Momentum

1
Momentum

• The secret of collisions explosions

2
Who Pushes Who

• Rin Tin Tin and the Refrigerator meet at the 50
  yard line

Mass 20 Kg Speed 17 m/s
Mass 160 Kg Speed 2 m/s
Who pushes who over the 50 yard line?
3
Momentum Mass x Velocity

• Whoever has the most momentum mv wins

Mass 20 Kg Speed 17 m/s
Mass 160 Kg Speed 2 m/s
Momentum 320 Kg m/s
Momentum 340 Kg m/s
4
Momentum mv

• Mass times velocity!
• Velocity is a vector but here we can usually
  think of it as speed
• Example A speeding car has a mass of 1000 Kg
  and a speed of 20 m/s. What is its momentum?
• mv 1000kg x 20 m/s 20,000 kg m/s

5
Unit of Momentum

• Kg m/s

No nickname like Newton maybe it could have
been called an Isaac.
Jump to conservation
6
Momentum is a Vector

• p mv
• Force is required to change the momentum of an
  object. Newton stated his 2nd law
• SF Dp/Dt
• The rate of change of momentum of a body equals
  the net force exerted on it
• Equivalent to F ma

7
Proof of equivalence of two forms of Newtons 2nd
Law

• SF Dp/Dt (mv mv0)/Dt
• m(v - v0)/ Dt mDv/Dt ma

Q Which form of the law is more general? (which
includes the possibility that the mass could
change?)
8
Example

• Water leaves a hose at a rate of 1.5 kg/s with
  speed 20 m/s and hits a car without splashing
  back. What force is exerted by the water on the
  car?
• F Dp/Dt (p final - pinitial )/ Dt (0
  30kg m/s)/1sec -30N

9
Momentum is Conserved

• The total momentum of an isolated system of
  bodies remains the same
• isolated means net external force is zero
• Momentum before momentum after
• m1v1 m2v2 m1v1 m2v2
• Applies to all interactions, especially
  collisions, explosion-like events, and dumpings
• Closely related to Newtons 3rd law

10
Law of Conservation of Momentum

• Momentum before momentum after
• m1v1 m2v2 m1v1 m2v2

Apostrophe thingee is pronounced prime
11
Two Kinds of Collision
Courtesy Deer Vally HS Espace Academy

• Inelastic - sticking
• Examples glue balls fly into each other,air
  track gliders with clay
• Elastic bouncing
• Examples hard balls or protons collide

Courtesy St. Mary College Physics Department
12
Two Kinds of Collision(video)

• Inelastic - sticking
• Examples glue balls fly into each other,air
  track gliders with clay
• Elastic bouncing
• Examples hard balls or protons collide

Courtesy Stephanie Wong
Courtesy St. Mary College Physics Department
13
Video Full Screen
14
New Vocabulary

• Momentum
• Conserved
• Isolated
• Elastic collision
• Inelastic collision

Mass times velocity
Stays the same
By itself, net force on it is zero
Objects bounce
Objects stick
15
Objects moving toward each other

• If two carts of equal mass approach each other
  with equal speed what is the total momentum
  before collision?

Answer zero
16
Dumping Example
Courtesy Easyhaul Cart Inc.

• A 10 kg cart rolls on a frictionless track at
  speed v. Suddenly 10 kg of rocks are dropped
  straight down into the cart. What happens to its
  speed? How come?

Answer v/2 momentum mv is conserved, m
is doubled so v must be halved.
17
Explain This

• A rock falls to earth. Is momentum conserved?
  Include earth in your explanation
• Does the earth really come up to meet the rock?

18
You Predict

• Glider moving with speed v hits glider of equal
  mass at rest. They stick. What will be speed of
  stuck together gliders after the collision?

Answer v/2
19
Railroad Cars CollideInelastically(stick)

• A 10,000 kg railcar moving 2.4 m/s hits and
  sticks with an identical car at rest. What is
  the final speed of the two cars?
• m1v1
  m2v2
  (10,000 kg) (2.4 m/s)
  (10,000 kg) (0m/s)
• 24,000 kg m/s 0 kg m/s (m1
  m2)v
• so v 24,000 kg m/s / 10,000 kg 10,000 kg
• v 24,000 kg m/s /20,000 kg 1.2 m/s

20
New example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider at
  rest. What is the final speed of the two joined
  together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s 0 kg m/s (4kg) (vf)
• vf 3 m/s

