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Physics 106P: Lecture 17 Notes

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What is the initial speed of the bullet v? What is the initial energy of the system? ... Hi Prof Selen ... moving horizontally with speed v strikes a stationary ... – PowerPoint PPT presentation

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Title: Physics 106P: Lecture 17 Notes


1
How many times does the letter F appear in the
following text
FINISHED FILES ARE THE RESULT OF YEARS OF
SCIENTIFIC STUDY COMBINED WITHTHE EXPERIENCE OF
YEARS
A) 2 B) 3 C) 4 D) 5 E) 6
2
Physics 211 Lecture 14Todays Agenda
  • Momentum Conservation
  • Inelastic collisions in one dimension
  • Inelastic collisions in two dimensions
  • Explosions
  • Comment on energy conservation
  • Ballistic pendulum

3
Center of Mass Motion Review
  • We have the following law for CM motion
  • This has several interesting implications
  • It tells us that the CM of an extended object
    behaves like a simple point mass under the
    influence of external forces
  • We can use it to relate F and A like we are used
    to doing.
  • It tells us that if FEXT 0, the total momentum
    of the system does not change.
  • The total momentum of a system is conserved if
    there are no external forces acting.

4
Lecture 14, Act 1Center of Mass Motion
Pucks
  • Two pucks of equal mass are being pulled at
    different points with equal forces. Which
    experiences the bigger acceleration?

(a) A1 ? A2 (b) A1 ? A2 (c) A1 A2
A1
(1)
T
M
F
A2
(2)
M
T
5
Lecture 14, Act 1Solution
  • We have just shown that MA FEXT
  • Acceleration depends only on external force, not
    on where it is applied!
  • Expect that A1 and A2 will be the same since F1
    F2 T F / 2
  • The answer is (c) A1 A2.
  • So the final CM velocities should be the same!

6
Lecture 14, Act 1Solution
  • The final velocity of the CM of each puck is the
    same!
  • Notice, however, that the motion of the particles
    in each of the pucks is different (one is
    spinning).

V
??
V
This one has more kinetic energy (rotation)
7
Momentum Conservation
  • The concept of momentum conservation is one of
    the most fundamental principles in physics.
  • This is a component (vector) equation.
  • We can apply it to any direction in which there
    is no external force applied.
  • You will see that we often have momentum
    conservation even when energy is not conserved.

8
Elastic vs. Inelastic Collisions
  • A collision is said to be elastic when kinetic
    energy as well as momentum is conserved before
    and after the collision.
    Kbefore Kafter
  • Carts colliding with a spring in between,
    billiard balls, etc.
  • A collision is said to be inelastic when kinetic
    energy is not conserved before and after the
    collision, but momentum is conserved.
    Kbefore ?
    Kafter
  • Car crashes, collisions where objects stick
    together, etc.

9
Inelastic collision in 1-D Example 1
  • A block of mass M is initially at rest on a
    frictionless horizontal surface. A bullet of
    mass m is fired at the block with a muzzle
    velocity (speed) v. The bullet lodges in the
    block, and the block ends up with a speed V. In
    terms of m, M, and V
  • What is the initial speed of the bullet v?
  • What is the initial energy of the system?
  • What is the final energy of the system?
  • Is kinetic energy conserved?

x
V
before
after
10
Example 1...
  • Consider the bullet block as a system. After
    the bullet is shot, there are no external forces
    acting on the system in the x-direction.
    Momentum is conserved in the x direction!
  • Px, i Px, f
  • mv (Mm)V

x
V
initial
final
11
Example 1...
  • Now consider the kinetic energy of the system
    before and after
  • Before
  • After
  • So

Kinetic energy is NOT conserved! (friction
stopped the bullet) However, momentum was
conserved, and this was useful.
12
Inelastic Collision in 1-D Example 2
M
m
ice
v 0
(no friction)
V
M m
v ?
13
Example 2...
Air track
Use conservation of momentum to find v after the
collision.
After the collision
Before the collision
Conservation of momentum
vector equation
14
Example 2...
  • Now consider the K.E. of the system before and
    after
  • Before
  • After
  • So

Kinetic energy is NOT conserved in an
inelastic collision!
15
Lecture 14, Act 2Momentum Conservation
  • 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.
  • Which box ends up moving faster?

(a) Box 1 (b) Box 2 (c)
same
2
1
16
Lecture 14, Act 2Momentum Conservation
  • 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
17
Lecture 14, Act 2Momentum Conservation
mvinit (Mm)V2
mvinit MV1 - mvfin
V2 mvinit / (Mm)
V1 (mvinit mvfin) / M
x
V1
V2
2
1
18
Inelastic collision in 2-D
  • Consider a collision in 2-D (cars crashing at a
    slippery intersection...no friction).

V
v1
m1 m2
m1
m2
v2
before
after
19
Inelastic collision in 2-D...
  • There are no net external forces acting.
  • Use momentum conservation for both components.

X
y
v1
V (Vx,Vy)
m1 m2
m1
m2
v2
20
Inelastic collision in 2-D...
  • So we know all about the motion after the
    collision!

V (Vx,Vy)
Vy
?
Vx
21
Inelastic collision in 2-D...
  • We can see the same thing using vectors

P
P
p2
?
p1
p1
p2
22
Halftime (in case of no music)
Hi Prof Selen I know this does not have much to
do with physics per se (well, maybe, the person
is rotating with some ... velocity) but I thought
it was interesting, maybe to use the i-clicker to
see which way most people see or
whatnot... Anyway, the link is http//www.news.co
m.au/dailytelegraph/story/0,22049,22535838-5012895
,00.html Regards Jurand
23
Explosion (inelastic un-collision)
24
Explosion...
Rocket Bottle
  • No external forces, so P is conserved.
  • Initially P 0
  • Finally P m1v1 m2v2 0
  • m1v1 - m2v2

M
25
Lecture 14, Act 3Center of Mass
  • A bomb explodes into 3 identical pieces. Which
    of the following configurations of velocities is
    possible?

(a) 1 (b) 2 (c) both

(1)
(2)
26
Lecture 14, Act 3Center of Mass
  • No external forces, so P must be conserved.
  • Initially P 0
  • In explosion (1) there is nothing to balance the
    upward momentum of the top piece so Pfinal ? 0.

(1)
27
Lecture 14, Act 3Center of Mass
  • No external forces, so P must be conserved.
  • All the momenta cancel out.
  • Pfinal 0.

(2)
28
Comment on Energy Conservation
  • We have seen that the total kinetic energy of a
    system undergoing an inelastic collision is not
    conserved.
  • Energy is lost
  • Heat (bomb)
  • 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.

29
Ballistic Pendulum
L
L
V0
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?
30
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 KU
energy E. (no non-conservative forces acting
after collision)
31
Ballistic Pendulum...
  • Stage 1 Momentum is conserved

in x-direction
  • Stage 2 KU Energy is conserved

Eliminating V gives
32
Ballistic Pendulum Demo
L
L
L
L
H
m
v
M m
M
d
  • In the demo we measure forward displacement d,
    not H

33
Ballistic Pendulum Demo...
Ballistic pendulum
for
for d ltlt L
Lets see who can throw fast...
34
Recap of todays lecture
  • Inelastic collisions in one dimension
  • Inelastic collisions in two dimensions
  • Explosions
  • Comment on energy conservation
  • Ballistic pendulum
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