Momentum

1
Momentum
2
Momentum

• A measure of how hard it is to stop a moving
  object.
• Related to both mass and velocity.
• Possessed by all moving objects.

3
Calculating Momentum

• For one particle
• p mv
• For a system of multiple particles
• P ?pi ?mivi
• Momentum is a vector!

4
(No Transcript)
5
Which has the most momentum?
6
Impulse (J)

• The product of an external force and time, which
  results in a change in momentum
• J F t
• J ?P
• Units N s or kg m/s

7
Impulse (J)
F(N)
3000
2000
area under curve
1000
0
t (ms)
0
1
2
3
4
8
Law of Conservation of Momentum

• If the resultant external force on a system is
  zero, then the vector sum of the momenta of the
  objects will remain constant.

?pb ?pa
9
Collisions

• Collisions are governed by Newton's laws.
• Newtons Third Law tells us that the force
  exerted by body A on body B in a collision is
  equal and opposite to the force exerted on body B
  by body A.

10
Collisions

• During a collision, external forces are ignored.
• The time frame of the collision is very short.
• The forces are impulsive forces (high force,
  short duration).

11
Collision Types

• Elastic (hard, no deformation)
• P is conserved, K is conserved
• Inelastic (soft deformation)
• P is conserved, K is NOT conserved
• Perfectly Inelastic (stick together)
• P is conserved, K is NOT conserved

12
Golf and Momentum

• Consider the elastic collision between the club
  head and the golf ball in the sport of golf.

13
Golf and Momentum

• Forces are on the clubhead and ball are equal and
  opposite.

14
Golf and Momentum

• The acceleration of the ball is greater because
  its mass is smaller.

15
Pool and Momentum

• Consider the elastic collision between a moving
  ball and a ball that is at rest in the sport of
  billiards.

16
Pool and Momentum

• The balls experience forces which are equal in
  magnitude and opposite in direction.

17
Pool and Momentum

• Since the balls have equal masses, they
  experience equal accelerations.

18
Explosion

• When an object separates suddenly, this is the
  reverse of a perfectly inelastic collision.
• Mathematically, it is handled just like an
  ordinary inelastic collision.
• Momentum is conserved, kinetic energy is not.
• Examples
• Cannons, Guns, Explosions, Radioactive decay.

19
Perfectly Inelastic Collision 1

• An 80 kg roller skating grandma collides
  inelastically with a 40 kg kid as shown. What is
  their velocity after the collision?

20
Perfectly Inelastic Collisions 2

• A train of mass 4m moving 5 km/hr couples with a
  flatcar of mass m at rest. What is the velocity
  of the cars after they couple?

21
Perfectly Inelastic Collisions 3

• A fish moving at 2 m/s swallows a stationary fish
  which is 1/3 its mass. What is the velocity of
  the big fish and after dinner?

22
Recoil Problem 1

• A gun recoils when it is fired. The recoil is the
  result of action-reaction force pairs. As the
  gases from the gunpowder explosion expand, the
  gun pushes the bullet forwards and the bullet
  pushes the gun backwards.

23
Sample Problem

• Suppose three equally strong, equally massive
  astronauts decide to play a game as follows The
  first astronaut throws the second astronaut
  towards the third astronaut and the game begins.
  Describe the motion of the astronauts as the game
  proceeds. Assume each toss results from the
  same-sized "push." How long will the game last?

24
Center of Mass

• Physicist like to deal with particles because it
  is relatively easy to deal with an object that
  has position and mass, but no real size.
• But what do you do if you have a real object with
  a non-zero size? Or if you have a collection of
  particles?
• You turn the object into a particle by pretending
  all the mass resides at the center of mass.

25
Calculate momentum of the balls before and after
the collision.
26
Center of Mass

• The point at which all of the mass of an object
  or system may be considered to be concentrated.

27
Center of Mass for solid objects
x

• Pick the geometric center of the object

x
28
Center of Mass for collection of points

• xcm ? mixi / M
• ycm ? miyi / M
• zcm ? mizi / M

29
Center of Mass Problem (SOS 8.10)

• A system consists of the following masses in the
  x,y plane 4 kg at (0, 5m), 7 kg at (3m, 8m),
  and 5 kg at (-3 m, -6m). Find the position of
  its center of mass.