Momentum and Its Conservation - Chapter Outline

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Momentum and Its Conservation - Chapter Outline

• Lesson 1 The Impulse-Momentum Change Theorem
• Lesson 2 The Law of Momentum Conservation

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Lesson 1 The Impulse-Momentum Change Theorem

• Momentum
• Momentum and Impulse Connection
• Real-World Applications

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Momentum

• Momentum can be defined as "mass in motion."
• The amount of momentum that an object has is
  dependent upon two variables how much stuff is
  moving and how fast the stuff is moving.

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Momentum equation
Momentum mass velocity
p m v
m mass in kg v velocity in m/s p momentum in
kgm/s
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Momentum is a vector quantity

• The direction of the momentum vector is the same
  as the direction of the velocity of the ball.
  Which is the same as the direction that an object
  is moving.

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Both variables - mass and velocity - are of equal
importance in determining the momentum of an
object

• Momentum is directly proportional to mass and
  momentum is directly proportional to velocity
• Consider a 0.5-kg physics cart loaded with one
  0.5-kg brick and moving with a speed of 2.0 m/s.
  Its momentum is 2.0 kgm/s. If the cart was
  instead loaded with three 0.5-kg bricks, then the
  total mass of the loaded cart would be 4.0
  kgm/s. A doubling of the mass results in a
  doubling of the momentum.
• Similarly, if the 2.0-kg cart had a velocity of
  8.0 m/s (instead of 2.0 m/s), then the cart would
  have a momentum of 16.0 kgm/s (instead of 4.0
  kgm/s). A quadrupling in velocity results in a
  quadrupling of the momentum.

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Momentum and Impulse Connection

• Momentum is defined as mass in motion. To stop
  the momentum, it is necessary to apply a force
  against its motion for a given period of time.
• The more momentum that an object has, the greater
  amount of force or a longer amount of time or
  both is required.
• As the force acts upon the object for a given
  amount of time, the object's velocity is changed
  and hence, the object's momentum is changed.

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A force acting for a given amount of time will
change an object's momentum.

• An unbalanced force always accelerates an object
  - either speeding it up or slowing it down.
• If the force acts opposite the object's motion,
  it slows the object down. Momentum would decrease
• If a force acts in the same direction as the
  object's motion, Momentum would increase
• A force will change the velocity of an object.
  And if the velocity of the object is changed,
  then the momentum of the object is changed.

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Revisit of Newton's second law

• Newton's second law Fnet m a
• a ?v / t

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Impulse

• The quantity Force time is known as impulse.

J Ft
F is the force in N t is time in s. J is the
impulse in Ns

• Impulse is a vector quantity, its direction is
  the same as the net force F.

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example

• If a halfback experienced a force of 800. N for
  0.90 s to the North, determine the impulse.

J Ft J 800 N x 0.90 s 720 Ns North A
change of momentum of the halfback is 720 kgm/s
North
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example

• A 0.10-kilogram model rockets engine is designed
  to deliver an impulse of 6.0 newton-seconds. If
  the rocket engine burns for 0.75 second, what
  average force does it produce?

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example

• In the diagram, a 60.-kilogram rollerskater
  exerts a 10.-newton force on a 30.-kilogram
  rollerskater for 0.20 second. What is the
  magnitude of the impulse applied to the
  30.-kilogram rollerskater?

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Impulse Change in momentum

• Since mv is momentum m?v is change in momentum
• The above is known as impulse-momentum change
  equation.
• In a collision, an object experiences a force for
  a specific amount of time that results in a
  change in momentum. The impulse experienced by
  the object equals the change in momentum of the
  object.

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example

• If the halfback experienced a force of 800 N for
  0.9 seconds, then we could say that the impulse
  was _______________
• This impulse would cause a momentum change of
  ____________
• In a collision, the impulse experienced by an
  object is always equal to the momentum change.

720 Ns
720 kgm/s
Note the unit Ns kgm/s
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A special case of collision - rebound

• A rebound is a special type of collision
  involving a direction change in addition to a
  speed change.
• The result of the direction change is a large
  velocity change.

• Example a 0.1 kg ball tennis ball bounces off
  the wall as shown. Determine the impulse on the
  ball for case A and case B.

Case A 1.5 kgm/s, left
Case A 5.8 kgm/s, left

• Rebound involves large velocity change and
  therefore large impulse and large force.

