Coefficient of Restitution: Tennis Ball
Today’s Topics:
 Coefficient of Restitution
 2D collisions
A regulation tennis ball has to bounce between a height of 53 to 56
inches when dropped from a height of 100 inches onto a concrete
floor. Determine the coefficient of restitution.
Final Relative Velocity
Type of Collision
Perfectly Inelastic
Zero; objects move together
Real World
Between two limits; defined by
__________________________
Perfectly Elastic
Same magnitude as original relative
velocity; opposite sign
A
D
e 
 v1  v2 
v1  v2
e=0
e=1
Perfectly ________
Perfectly ________
B
EF 151 Fall, 2014 Lecture 3-7a
1
Car Crash
Two cars – same mass – collide
head-on. After the collision the
cars skid with their brakes locked
as shown. Determine the speed of
car B and the effective coefficient
of restitution.
vA = 5 km/hr (1.4 m/s) right
uk = 0.3
C
EF 151 Fall, 2014 Lecture 3-7a
2
Collisions in 2 dimensions
A
vA
v A
A
v B
B
A
plane of _______
1m
4m
B
Which car had greater
speed before collision?
vB
B
y
x
line of _______
x motion - ________
v AX 
EF 151 Fall, 2014 Lecture 3-7a
 v1  v2 
v1  v2
e 
3
EF 151 Fall, 2014 Lecture 3-7a
vBX 
y motion: Forces and impulse
m A v AY  mB v BY  m A vAY  mB vBY
e 

 vAY  vBY

v AY  vBY
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Example: Shooting Pool I
Example: Shooting Pool I
The cue ball A is given an initial speed
of 5 m/s. It makes direct perfectly
elastic impact with ball B, giving ball B a
speed of 5 m/s. Ball B then makes
contact with cushion C (e = 0.6). Each
ball has a mass of 0.4 kg. Neglect
friction and the size of each ball.
e=0.6
Determine the speed of ball B and the
angle θ after ball B hits cushion C.
If e=1, will θ be:
A. >30°
B. =30°
C. <30°
EF 151 Fall, 2014 Lecture 3-7a
If e=0, will θ be:
A. =30°
B. 30°< θ < 90°
C. =90°
If e=0.6, will θ be:
A. >30°
B. =30°
C. <30°
5
EF 151 Fall, 2014 Lecture 3-7a
6