Momentum

1
Momentum

• Mrs. Kay
• Physics 11

2

• Momentum can be defined as "mass in motion."
• p m v
• the symbol for the quantity momentum is p, where
  m is mass and v is velocity.
• The units for momentum would be mass units times
  velocity units (kgm/s)

3

• Momentum is a vector, because velocity is a
  vector.
• The direction of the momentum is the same as the
  direction of the velocity that the object is
  moving.

4

• an object has a large momentum if either its mass
  or its velocity is large
• Mack truck and a roller skate moving down the
  street at the same speed. The considerably
  greater mass of the Mack truck gives it a
  considerably greater momentum.
• If the Mack truck was at rest and the roller
  skate was moving, then the skate would have a
  greater momentum

5
Practice

• 1. Determine the momentum of a ...
• 60-kg halfback moving eastward at 9 m/s.
• 1000-kg car moving northward at 20 m/s.
• 40-kg freshman moving southward at 2 m/s.

6

• 2. A car possesses 20 000 units of momentum. What
  is the car's new momentum if ...
• its velocity were doubled.
• its velocity were tripled.
• its mass were doubled (by adding more passengers
  and a greater load)
• both its velocity were doubled and its mass were
  doubled.

7

• An object with momentum is going to be hard to
  stop.
• To stop such an object, you must apply a force
  against its motion for a given period of time.
• The more momentum the harder it is to stop.

8

• 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.
• If a force acts in the same direction as the
  object's motion, then the force speeds the object
  up.

9
Combining Ideas

• Newtons 2nd Law and the theory of momentum

10

• In physics, the quantity Forcetime is known as
  the impulse. And since the quantity mv is the
  momentum, the quantity m"Delta "v must be the
  change in momentum. The equation really says that
  the
• Impulse Change in momentum

11
Collisions

• collisions are governed by the laws of momentum
• an object experiences a force for a specific
  amount of time which results in a change in
  momentum

12
collision of a ball with a wall

• The diagrams below depict the changes in velocity
  of the same ball.

13
Graphing Diagrams
14
Rebound Collisions

• the greater the rebound effect, the greater the
  acceleration, momentum change, and impulse.
• A rebound is a special type of collision
  involving a direction change the result of the
  direction change is large velocity change.

15
Elastic Collisions

• Collisions in which objects rebound with the same
  speed (and thus, the same momentum and kinetic
  energy) as they had prior to the collision are
  known as elastic collisions.
• characterized by a large velocity change, a large
  momentum change, a large impulse, and a large
  force.

16
Problem

• A 0.50-kg cart (1) is pulled with a 1.0-N force
  for 1 second another 0.50 kg cart (2) is pulled
  with a 2.0 N-force for 0.50 seconds.
• Which cart (1 or 2) has the greatest
  acceleration? Explain.
• Which cart (1 or 2) has the greatest impulse?
  Explain
• Which cart (1 or 2) has the greatest change in
  momentum? Explain.

17
Answers

• 1 a) Cart 2 Acceleration depends on force and
  mass. They have the same mass, but cart 2 has a
  greater force acting upon it.
• b) The impulse is the same for both of them, it
  depends upon force and time.
• c) Momentum is also the same for both because
  it is the same as the impulse

18
http//www.learner.org/exhibits/parkphysics/bumper
cars/
19

• For questions that calculate the change in
  momentum for a single object, where its mass does
  not change use
• ?ppf-pimvf-mvim(v f-vi)

20
Law of Conservation of Momentum

• Total momentum of a system remains the same when
  the net external force acting on the system is
  zero.
• General formula for two objects
• ??p(m1v1fm2v2f)- (m1v1im2v2i) 0
• OR
• m1v1i m2v2i m1v1f m2v2f
• OR (in book)
• m1v1 m2v2 m1v1 m2v2

21
Practice

• Two ice skaters, with masses of 45kg and 65kg are
  initially at rest . They push off each other and
  the 45kg skater moves away with a velocity of
  6m/s North. Find the final velocity of the 65kg
  ice skater.
• KNOW ml45kg m265kg vlf6m/s pi and pf0

22
Solution

• m1v1f m2v2f 0
• v2f -(m1v1f) / m2
• - (45kg x 6m/s) / 65kg
• -4.2 m/s
• Negative sign means opposite direction

23
Elastic Collisions

• Perfectly elastic collisions are those in which
  no kinetic energy is lost in the collision.

24
(No Transcript)
25
Inelastic Collisions

• Total kinetic energy of a system is not
  conserved.
• Referred to as sticky collisions, because the
  colliding objects become attached.

26
Inelastic Collisions
27
Problem

• A 6kg block has an initial velocity of 5m/s and
  it collides with a stationary block with a mass
  of 4kg on a frictionless surface. After the
  collision the blocks are attached. What will be
  their final velocity?
• Given m16kg m24kg v1i5m/s v2i0m/s vf(12)?

28
Solution

• m1v1i m2v2i m1vf m2vf
• m1v1i m2v2i m1m2 (vf)
• vf m1v1i m2v2i
• ( m1m2)
• (6kg x 5m/s) (4kg x 0m/s)
• (6kg 4kg)
• 3.0m/s

29
Practice

• Pg185 5-6
• Pg 193 1-3