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Example fill in blanks
-40
-40
-4000
-40
-400
-4
-200
-20000
-4
-200
25
0.01
-4
-200
-200

Note 1. the impulse is always equal to the
momentum change 2. force and time are inversely
proportional
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Example J Ft m?v

• A bullet traveling at 5.0 x102 m/s is brought to
  rest by an impulse of 50. Ns.  What is the mass
  of the bullet?

J m?v - 50 Ns m (0 5.0 x 102 m/s) m 1.0
x 10-1 kg
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Example J Ft m?v

• A 5.00 kg mass is traveling at 100. m/s.
  Determine the speed of the mass after an impulse
  of 30.0 Ns is applied.

Given m 5.00 kg vi 100. m/s J 30.0
Ns Find vf ? m/s
Solution J ?p m (vf - vi) 30.0 Ns (5.00
kg)(vf 100. m/s) vf 106 m/s
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example

• A 1,000-kilogram car traveling due east at 15
  meters per second is hit from behind and receives
  a forward impulse of 8,000 newton-seconds.
  Determine the magnitude of the car's change in
  momentum due to this impulse.

8,000 kgm/s
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example

• If a net force of 10. newtons acts on a
  6.0-kilogram mass for 8.0 seconds, what is the
  total change of momentum of the mass?

Impulse equals to change of momentum J Ft
(10. N)(8.0 s) 80. kgm/s
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example

• A student drops two eggs of equal mass
  simultaneously from the same height.  Egg A lands
  on the tile floor and breaks.  Egg B lands
  intact, without bouncing, on a foam pad lying on
  the floor. 

• Both eggs have the same impulse
• Egg A has shorter time of impact, and bigger
  impact force.
• Egg B has longer time of impact, and smaller
  impact force

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question

• True or False?
• When a dish falls, the impulse is less if it
  lands on a carpet than if lands on hard floor.

• False. the impulse would be the same for either
  surface because the same momentum change occurs
  for each. It is the force that is less for the
  impulse on the carpet because of the greater time
  of momentum change.

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Check your understanding
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practice

• Castle learning Momentum Impulse connection
  practice

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Real-World Applications

• The effect of collision time upon the amount of
  force an object experiences
• The effect of rebounding upon the velocity change
  and hence the amount of force an object
  experiences.

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The Effect of Collision Time upon the Force
Combinations of Force and Time Required to
Produce 100 units of Impulse
The greater the time over which the collision
occurs, the smaller the force acting upon the
object. To minimize the effect of the force on
an object involved in a collision, the time must
be increased. To maximize the effect of the
force on an object involved in a collision, the
time must be decreased.

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Reduce force by increase time

• Air bags are used in automobiles because they are
  able to minimize the affect of the force on an
  object involved in a collision. Air bags
  accomplish this by extending the time required to
  stop the momentum of the driver and passenger.
• Padded dashboards also reduces force by increase
  time.
• A boxer rides the punch in order to extend the
  time of impact of the glove with their head.
• Nylon ropes are used in the sport of
  rock-climbing because of its ability to stretch.
  The rock climber can appreciate minimizing the
  effect of the force through the use of a longer
  time of impact .

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Increase velocity by increasing time Ft m?v

• In racket and bat sports, hitters are often
  encouraged to follow-through when striking a
  ball.

• In this situation, both the force applied (as
  hard as you can) and the mass (the mass of the
  ball) are constant. By following through, the
  hitter increases the time, the result is
  increasing the balls velocity.

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The Effect of Rebounding

• Bouncing off each other is known as rebounding.
  Rebounding involves a change in the direction of
  an object rebounding situations are
  characterized by
• a large velocity change
• a large momentum change.
• a large impulse

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• The importance of rebounding is critical to the
  outcome of automobile accidents.
• Automobiles are made with crumple zones. Crumple
  zones minimize the affect of the force in an
  automobile collision in two ways.
• By crumpling, the car is less likely to rebound
  upon impact, thus minimizing the momentum change
  and the impulse.
• The crumpling of the car lengthens the time over
  which the car's momentum is changed by
  increasing the time of the collision, the force
  of the collision is greatly reduced.

