal and
  rebounds at 60 to the normal.