6 Overview
• Momentum and its Conservation
• Collisions and Impulse
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Homework:
RQ: 2, 3, 4, 5, 8, 16, 18, 19.
Ex: 14, 24, 31, 35, 47, 51.
Problems: 1, 3, 6.
1
How do we measure amount of
motion?
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velocity (how fast)
mass (how much)
with equal importance
mass x velocity = “momentum”
2
Momentum
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Momentum = mv
SI Unit: kg·m/s
Ex. 1000kg car moves at 8m/s.
mv = (1000kg)(8m/s) = 8,000 kg·m/s
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Motion and Its Conservation
Not
Conserved
Conserved
Conserved
Not
Not
Conserved
Conserved
stops
smooth and level
rough
4
Impulse and Momentum
• Impulse = Ft
• consequence of Newton’s 2nd law that Ft =
change in momentum
• F = ma
• Ft = mat
• Ft = (m)(at)
• Ft = (m)(Dv)
• N·s = kg·m/s
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Impulse Example
• A braking force of 4000N acts for 0.75s on
a 1000kg car moving at 5.0m/s.
• impulse = Ft = (4000N)(0.75s) = -3000
N·s
• Ft = mDv = -3000 kg·m/s
• initial momentum = mvi = (1000)(5) =
5000
• final momentum = mvi + mDv
• = 5000 kg·m/s + (-3000 kg·m/s)
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• = 2000 kg·m/s
Collisions
• ‘brief’ interaction (between masses)
• Types:
• Inelastic (heat, sound, etc. are generated).
Ex. Almost all collisions are inelastic.
• Elastic (no heat, sound, etc. is created).
Ex. Two magnets ‘collide’ without
touching.
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Conservation of Momentum
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two objects “bump” into one another
forces are opposite by Newton’s 3rd Law
e.g., object 1: -Ft, object 2: +Ft
net impulse to System = -Ft + Ft = 0
net change in momentum due to the bump
is zero.
• If no other net-force acts, Then total
momentum of objects is same
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Effect of Interactions
m1
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m2
bigger mass moves slower
smaller mass moves faster
momentums are equal and opposite
momentum of system is unchanged
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2 Object Momentum Conservation
• momentum before = momentum after
• (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final
• When can we use this equation?
• When net force due to all other objects acting
on 1 and 2 is zero.
• Or, very soon after collision ends
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when can momentum
conservation be used?
• objects are on a level, frictionless surface
(e.g. physics lab)
• collision forces much bigger than friction
(often)
• Ex. Rail-car collision force
much bigger than
wheel friction
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Ex. completely inelastic collision
• equal mass rail cars collide
and connect together
• m1 = m2 = m
• i) v1 = 10 v2 = 0
• f) v1 = v2 = vfinal = ?
• (m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final
• m(10) + m(0) = mvfinal + mvfinal .
• 10m = 2mvfinal
• 5 = vfinal
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Ex. 2m versus m
• m1 = 6kg collides with m2 = 3kg.
• i) v1 = 5m/s v2 = 0
• f) v1 = v2 = vfinal = ? (complete inelastic)
• (m1v1)initial + (m2v2)initial = (m1v1)final +
(m2v2)final
• (6kg)(5m/s) + (3kg)(0) = (6kg)(vf)+(3kg)(vf)
• 30kgm/s = (9kg)(vf)
• vf = (30/9)m/s = 3.3m/s
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Ex. 1500kg hits 1000kg
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m1 = 1500kg collides with m2 = 1000kg.
i) v1 = 10m/s v2 = 0
f) v1 = v2 = vfinal = ? (complete inelastic)
try it yourself first
(m1v1)initial + (m2v2)initial = (m1v1)final + (m2v2)final
• (1500kg)(10m/s) + (1000kg)(0) = (1500kg)(vf)+(1000kg)(vf)
• 15,000kgm/s = (2500kg)(vf)
• vf = (15,000/2500)m/s = 6.0m/s
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Two Dimensional Collisions
• Vector System Momentum: conserved in
many situations (at least for a short time)
Example:
pool game, cue ball strikes another ball
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Final Momentum = Initial Momentum
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Bouncing Motion
• bouncing creates more force than stop
• bouncing is two actions: stop & start is
more action than stop alone.
• : D(mv) = final mom. – initial mom.
• Stop:
D(mv) = 0 – mv = – mv
Bounce: D(mv) = –mv – mv = – 2mv
• change in momentum is double for elastic
bounce, thus the impluse is double
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Summary
• mv = momentum
• Impulse = Ft = D(mv)
• momentum is conserved in collisions when
all other forces are small compared to the
collision forces
• momentum is a vector and can be
conserved in one, two, or three
dimensions.
• bouncing causes greater force than a stop
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19
(cont.) Ex. 1500kg hits 1000kg
• impulse received by m2 = change in
momentum of m2 = m2(Dv)
• Ft = m2(Dv) = (1000kg)(6m/s – 0m/s)
• Ft = m2(Dv) = 6000kgm/s
• F = (6000kgm/s)/t
• if t = 1s:
F = (6000kgm/s)/1s = 6,000N
• if t = 0.01s: F = (6000kgm/s)/0.01s = 600,000N
• cars have crumple zones to increase the
collision time & reduce the force
20
Whenever an interaction occurs in a system, forces
occur in equal and opposite pairs. Which of the
following do not always occur in equal and opposite
pairs?
1. Impulses.
2. Accelerations.
3. Momentum changes.
4. All of these occur in equal and opposite pairs.
5. None of these do.
21
Whenever an interaction occurs in a system, forces
occur in equal and opposite pairs. Which of the
following do not always occur in equal and opposite
pairs?
1. Impulses.
2. Accelerations.
3. Momentum changes.
4. All of these occur in equal and opposite pairs.
5. None of these do.
22
An ice sailcraft is stalled
on a frozen lake on a
windless day. A large fan
blows air into the sail. If
the wind produced by the
fan strikes and bounces
backward from the sail,
the sailcraft will move
1. to the left (backward).
2. to the right (forward).
3. not at all.
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An ice sailcraft is stalled
on a frozen lake on a
windless day. A large fan
blows air into the sail. If
the wind produced by the
fan strikes and bounces
backward from the sail,
the sailcraft will move
1. to the left (backward).
2. to the right (forward).
3. not at all.
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Practicing Physics
• p31 #4
• p32 #5
• p33 #1
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