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example

• A constant force can act on an object for
  different lengths of time. As the length of time
  the force acts increases,
• the impulse imparted to the object
• decreases
• increases
• remains the same
• The momentum of the object
• decreases
• increases
• remains the same

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question

• A cannonball shot from a long-barrel cannon
  travels faster than one shot from a short-barrel
  cannon because the cannonball receives a greater
• a. force.
• b. impulse.
• c. both A and B
• d. neither A nor B

A cannonball shot from a cannon receive the same
force regardless of the length of its barrel. A
long-barrel will take longer time (t) for the
cannonball to travel. Since J Ft m?v, the
longer the time, the bigger the impulse, the
faster it will travel.
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Lesson 2 The Law of Momentum Conservation

• The Law of Action-Reaction (Revisited)
• Momentum Conservation Principle
• Isolated Systems
• Momentum Conservation in Collisions
• Using Equations as a "Recipe" for Algebraic
  Problem-Solving
• Using Equations as a Guide to Thinking
• Momentum Conservation in Explosions

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The Law of Action-Reaction (Revisited)

• In a collision between two objects, both objects
  experience forces that are equal in magnitude and
  opposite in direction in accord with Newtons 3rd
  Law.

While the forces are equal in magnitude and
opposite in direction, the accelerations of the
objects are not necessarily equal in magnitude.
According to Newton's second law of motion, the
acceleration of an object is dependent upon both
force and mass.
Bigger mass has smaller acceleration, smaller
mass has bigger acceleration
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3rd law - check your understanding

• practice

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Momentum Conservation Principle

• The law of momentum conservation can be stated as
  follows.
• For a collision occurring between object 1 and
  object 2 in an isolated system, the total
  momentum of the two objects before the collision
  is equal to the total momentum of the two objects
  after the collision. That is, the momentum lost
  by object 1 is equal to the momentum gained by
  object 2.

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• Consider a collision between two objects - object
  1 and object 2.

1.
2.
3.
4.
m1?v1 -m2?v2
m1(v1 v1) -m2(v2 v2)
m1v1 m2v2 m1v1 m2v2
p(before) p(after)
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Momentum is conserved
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Consider a fullback plunges across the goal line
and collides in midair with the linebacker in a
football game. The linebacker and fullback hold
each other and travel together after the
collision. Before the collision, the fullback
possesses a momentum of 100 kgm/s, East and the
linebacker possesses a momentum of 120 kgm/s,
West. The total momentum of the system before the
collision is _____________________. Therefore,
the total momentum of the system after the
collision must also be __________________
20 kgm/s, West
20 kgm/s, West.
Vector diagram for the situation
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• consider a medicine ball is thrown to a clown who
  is at rest upon the ice the clown catches the
  medicine ball and glides together with the ball
  across the ice.
• The momentum of the medicine ball is 80 kgm/s
  before the collision. The momentum of the clown
  is 0 kgm/s before the collision. The total
  momentum of the system before the collision is
  ______________
• Therefore, the total momentum of the system after
  the collision must also be ________________. The
  clown and the medicine ball move together as a
  single unit after the collision with a combined
  momentum of 80 kgm/s. Momentum is conserved in
  the collision.

80 kgm/s.
80 kgm/s.
Vector diagram for the situation
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example

• Four billiard balls, each of mass .5 kg, all are
  traveling in the same direction on a billiard
  table, with speeds 2 m/s, 4 m/s, 8 m/s and 10
  m/s. What is the linear momentum of this system?
• If all four balls collide, what is the total
  momentum after the collision?

ptotal p1 p2 p3 p4 ptotal (0.5 kg)(2
m/s 4 m/s 8 m/s 10 m/s) ptotal 12 kgm/s
12 kgm/s
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example

• A 2.0-kilogram ball traveling north at 5.0 meters
  per second collides head-on with a 1.0 kilogram
  ball traveling south at 8.0 meters per second.
  What is the magnitude of the total momentum of
  the two balls after collision?

m1v1 m2v2 m1v1 m2v2
m1 2.0 kg v1 5.0 m/s m2 1.0 kg v2 -8.0
m/s
pafter ?
m1v1 m2v2 pafter (2.0 kg)(5.0 m/s) (1.0
kg)(-8.0 m/s) pafter 2 kgm/s, north pafter
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Check your understanding

• practice

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Isolated Systems

• Total system momentum is conserved for collisions
  occurring in isolated systems. But what makes a
  system of objects an isolated system?

• A system is a collection of two or more objects.
  An isolated system is a system which is free from
  the influence of a net external force which
  alters the momentum of the system.

• A system in which the only forces which
  contribute to the momentum change of an
  individual object are the forces acting between
  the objects themselves can be considered an
  isolated system.

