Announcements
1. HW5 due Feb 25.
2. Prof. Reitze office hour this week:
Friday 3 – 5 pm, (Wednesday 11-noon cancelled)
3. Midterm1:
grades posted in e-learning
solutions and grade distribution posted on website
if you want to look at your scantron, see Prof. Chan
before March 3.
Recap: conservation of Momentum
• The momentum of
each object will
change
• The total momentum
of the system remains
constant
4. Make-up exam: April 21, 7:30 pm
covers all material in the course.
need to let Prof. Chan and Prof. Reitze know in advance
if you need to miss the midterms or final.
location TBA
Recap: Collisions
• Momentum is conserved in any collision
• Elastic collisions: kinetic energy is also conserved.
• Inelastic collisions
– Kinetic energy is not conserved
Types of Collisions
• Elastic collision
– both momentum and kinetic energy are
conserved
• Actual collisions
• Some of the kinetic energy is converted into other types
of energy such as heat, sound, work to permanently
deform an object
– Most collisions fall between elastic and
perfectly inelastic collisions
– Perfectly inelastic collisions occur when the
objects stick together
• Not all of the KE is necessarily lost
73. A tennis ball of mass 57.0 g is held just above a
basketball of mass 590 g. With their centers vertically
aligned, both balls are released from rest at the same time,
to fall through a distance of 1.20 m, as shown in Figure
P6.69. (a) Find the magnitude of the downward velocity
with which the basketball reaches the ground. (b) Assume
that an elastic collision with the ground instantaneously
reverses the velocity of the basketball while the tennis ball
is still moving down. Next, the two balls meet in an elastic
collision. (b) To what height does the tennis ball rebound?
1.2 m
1.2 m
vT
vB
1
Momentum conservation:
m1v1i + m2v2i = m1v1f + m2v2f
1.2 m
1.2 m
1.2 m
vT
vT
Elastic collision: kinetic energy conservation
vB
Only for 1 dimensional elastic collisions
v 1i − v 2i = −( v 1f − v 2 f )
or
v1i + v1f = v2i + v2f
vB'
(1/2)m1v1i2 + (1/2)m2v2i2 = (1/2)m1v1f2 + (1/2)m2v2f2
Inelastic collisions
Kinetic energy is not conserved
Momentum is still conserved
Perfectly Inelastic collisions
Objects stick together after collision
Ballistic pendulum
6.62 Two blocks of masses m1 = 2 kg and m2 = 4 kg are
each released from rest at a height of 5 m on a frictionless
track and undergo an elastic head-on collision. (a)
Determine the velocity of each block just before the
collision. (b) Determine the velocity of each block
immediately after the collision. (c) Determine the
maximum heights to which m1 and m2 rise after the
collision.
2
airplanes
need Air
Rocket Propulsion
Rocket Propulsion, 2
• 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
• The rocket is accelerated as a result of the
thrust of the exhaust gases
• This represents the inverse of an inelastic
collision
– This is different than propulsion on the earth
where two objects exert forces on each other
– Momentum is conserved
– Kinetic Energy is increased (at the expense of
the stored energy of the rocket fuel)
• Road on car
• Train on track
Rocket Propulsion
3