Notes Ch'8

1
Notes Ch.8

• Momentum
• Momentum intro

2
8.1 The Nature of Momentum

• Momentum is the product of the mass of a body and
  its velocity.
• The units for momentum are kilogrammeters/second
  (kgm/s).
• Momentum is a vector quantity. The momentum
  vector points in the same direction as the
  velocity vector.
• pm?
• p is momentum
• m is mass
• ? is velocity
• Momentum

3
8.2 Momentum and Newton's second law

• SF ma m??v/?t Newtons 2nd law
• p mv momentum
• p/?t m ?v/?t divide both sides by ?t
• SF ?p/?t - so the net force on an object equals
  its change in momentum divided by time
• Newtons second law was written in terms of
  momentum instead of forces.
• Pmv

4
8.3 Impulse

• Impulse is the product of a force and the time
  interval during which it acts
• So
• Hence impulse produces a change in momentum.
• A net force is required to accelerate an object,
  changing its velocity and its momentum.
• The greater the net force, or the longer the
  interval of time it is applied, the more the
  object's momentum changes, which is the same as
  saying the impulse increases.
• Impulse

5
8.4 Physics at play hitting a baseball

• The bat exerts force on the baseball in the very
  brief period of time they are in contact. The
  amount of force varies over this brief interval.
• At the moment of contact, the bat and ball are
  moving toward each other. The force on the ball
  increases as they come together and the ball
  compresses against the bat.
• The force applied to the ball during the time it
  is in contact with the bat is responsible for the
  balls change in momentum.
• baseball

6
8.5 Interactive checkpoint force graph and
impulse
7
8.6 The Conservation of Momentum

• Law of Conservation of Momentum When no external
  forces are acting on a system of objects, the
  total vector momentum of the system remains
  constant.
• This is a special case of Newtons Third Law
• The total momentum of an isolated system is
  constant.
• An isolated system is one that does not interact
  with its environment.
• Momentum can transfer from object to object
  within this system but the vector sum of the
  momenta of all the objects remains constant.
• Conservation of Momentum

8
8.7 Derivation conservation of momentum from
Newtons laws

• 8.8 Interactive checkpoint astronaut
• 8.9 Interactive checkpoint bumper cars

9
8.10 Collisions

• In a collision, one moving object briefly strikes
  another object. During the collision, the forces
  the objects exert on each other are much greater
  than the net effect of other forces acting on
  them, so we may ignore these other forces.
• In any collision, the systems total amount of
  energy must be the same before and after, because
  the law of conservation of energy must be obeyed.

10
8.10 Elastic Collisions

• When objects collide and rebound without loss of
  kinetic energy it is an elastic collision. EX.
  Gas molecules.
• If the collision is in two dimensions a vector
  diagram must be used to calculate the momenta of
  the objects before and after collision. Total
  vector momentum before and after the collision
  must be equal. This applies to all collisions in
  2-dimensions.
• In collisions between a moving ball and a
  stationary ball of the same mass the balls will
  move off at right angles to one another unless
  the collision is head on (linear).
• Elastic Collision

11
8.10 Inelastic Collisions

• Collisions between bodies where they stick
  together and move off in a straight line.
• Total momentum before and after the collision is
  equal.
• ma?a mb?b mab ?ab
• When carts of equal but opposite momenta collide
  the total momentum of the system will be zero.
  Momentum is conserved but not Kinetic Energy
• Inelastic Collision

12
8.11 Sample problem elastic collision in one
dimension

• 8.12 Interactive checkpoint another one
  dimensional collision problem
• 8.13 Clicky-clack balls
• 8.14 Physics at play elastic collisions and
  sports
• 8.15 Interactive problem shuffleboard collisions
• 8.16 Sample problem elastic collision in two
  dimensions
• 8.17 Interactive problem multi-dimensional
  collision

13
8.18 Inelastic collisions

• Inelastic collision The collision results in a
  decrease in the systems total kinetic energy.
• Kinetic energy transforms into other forms of
  energy.
• The kinetic energy after an inelastic collision
  is less than the kinetic energy before the
  collision.
• Inelastic collisions II
• 8.19 Sample problem ballistic pendulum

14
8.20 Center of mass

• Center of mass Average location of mass. An
  object can be treated as though all its mass were
  located at this point.
• When an object is symmetrical and made of a
  uniform material, such as a solid sphere of
  steel, the center of mass is at its geometric
  center.
• The center of mass does not have to lie inside
  the object. For example, the center of mass of a
  doughnut lies in the middle of its hole.
• center of mass

15
8.21 Center of mass and motion

• 8.22 Sample problem moving a raft

16
8.23 Center of mass and collisions

• In general, when there is no external force on a
  system, the velocity of the center of mass is
  constant for any collision, elastic or not.
• Since there is no net force on the system, there
  is no acceleration of the center of mass.
• The momentum of the center of mass of this system
  is also constant.
• Collisions and center of mass
• 8.24 Interactive summary problem types of
  collisions