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No
friction
The friction between the carpet and the floor and
the applied force exerted by Hans are both
external forces.
No

yes
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• Because of the inevitability of friction and air
  resistance in any real collision, one might can
  conclude that no system is ever perfectly
  isolated.

• In any real collision, resistance forces such as
  friction and air resistance are inevitable.
  However, compared to the impact force, they are
  very small, and they can be ignored.

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Using Equations for Algebraic Problem-Solving

• Total system momentum is conserved for collisions
  between objects in an isolated system.

pbefore pafter
m1v1 m2v2 m1v1 m2v2
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Example

• A 3000-kg truck moving with a velocity of 10 m/s
  hits a 1000-kg parked car. The impact causes the
  1000-kg car to be set in motion at 15 m/s.
  Assuming that momentum is conserved during the
  collision, determine the velocity of the truck
  immediately after the collision.

It is a collision problem, momentum is conserved.
m1v1 m2v2 m1v1 m2v2
m1 3000 kg v1 10 m/s m2 1000 kg v2 0
v1 ? v2 15 m/s
(3000 kg)(10 m/s) 0 (3000 kg)v (1000
kg)(15 m/s)
30000 kgm/s (3000 kg)v 15000 kgm/s
v 5 m/s
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Example

• A 15-kg medicine ball is thrown at a velocity of
  20 km/hr to a 60-kg person who is at rest on ice.
  The person catches the ball and subsequently
  slides with the ball across the ice. Determine
  the velocity of the person and the ball after the
  collision.

m1v1 m2v2 m1v1 m2v2
m1 15 kg v1 20 km/hr m2 60 kg v2 0

v1 v2 v
(15 kg)(20 km/hr) (60 kg)(0)(15 kg)v (60
kg)v
300 kgkm/hr (75 kg)v
v 4 km/hr
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Example

• A 0.150-kg baseball moving at a speed of 45.0 m/s
  crosses the plate and strikes the 0.250-kg
  catcher's mitt (originally at rest). The
  catcher's mitt immediately recoils backwards (at
  the same speed as the ball) before the catcher
  applies an external force to stop its momentum.
  Determine the post-collision velocity of the mitt
  and ball.

m1v1 m2v2 m1v1 m2v2
m1 0.150 kg v1 45.0 m/s m2 0.250 kg v2
0
v1 v2 v
(0.15 kg)(45.0 m/s) 0 (0.15 kg)v (0.25 kg)v
6.75 kgm/s (0.40 kg)v
v 16.9 m/s
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Elastic and inelastic collisions

• The two collisions above are examples of
  inelastic collisions.
• An inelastic collision is a collision in which
  the kinetic energy of the system of objects is
  not conserved. It is transformed into other
  non-mechanical forms of energy such as heat
  energy and sound energy.
• To simplify matters, we will consider any
  collisions in which the two colliding objects
  stick together and move with the same
  post-collision speed to be an extreme example of
  an inelastic collision.
• In an elastic collision, the two objects do not
  stick together. they will bounce off each other.
• In an elastic collision, kinetic energy is
  conserved.

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Elastic or inelastic collision?
Inelastic collision
elastic collision
Inelastic collision
elastic collision
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A special case of collision inelastic - the two
objects stick together have the same speed after
collision
m1v1 m2v2 m1v1 m2v2
Since the two objects stick together after the
collision, v1 v2 v
m1v1 m2v2 (m1 m2)v
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example

• You are outside the space shuttle when your
  fellow astronaut of equal mass is moving towards
  you at 2 m/s (with respect to the shuttle). If
  she collides with you and holds onto you, then
  how fast (with respect to the shuttle do you both
  move after the collision?

m1v1 m2v2 (m1 m2)v2
m1 m2 m v1 2 m/s v2 0 m/s v1 v2
v
Inelastic collision - the two objects stick
together have the same speed after collision.
m(2 m/s) (2m)v v 1 m/s
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example

• A large fish is in motion at 2 m/s when it
  encounters a smaller fish which is at rest. The
  large fish swallows the smaller fish and
  continues in motion at a reduced speed. If the
  large fish has three times the mass of the
  smaller fish, then what is the speed of the large
  fish (and the smaller fish) after the collision?

m1v1 m2v2 (m1 m2)v2
m1 3m2 v1 2 m/s v2 0 m/s v1 v2 v
3m2(2 m/s) 0 (3m2 m2)v
Inelastic collision, objects have the same speed
after collision
v 1.5 m/s
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practice

• A large fish is in motion at 5 km/hr when it
  encounters a smaller fish which is at rest. The
  large fish swallows the smaller fish and
  continues in motion at a reduced speed. If the
  large fish has four times the mass of the smaller
  fish, then what is the speed of the large fish
  (and the smaller fish) after the collision?

v 4 km/hr
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• A railroad diesel engine has 4 times the mass of
  a boxcar. A diesel coasts backwards along the
  track at 5 km/hr and couples together with the
  boxcar (initially at rest). How fast do the two
  trains cars coast after they have coupled
  together?

