Collisions in 1D

1
Collisions in 1-D
2
Work-Energy theorem is TRUE just USELESS.
30 m/s
30 m/s
KE 1,080,000 J
1200 kg
1200 kg
v0
maximallyinelastic
KE 0 J
10 m/s
10 m/s
inelastic
KE 120,000 J
elastic
KE 1,080,000 J
3
Tarzan Swing
Impulse-momentum theorem is TRUE just USELESS.
4
Some collisions look like explosions
An astronaut is motionless in outer space. Upon
command, the propulsion unit strapped to his back
ejects some gas with a velocity of 32 m/s, and
the astronaut recoils with a velocity of -0.30
m/s. After the gas is ejected, the mass of the
astronaut is 160 kg. What is the mass of the
ejected gas?
5
Some collisions look like explosions
Conservation of Energy or Conservation of
Momentum?
pi 0
pi pf
0 (160 kg)(-0.30 m/s) mg(32 m/s)
mg 1.5 kg
pf (160 kg)(-0.30 m/s) mg(32 m/s)
6
Momentum is conserved during a collision
What does this mean?

• Total momentum for the system adds up to zero
  before and after the collision.
• Total momentum for the system stays the same
  before and after the collision.

7
From Last Day
A boxcar traveling at 10 m/s approaches a string
of 4 identical boxcars sitting stationary on the
track. The moving boxcar collides and links with
the stationary cars and the five move off
together along the track. What is the final
speed of the five cars immediately after the
collision? (You may take the mass of each boxcar
to be 18537 kg.)
8
mcar 18,537 kg
9
What if the first car bounces?
mcar 18,537 kg
10
Sometimes it appears that momentum is not
conserved
11
m 1 kg
h 5 m
12
Ei mgh Ei 50 J
m 1 kg
h 5 m
50 J 1/2 mv2 v2 100 v 10 m/s
v 10 m/s
13
m 1 kg
h 5 m
v 0 m/s
14
What about the momentum?
v 10 m/s
Where does the energy go?
v 0 m/s
15
pi pf 10 kg m/s 0 kg m/s huh?
pi 10 kg m/s
pf 0 kg m/s
16
Need to include everything that bumps in our
system.
mbvib ME(0) (mb ME)vf 10 kg m/s 6 x 1024
kg vf
vf 2 x 10-24 m/s
pi 10 kg m/s
pf 0 kg m/s
17
What about the energy of the Earth?
vf 2 x 10-24 m/s
Ef ½ mv2 Ef ½ (6 x 1024 kg) (2 x 10-24
m/s)2 Ef 1.2 x 10-23 J Ei 50 J
pi 10 kg m/s
pf 0 kg m/s
18
Practice problem
2 kg
1.25 m
KE 25 J
4 kg