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Momentum and Impulse

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Title: Momentum and Impulse


1
Momentum and Impulse
2
What is Momentum?
  • Momentum The product of the mass and velocity
    of an object. Has magnitude and direction.
  • Momentum p mv
  • P momentum
  • M mass
  • V velocity
  • Units kgm/s

3
Inertia?
  • Remember Newtons 1st Law?
  • An object at rest will stay at rest
  • and
  • An object in motion will stay in motion in the
    same speed and direction unless acted on by an
    outside force.

4
Whats Inertia Got to Do with It?
  • Momentum is directly related to the second part
    of Newtons 1st Law
  • An object in motion stays in motion (same speed
    and direction) unless acted on by a force

5
Lets practice
  • A 1200 kg car drives west at 25 m/s for 3 hours.
    What is the cars momentum?
  • Identify the variables
  • 1200 kg mass
  • 25m/s, west velocity
  • 3 hours time
  • P mv 1200 x 25 30000 kg m/s, west

6
How hard is it to stop a moving object?
  • Impulse Product of force and time interval
    during which the force acts. Impulse equals
    momentum change.
  • Impulse F?t
  • F force (N)
  • ?t time elapsed (s)
  • Units Ns

7
How hard is it to stop a moving object?
  • Using Newtons 2nd Law we get
  • Impulse change in momentum
  • F?t m?v

8
Why does an egg break or not break?
  • An egg dropped on a tile floor breaks, but an egg
    dropped on a pillow does not. Why?
  • F?t m?v
  • In both cases, m and ?v are the same.
  • If ?t goes up, what happens to F, the force?
  • Right! Force goes down. When dropped on a
    pillow, the egg starts to slow down as soon as it
    touches it. A pillow increases the time the egg
    takes to stops.

9
Practice Problem
  • A 57 gram tennis ball falls on a tile floor. The
    ball changes velocity from -1.2 m/s to 1.2 m/s
    in 0.02 s. What is the average force on the
    ball?
  • Identify the variables
  • Mass 57 g 0.057 kg
  • ?velocity 1.2 (-1.2) 2.4 m/s
  • Time 0.02 s
  • using F?t m?v
  • F x (0.02 s) (0.057
    kg)(2.4 m/s)
  • F 6.8 N

10
Car Crash
  • Would you rather be in a head on collision
    with an identical car, traveling at the same
    speed as you, or a brick wall?
  • Assume in both situations you come to a
    complete stop.
  • Take a guess

http//techdigestuk.typepad.com/photos/uncategoriz
ed/car_crash.JPG
11
Car Crash (cont.)
  • The answer is
  • It Does Not Matter!
  • Look at F?t m?v
  • In both situations, ?t, m, and ?v are the same!
    The time it takes you to stop depends on your
    car, m is the mass of your car, and ?v depends
    on how fast you were initially traveling.

12
Conservation of Momentum
13
Conservation of Momentum
  • Just like energy, momentum is conserved.
  • The total momentum at the start will equal the
    total momentum at the end

14
Vectors!
  • Remember that momentum is a vector value, so if
    two momentums are in opposite directions, they
    are opposite signs and end up cancelling (at
    least in part)

15
Two Flavors!!
  • Collisions may be
  • Elastic the objects completely bounce off each
    other
  • Billiards (pool) ball have elastic
    collisions
  • Inelastic the objects stick together at the
    collision and travel together thereafter
  • Car Crashes have become inelastic with
    better engineering

16
Momentum Formulas
  • The standard formula for momentum is
  • Pmv
  • What happens if we have two objects that collide
    and bounce off each other..elastic??
  • We can make a formula for this due to the
    conservation of momentum!
  • M1V1i M2V2i M1V1f M2V2f

17
Practice Elastic
  • A 50 kg skater traveling at 10 m/s hits a 40 kg
    skater sitting still, imparting all his momentum
    into the 2nd skater. What is the velocity of the
    2nd skater?
  • M1V1i M2V2i M1V1f M2V2f
  • (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(0 m/s)
    (40 kg)V2f
  • (500 kgm/s) (0 kgm/s) (0 kgm/s) (40
    kg)V2f
  • 12.5 m/s V2f

18
Practice Problem
  • A 50 kg skater traveling at 10 m/s hits a 40 kg
    skater sitting still. The 1st skater ends up at 2
    m/s. What is the velocity of the 2nd skater?
  • M1V1i M2V2i M1V1f M2V2f
  • (50 kg)(10 m/s) (40 kg)(0 m/s) (50 kg)(2 m/s)
    (40 kg)V2f
  • (500 kgm/s) (0 kgm/s) (100 kgm/s) (40
    kg)V2f
  • 10 m/s V2f

19
Practice Problem
  • A 50 kg skater traveling at 20 m/s hits a 40 kg
    skater moving in the same direction at 3 m/s. The
    1st skater ends up at 5 m/s. What is the velocity
    of the 2nd skater?
  • M1V1i M2V2i M1V1f M2V2f
  • (50 kg)(20 m/s) (40 kg)(3 m/s) (50 kg)(5 m/s)
    (40 kg)V2f
  • (1000 kgm/s) (120 kgm/s) (125 kgm/s) (40
    kg)V2f
  • 24.875 m/s V2f

20
Inelastic Collision Formula
  • Since the objects travel together after the
    collision, we have a slightly different formula
    for inelastic collisions
  • M1V1i M2V2i (M1 M2)Vf
  • This shows the final momentum is created by the
    total mass of the two objects together

21
Practice Inelastic
  • A 50 kg skater traveling at 20 m/s picks up a 40
    kg passenger skating sitting still, what is the
    velocity of the two skaters?
  • M1V1i M2V2i (M1 M2)Vf
  • (50 kg)(20 m/s) (40 kg)(0 m/s) (90 kg)Vf
  • (1000 kgm/s) (0 kgm/s) (90 kg)Vf
  • 11.1 m/s Vf

22
Practice Problem
  • A 50 kg skater traveling at 20 m/s picks up a 40
    kg passenger skating in the same direction at 5
    m/s, what is the velocity of the two skaters?
  • M1V1i M2V2i (M1 M2)Vf
  • (50 kg)(20 m/s) (40 kg)(5 m/s) (90 kg)Vf
  • (1000 kgm/s) (200 kgm/s) (90 kg)Vf
  • 13.3 m/s Vf

23
Practice Problem
  • A 50 kg skater traveling at 20 m/s picks up a 40
    kg passenger skating in the opposite direction at
    5 m/s, what is the velocity of the two skaters?
  • M1V1i M2V2i (M1 M2)Vf
  • (50 kg)(20 m/s) (40 kg)(-5 m/s) (90 kg)Vf
  • (1000 kgm/s) - (200 kgm/s) (90 kg)Vf
  • 8.89 m/s Vf
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