4 km/hr
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• The process of solving this types of problem
  which one of the two objects is at rest before
  the collision and both objects move at the same
  speed after the collision, involves using a
  conceptual understanding of the equation for
  momentum (pmv).
• This equation becomes a guide to thinking about
  how a change in one variable effects a change in
  another variable.

• As mass increases, velocity decreases.
• A twofold increase in mass, results in a twofold
  decrease in velocity (the velocity is one-half
  its original value) a threefold increase in mass
  results in a threefold decrease in velocity (the
  velocity is one-third its original value)

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example

• Cart A (50. kg) approaches cart B (100. kg
  initially at rest) with an initial velocity of
  30. m/s. After the collision, cart A locks
  together with cart B. both travels with what what
  velocity?

Before collision
after collision
m(A) 50 kg, v(A) 30. m/s m(B) 100. kg,
v(B) 0
v(A) v(B) v ?
m(A)v(A) m(B)v(B) m(A)v
m(B)v (50.kg)(30.m/s) (100.kg)(0) (50.kg)v
(100.kg)v
v 10. m/s
mass increases by 3 times (50 kg to 150 kg),
speed decrease by 3 times (30 m/s to 10 m/s)
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example

• A railroad diesel engine coasting at 5.0 km/h
  runs into a stationary flatcar. The diesels mass
  is 8,000. kg and the flatcars mass is 2,000. kg.
  Assuming the cars couple together, how fast are
  they moving after the collision?

Before collision
after collision
m(A) 8000. kg, v(A) 5.0 km/h m(B) 2000. kg,
v(B) 0
v(A) v(B) v ?
m(A)v(A) m(B)v(B) m(A)v m(B)v
(8000.kg)(5.0km/h) (2000.kg)(0) (8000.kg)v
(2000.kg)v
v 4.0 km/h
mass increases by 1.25 times (8000 kg to 10000
kg), speed decrease by 1.25 times (50 m/s to 40
m/s)
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Example (pay attention to directions)

• Cart A (50. kg) moving with an initial velocity
  of 30. m/s approaches cart B (100. kg moving with
  initial velocity of 20. m/s towards cart A. The
  two carts lock together and move as one.
  Calculate the magnitude and the direction of the
  final velocity.

Before collision
after collision
m(A) 50 kg, v(A) 30. m/s m(B) 100. kg, v(B)
-20. m/s
v(A) v(B) v ?
Momentum before Momentum after m(A)v(A)
m(B)v(B) m(A)v m(B)v
(50.kg)(30.m/s) (100.kg)(-20. m/s) (50.kg)v
(100.kg)v
v 3.3 m/s to the left
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example

• A block of mass M initially at rest on a
  frictionless horizontal surface is struck by a
  bullet of mass m moving with horizontal velocity
  v. What is the velocity of the bullet-block
  system after the bullet embeds itself in the
  block?

Before collision
after collision
mv M(0)
(m M)v
mv 0 (m M)v
v mv / (Mm)
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example

• A woman with horizontal velocity v1 jumps off a
  dock into a stationary boat. After landing in the
  boat, the woman and the boat move with velocity
  v2. Compared to velocity v1, velocity v2 has
• the same magnitude and the same direction
• the same magnitude and opposite direction
• smaller magnitude and the same direction
• larger magnitude and the same direction

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Check your understanding

• practice

66
Another special case of collision - Explosions

• Total system momentum is conserved for collisions
  between objects in an isolated system, there are
  no exceptions to this law.
• This same principle of momentum conservation can
  be applied to explosions.

