6 Overview

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6 Overview

• Momentum and its Conservation
• Collisions and Impulse
• Homework
• RQ 2, 3, 4, 5, 8, 16, 18, 19.
• Ex 14, 24, 31, 35, 47, 51.
• Problems 1, 3, 6.

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How do we measure amount of motion?

• velocity (how fast)
• mass (how much)
• with equal importance
• mass x velocity momentum

3
Momentum

• Momentum mv
• SI Unit kgm/s
• Ex. 1000kg car moves at 8m/s.
• mv (1000kg)(8m/s) 8,000 kgm/s

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Motion and Its Conservation
Not Conserved
Not Conserved
Not Conserved
Conserved
Conserved
stops
smooth and level
rough
5
Impulse and Momentum

• Impulse Ft
• consequence of Newtons 2nd law that Ft change
  in momentum
• F ma
• Ft mat
• Ft (m)(at)
• Ft (m)(Dv)
• Ns kgm/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 Ns
• Ft mDv -3000 kgm/s
• initial momentum mvi (1000)(5) 5000
• final momentum mvi mDv
• 5000 kgm/s (-3000 kgm/s)
• 2000 kgm/s

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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

• two objects bump into one another
• forces are opposite by Newtons 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

• 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 collideand 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

• 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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(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

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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.
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1. Impulses.2. Accelerations.3. Momentum
changes.4. All of these occur in equal and
opposite pairs.5. None of these do.
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?
23
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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1. to the left (backward).2. to the right
(forward).3. not at all.
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
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Practicing Physics

• p31 4
• p32 5
• p33 1