Momentum and change in momentum

1
Momentum and change in momentum
2
Which would you rather get hit by?

• 1 bowling ball?

• 1 marble ?

3
On what information does your answer depend?
4
Car Crashes

• Why do some people survive and others do not?

5
Definition of momentum
6
Momentum

• A quantity of motion found by multiplying an
  objects mass by its velocity
• Is a vector value (Magnitude and direction are
  important)

7
Momentum

• Pain upon impact
• Inertia in motion

8
Units of momentum

• Kg m/s

9
What has momentum?
10
What has more momentum?

• The statue of liberty or a SUV moving at 60 mph
  down the road?

11
Examples of momentum

• Anything with mass that is in motion
• Any object that is not moving has NO momentum

12
Determination of an objects momentum value
13
Equation of momentum

• P m v

14
How an objects momentum changes is more useful
than the momentum value at any point in time
15
Change in momentum

• Impulse

16
Newtons Cradle
17
Impulse

• The measure of a change in momentum
• Symbol ?p , units are the same
• Any object that changes its mass or velocity over
  time changes its momentum
• Any change in momentum requires a net force,
  acceleration
• Any application of a net force, results in a
  change of momentum of the object

18
Examples of net force changing momentum

• Hockey stick on a puck
• Wall on a car
• Bat on a softball

19
WHAT CAR HAS THE GREATER IMPULSE?

• The Red car that was going 45 mph stopped by the
  Brick Wall
• Or
• The same red car that was going 45 mph and
  stopped by application of Brakes

20
Answer

• They have the same change in momentum
• But the results of the change in momentum to each
  car is very different
• The car hitting a brick wall will have more force
  applied over a shorter time

21
Newtons second law and ?p

• How does 2nd law relate to momentum?
• Acceleration the change in velocity over change
  in time a ?v / ?t
• Rewrite the 2nd law in terms of the change of
  momentum (This is how Newton presented the law)

22
The Impulse momentum theorem

• Fnet ma m ?v / ?t, rearrange to form
  theorem
• m?v ?p Fnet ?t
• ?v vf - vi

23
Which parts of the equation the impulse?

• Impulse F ?t
• Impulse m ?v
• Impulse pf - pi

24
Important

• For a given crash involving vehicles with
  identical masses, undergoing identical changes in
  velocity
• the impulse is constant regardless of how the
  crash occurs
• Impulse m?v

25
Time and force

• The length of time it takes for the crash to be
  complete determines the amount of force applied
  during the crash
• All of the measure found below extend the time of
  the crash, reducing applied force to passengers
• Seat belts
• Foam padding
• Air Bags
• Crumple zones

26
Time and force

• The longer the time allowed to exert a force, the
  less force is exerted

27
Again

• What causes a change in the momentum?

28
Change of momentum and Sports

• Baseball/ softball
• Golf

29
(No Transcript)
30
Catching a ball
31
To catch a ball

• Your hand must apply force to the ball to make it
  stop moving,
• The longer you can make the time spent applying
  force to the ball, the less force is needed

32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
Applications of momentum
36
What determines if you live or die in an auto
accident?
37
Safety features
38
Safety features in cars that protect you during a
crash

• Seat belt
• Air bags
• Cushioned dashboard, steering weel
• Padded headrest
• Crumple zones

39
The way to survive an accident

• Drive a car with
• Seat-belts
• Air bag
• Crumple zones
• Soft dashboards/padded steering wheels
• What benefit do these features provide?

40
What value do safety features extend?

• The time of the crash
• Impulse Force x time

41
What value is decreased as a result of those
safety features?

• The amount of force needed to stop the car (and
  you)

42
The purpose of most safety features in a car is
to lengthen the time of the accident

• Air bags

43
Air Bags

• The air bag increases the time of the collision
• It will also absorb some of the energy from the
  body
• It will spread out the area of contact
• decreases the pressure
• helps prevent penetration wounds

44
Pressure

• P F / A
• F total force applied
• A area over which the force was applied
• Units N/m or Pascals

45
Seat belts
46
Padding on dashboard, seats and steering wheel
47
Crumple zones

• It takes time for the parts of the car in the
  crumple zone to be crushed, less force applied to
  the passenger section

48
Any other means to protect the passengers during
a collision?
49
Other examples of change in momentum

• Catching a Foul Ball

• Being hit by a foul ball

50
Again

• The main point of all safety devices in cars is
  to extend the time of the impact between human
  and car

51
Answer

• The amount of force applied is related to the
  length of time required to bring the driver to a
  stop
• The longer the time, the less force required

52
Average Force in Impulse

• The average force can be thought of as the
  constant force that would give the same impulse
  to the object in the time interval as the actual
  time-varying force gives in the interval

53
Average Force cont.

• The impulse imparted by a force during the time
  interval ?t is equal to the area under the
  force-time graph from the beginning to the end of
  the time interval
• Or, to the average force multiplied by the time
  interval

54
Homework

• Pg 233 problems 1-5
• Do not do 3 if we have not discussed no constant
  forces

55
Homework answers

• 1a) 23,200 kg m/s eastward
• 1b) 38.4 km/h eastward, 10.7 m/s eastward
• 3a) 2.7 m/s same direction as original velocity
• 3b) 1.3 m/s in the same direction as original
  velocity
• 5a) 7,800 N opposite direction of motion
• 5b) 800 kg (too heavy to lift)

56
Angular momentum
57
Definition

• If something has mass and is rotating, it has
  angular momentum
• How much depends on
• Amount of mass, location, shape (MoI)
• Rotational velocity
• L I? where I MoI, ? ang velocity

58
Examples of angular momentum in real life
59
Angular momentum
60
Skaters in a spin

• How do skaters spin faster?
• Is there an outside force-torque being applied?

61
Change in angular momentum

• ?L Lf LI I??
• Just like linear momentum, change in angular
  momentum requires a Net force that causes change
  in rotation (Thus a net Torque) over time.
• T ?t I ??

62
Question

• A old fashioned top (with a moment of inertia of
  4.2 Kg m2)is spun by a rope that applies 155 Nm
  of torque when pulled. If Susie pulls on the
  rope for 1.2 seconds
• A) What is the change in the angular momentum?
• B) What is the change in the angular velocity if
  top starts from rest?

63
Homework

• Pg 235
• Questions 6-12