Momentum before the explosion is zero. so the
momentum after the explosion is also zero.
m1v1 m2v2 m1v1 m2v2
0 m1v1 m2v2
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• Consider a homemade cannon.

p(after) 0 p(cannon) p(ball) 0
p(before) 0

• In the exploding cannon, total system momentum is
  conserved.
• The system consists of two objects - a cannon and
  a tennis ball.
• Before the explosion, the total momentum of the
  system is zero since the cannon and the tennis
  ball located inside of it are both at rest.
• After the explosion, the total momentum of the
  system must still be zero. If the ball acquires
  50 units of forward momentum, then the cannon
  acquires 50 units of backwards momentum. The
  vector sum of the individual momentum of the two
  objects is 0. Total system momentum is conserved.

68

• Consider two low-friction carts at rest on a
  track. The system consists of the two individual
  carts initially at rest. The total momentum of
  the system is zero before the explosion. When the
  pin is tapped, an explosion-like impulse sets
  both carts in motion along the track in opposite
  directions. One cart acquires a rightward
  momentum while the other cart acquires a leftward
  momentum. If 20 units of forward momentum are
  acquired by the rightward-moving cart, then 20
  units of backwards momentum is acquired by the
  leftward-moving cart. The vector sum of the
  momentum of the individual carts is 0 units.
  Total system momentum is conserved.

69
Equal and Opposite Momentum Changes

• Just like in collisions, the two objects involved
  encounter the same force for the same amount of
  time directed in opposite directions. This
  results in impulses which are equal in magnitude
  and opposite in direction. And since an impulse
  causes and is equal to a change in momentum, both
  carts encounter momentum changes which are equal
  in magnitude and opposite in direction. If the
  exploding system includes two objects or two
  parts, this principle can be stated in the form
  of an equation as
• If the masses of the two objects are equal, then
  their post-explosion velocity will be equal in
  magnitude (assuming the system is initially at
  rest). If the masses of the two objects are
  unequal, then they will be set in motion by the
  explosion with different speeds. Yet even if the
  masses of the two objects are different, the
  momentum change of the two objects will be equal
  in magnitude.

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example

• A 2.0-kilogram toy cannon is at rest on a
  frictionless surface. A remote triggering device
  causes a 0.005-kilogram projectile to be fired
  from the cannon. Which equation describes this
  system after the cannon is fired?
• mass of cannon mass of projectile 0
• speed of cannon speed of projectile 0
• momentum of cannon momentum of projectile 0
• velocity of cannon velocity of projectile 0

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example

• A 2-kilogram rifle initially at rest fires a
  0.002-kilogram bullet. As the bullet leaves the
  rifle with a velocity of 500 meters per second,
  what is the momentum of the rifle-bullet system?

0
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Solving Explosion Momentum Problems

• A 56.2-gram tennis ball is loaded into a 1.27-kg
  homemade cannon. The cannon is at rest when it is
  ignited. Immediately after the impulse of the
  explosion, a photogate timer measures the cannon
  to recoil backwards a distance of 6.1 cm in
  0.0218 seconds. Determine the post-explosion
  speed of the cannon and of the tennis ball.

Given Cannon m 1.27 kg d 6.1 cm t
0.0218 s Ball m 56.2 g 0.0562 kg

• The strategy for solving for the speed of the
  cannon is to recognize that the cannon travels
  6.1 cm at a constant speed in the 0.0218 seconds.
   
• vcannon d / t (6.1 cm) / (0.0218 s) 280
  cm/s (rounded

• The strategy for solving for the post-explosion
  speed of the tennis ball involves using momentum
  conservation principles. mball vball -
  mcannon vcannon
• vball 63.3 m/s

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example

• A 60. kg man standing on a stationary 40. kg boat
  throws a .20 kg baseball with a velocity of 50.
  m/s. With what speed does the boat move after the
  man throws the ball? Assume no friction between
  the water and the boat.

v(boat) -0.1 m/s (in the opposite direction of
the baseball)
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example

• In the diagram, a 100.-kilogram clown is fired
  from a 500.-kilogram cannon.  If the clown's
  speed is 15 meters per second after the firing,
  then what is the recoil speed (v) of the cannon?

3.0 m/s
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example

• An 8.00-kilogram ball is fired horizontally from
  a 1.00 103-kilogram cannon initially at rest.
  After having been fired, the momentum of the ball
  is 2.40 103 kgm/s east. Neglect friction.
  What is the direction of the cannons velocity
  after the ball is fired?

P(before) P(after) 0 2.40 x 103 kgm/s
P(cannon) P(cannon) - 2.40 x 103 kgm/s The
direction of the cannons velocity is West
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Check your understanding

• Conservation of momentum
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79
Momentum practice

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