Collisions and Rocket Motion
Perfectly Elastic Collisions (no external forces)
Initial kinetic energy = Final kinetic energy
Example: Baggage Cart
m1v1 + m2 v2 = m1v1′ + m2 v2′
Given: A 43 pound baggage cart is moving at 2.3 ft/sec to the right. A 28
pound bag is thrown on the cart with a speed of 4.7 ft/sec to the right.
Required: (a) Final velocity of the bag and cart.
(b) Energy lost in the process.
1
2
m1v12 + 12 m2 v22 = 12 m1v1′ 2 + 12 m2 v2′ 2
v1 is initial velocity of mass 1; v2 is initial velocity of mass 2
v'1 is final velocity of mass 1; v'2 is final velocity of mass 2
Using algebra, obtain equation for relative velocities
v1 − v2 = −(v1′ − v2′ )
In an elastic collision, the relative velocity
changes _______, but not __________.
EF 151 Fall, 2010 Lecture 3-6
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Example: Perfectly Elastic Collision
2
Perfectly Elastic Collisions (no external forces)
Given: A 14 lb bowling ball is going down the alley at 27 ft/s.
It directly strikes a single 3.5 lb pin. Assume the collision to
be perfectly elastic.
Required: The velocities of the bowling ball and pin after the
collision.
EF 151 Fall, 2010 Lecture 3-6
EF 151 Fall, 2010 Lecture 3-6
v1 − v2 = −(v1′ − v2′ )
m1v1 + m2 v2 = m1v1′ + m2 v2′
m1
3
v1
m2
v2
Billiard Ball
v
Billiard Ball
0
Billiard Ball
v
Bowling
Ball
0
Bowling
Ball
v
Billiard Ball
0
EF 151 Fall, 2010 Lecture 3-6
v1’
v2’
A.
B.
C.
D.
E.
-2v
-v
0
v
2v
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Example: 2D Perfectly Elastic Collision
Rocket Motion
Given: An air puck with a mass of 0.15 kg and velocity (-1.7î - 2.0ĵ)m/s
collides with a second air puck of mass 0.22 kg and a velocity of
(3.6î)m/s. Assume the collision to be perfectly elastic.
Required: The velocities of the air pucks after the collision in
magnitude-angle format.
• Mass of rocket __________ as fuel is burned
• Rocket characterized by:
• _______________ of hot gasses with respect to
rocket, uex
• __________________ or change of mass of
rocket, dm/dt
• ________ of rocket, uex(dm/dt)
EF 151 Fall, 2010 Lecture 3-6
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Rocket Motion
Rocket speed
EF 151 Fall, 2010 Lecture 3-6
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Example: Space Shuttle Solid Boosters
m 
v = uex ln 0 
 m
Given: The space shuttle burns 49% of its launch weight of 4.5 million
pounds in the first 75 seconds. The exhaust velocity of the gasses is
7200 ft/sec.
Required: (a) Velocity of shuttle after 75 sec burn
(b) Acceleration at lift-off
m0 = initial mass
m = m0 – (dm/dt)t
Rocket speed in the presence of gravity
m 
v = uex ln 0  − gt
 m
Gravity will be assumed to be constant, but it actually decreases
with height above the earth’s surface.
Thrust = uex
EF 151 Fall, 2010 Lecture 3-6
dm
dt
7
EF 151 Fall, 2010 Lecture 3-6
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