21
Next example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider moving
  to the right at 1.0 m/s. What is the final speed
  of the two joined together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s 1kg m/s 13 kg m/s (4.0 kg)
  (vf)
• vf 3.25 m/s

22
Next example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider moving
  to the right at 2.0 m/s. What is the final speed
  of the two joined together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s 1 kg x 2 m/s 14 kg m/s 4.0 kg vf
• vf 3.50
  m/s

23
Next example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider moving
  to the left at 1.0 m/s. What is the final speed
  of the two joined together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s 1 kg x 1 m/s 11 kg m/s 4.0 kg vf
• vf 2.75
  m/s

24
Next example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider moving
  to the left at 5.0 m/s. What is the final speed
  of the two joined together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s - 1kg x 5 m/s 7 kg m/s 4.0 kg
  vf
• vf 1.75
  m/s

25
Next example

• A 3 kg glider moves to the right at 4.0 m/s and
  collides inelastically with a 1 kg glider moving
  to the left at 20.0 m/s. What is the final speed
  of the two joined together gliders?
• m1v1 m2v2 (m1 m2) vf
• 12 kg m/s - 1kg x 20 m/s -8 kg m/s 4.0 kg
  vf
• vf -2.00
  m/s

26
Sled Collision

• Kids on a sled, total mass 100kg move to the
  right at 4.0 m/s. They collide inelastically
  with other kids, mass 150 kg, moving to the left
  at 2.5 m/s. Find the final velocity of the two
  sleds.

27
solution

• m1v1 m2v2
  (m1 m2)v
• 100Kg x 4m/s 150Kg x 2.5m/s
• 400 Kg m/s 375 Kg m/s
• 25 Kg m/s
  250 Kg x Vf
• Vf 0.1 m/s

28
Sled Collision in reverse

• Kids on a sled, total mass 100kg move to the
  right at unknown speed v. They collide
  inelastically with other kids, mass 150 kg,
  moving to the left at 2.5 m/s. The final
  velocity of the two sleds is 0.2 m/s. Find v

29
Explosion like Event

• If a stationary student on a skateboard throws a
  rock with momentum 10 kg m/s, what momentum will
  the student get?

Answer -10 kg m/s (Newtons 3rd Law)
30
Recoil of a pistol (an explosion-like event)

• What is the recoil velocity of a 1 kg pistol
  that shoots a .02 kg bullet at 400 m/s?
• Initial momentum 0
• mBvB
  mpvp
• (0.02kg x 400 m/s) 1kg x vp
  
• vp - 8 m/s Q Does the shooter recoil too?

Skip Think and Solve 63 65
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Think and Solve
63) m1v1 m2v2 m1v1 m2v2
Let mass of flat car m Then
mass of diesel engine 4m v1
5 km/h v2 0 4 m X 5 km/h 0 5 m X
Vf 20 m 5m X Vf
Vf 4 km/h
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65) A) 5 kg X 1 m/s 0 6 kg X Vf
Vf 5/6 m/s B) 5 kg X 1
m/s 1 kg X 4 m/s 6 kg X Vf
5 kg m/s 4 kg m/s 6 kg X Vf
1 kg m/s 6 kg Vf
Vf 1/6 m/s
33
Impulse Why should you

• Bend your knees when you land?
• Pull back when the baseball enters
• your mitt?
• Follow through when you swing?
• Not walk into a punch?
• (like Mike Tyson did)

34
Impulse

• Impulse F Dt Dp
• Impulse is product of force and time during
  which force acts
• Impulse equals change of momentum
• F is usually non uniform and time interval is
  usually short

35
You Predict

• Two gliders of equal mass collide elastically.
  The first is moving with speed v. The second is
  at rest. What happens?

First one stops, second moves off at speed v
But why? Find the answer yourself and get extra
credit
36
Energy Conservation in Elastic and Inelastic
Collisions

• Elastic kinetic energy is conserved as well as
  momentum and total energy
• Inelastic kinetic energy is not conserved
  some energy turns into heat
• Elastic bounce
• Completely inelastic - stick

37
Ballistic Pendulum

• A bullet of mass m is fired into a block of wood
  of mass M suspended from a string. The bullet
  remains in the block which rises a height h.
  What was the speed of the bullet? Show that
• v (2gh)1/2(m M)/m
• 
  

h
38
Collisions in Two Dimensions

• Remember momentum p is a vector
• x and y components are conserved separately
• What is the total vertical momentum?

q1
q2