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Physics 2211, Spring 2002

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The ball is in contact with the ground for a very short ... The diagram shows the force vs. time for a typical collision. ... Bending of metal (crashing cars) ... – PowerPoint PPT presentation

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Title: Physics 2211, Spring 2002


1
Physics 2211 Lecture 22Todays Agenda
  • Impulse
  • Conservation of momentum
  • Inelastic collisions in one dimension
  • Elastic collisions in one dimension

2
Collision time scales
  • Collisions typically involve interactions that
    happen quickly.

3
Collision time scales
  • During this brief time, the forces involved can
    be quite large

?t
t1
t5
t2
t4
t3
p1
p2
p3 0
p5
p4
F2
F4
F3
4
Force and Impulse
5
Force and Impulse
6
Force and Impulse
  • Two different collisions can have the same
    impulse since dependsonly on the change in
    momentum,not the nature of the collision.

same area
F
t
?t
?t
ti
tf
ti
tf
?t big, F small
?t small, F big
7
Force and Impulse
soft spring
F
stiff spring
t
?t
?t
ti
tf
ti
tf
?t big, F small
?t small, F big
8
Force and Impulse
  • We can use the notion of impulse to define
    average force, which is a useful concept.

The time average of a force for the time interval
?t tf - ti is
9
Force and Impulse
soft spring
Fav
F
stiff spring
Fav
t
?t
?t
ti
tf
ti
tf
?t big, Fav small
?t small, Fav big
10
Force and ImpulseBaseball Example
  • A pitcher pitches the ball (m .7 kg) at 145
    km/hr (about 90 mph).
  • The batter makes contact with the ball for .001 s
    causing the ball to leave the bat going 190 km/hr
    (about 120 mph).
  • Find the average force on the ball, disregarding
    gravity.

11
Baseball Example
12
Conservation of Linear MomentumReview
  • Conservation of Linear Momentum

13
Comment on Energy Conservation
  • Total kinetic energy of a system undergoing an
    inelastic collision is not conserved.
  • Energy is lost
  • Heat (bullet in block)
  • Bending of metal (crashing cars)
  • Kinetic energy is not conserved since work is
    done during the collision!
  • Momentum along a certain direction is conserved
    when there are no external forces acting in this
    direction.
  • In general, momentum conservation is easier to
    satisfy than energy conservation.

14
Conservation of Momentum Example
  • Two balls of equal mass are thrown horizontally
    with the same initial velocity. They hit
    identical stationary boxes resting on a
    frictionless horizontal surface.
  • The ball hitting box 1 bounces back, while the
    ball hitting box 2 gets stuck (totally inelastic
    collision).
  • Which box ends up moving faster?

15
Conservation of Momentum Example
  • Since the total external force in the x-direction
    is zero, momentum is conserved along the x-axis.
  • In both cases the initial momentum is the same
    (mv of ball).
  • In case 1 the ball has negative momentum after
    the collision, hence the box must have more
    positive momentum if the total is to be
    conserved.
  • The speed of the box in case 1 is biggest!

x
V1
V2
2
1
16
Conservation of Momentum Example
17
Conservation of Momentum Example
  • Is case1 an elastic collision?

18
Ballistic Pendulum
L
L
V 0
L
L
H
m
v
M m
V
M
  • A projectile of mass m moving horizontally with
    speed v strikes a stationary mass M suspended by
    strings of length L. Subsequently, m M rise
    to a height of H.

Given H, what is the initial speed v of the
projectile?
19
Ballistic Pendulum
  • Two stage process

1. m collides with M, inelastically. Both M and
m then move together with a velocity V (before
having risen significantly).
2. M and m rise a height H, conserving K U
energy E. (no non-conservative forces acting
after collision)
20
Ballistic Pendulum
  • Stage 1 Momentum is conserved

in x-direction
21
Elastic Collisions
  • Elastic means that kinetic energy is conserved as
    well as momentum.
  • This gives us more constraints
  • We can solve more complicated problems!!
  • Billiards (2-D collision)
  • The colliding objectshave separate motionsafter
    the collision as well as before.
  • Start with a simpler 1-D problem

Initial
Final
22
Elastic Collision in 1-D
m2
m1
initial
v1i
v2i
x
23
Elastic Collision in 1-D
Conserve PX
Conserve Kinetic Energy
The rate of approach rate of recession
24
Basketball Demo
  • Carefully place a small rubber ball (mass m) on
    top of a much bigger basketball (mass M). Drop
    these from some height. The height reached by the
    small ball after they bounce is 9 times the
    original height!! (Assumes M gtgt m and all bounces
    are elastic).
  • Understand this using the speed of approach
    speed of recession property we just proved.

3v
m
v
v
v
v
M
v
(a)
(b)
(c)
25
Basketball Demo
26
Recap of todays lecture
  • Impulse
  • Conservation of momentum
  • Inelastic collisions in one dimension
  • Elastic collisions in one dimension
  • Review Section 8.6 inTipler
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