Announcements
•
Exam 1: You will get back your exam next
Tuesday, after which you can double check that
the grading is correct.
•
You will not get back your scantron.
•
If the answers on your scantron and your exam
are different, only the one on the scantron will
count.
Recap: conservation of Momentum
• In a collision, the
momentum of each
object will change.
• The total momentum
of the system remains
constant
Momentum
conservation
For 1D “head-on” collisions:
Perfectly inelastic collisions
(m1 and m2 stick together):
m1v1i + m2v2i = (m1+m2)vf
Elastic collision: kinetic energy conservation
(1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2 + (1/2)m2v2f2
equivalent
v 1i − v 2i = −( v 1f − v 2 f )
1.2 m
1.2 m
1.2 m
vT
vT
vB
vB'
airplanes
need Air
Rocket Propulsion
• The operation of a
rocket depends on the
law of conservation of
momentum as applied to
a system, where the
system is the rocket plus
its ejected fuel
• different than
propulsion on the earth
where two objects exert
forces on each other
• Road on car
• Train on track
Rocket Propulsion, 2
• The rocket is accelerated as a result of the
thrust of the exhaust gases
• This represents the inverse of an inelastic
collision
– Momentum is conserved
– Kinetic Energy is increased (at the expense of
the stored energy of the rocket fuel)
Milk jug rocket
Milk jug rocket
V
v
Rocket Propulsion
M = rocket
∆m = fuel to be ejected
Objects in flight
How do airplanes fly?
How do rockets fly?
How does superman fly?
???
Glancing Collisions
• pi = pf Î pix = pfx and piy = pfy
• Momentum is conserved in the x direction
and in the y direction, separately.
Glancing Collisions
• the total momentum of the system in each direction is
conserved
ƒ
m1v 1ix + m2 v 2ix = m1v 1fx + m2 v 2 fx and
m1v 1iy + m2 v 2iy = m1v 1fy + m2 v 2 fy
For the figure above:
m1v1i = m1v1f cos θ + m2v2f cos φ (x-component)
0 = m1v1f sin θ - m2v2f sin φ (y-component)
Glancing elastic collisions: KE is conserved
KE is a scalar Î KE conservation equation is
the same for glancing and head-on collisions.
1
1
1
1
2
2
2
2
m1v1i + m2 v2i = m1v1 f + m2 v2 f
2
2
2
2
v1i + v1f = v2i + v2f
Only for 1D head-on elastic collisions
Two ice hockey pucks slide without friction on a flat surface of
ice. They collide and remain stuck together. Find the velocity
after the collision.
1 kg
A
30ο
7 m/s
5 m/s
θ=?
A
B
Vf = ?
0.2 kg
B
What is the x component of final velocity Vf?
1 kg
A
30ο
7 m/s
5 m/s
A
B
Vfx = ?
0.2 kg
B