Coefficient of Restitution
Coefficient of Restitution: Tennis Ball
Given: 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.
Required: Coefficient of restitution of regulation tennis ball
Final Relative Velocity
Type of Collision
Perfectly Inelastic
Zero; objects move together
Real World
Between two limits; defined by coefficient of
restitution
Perfectly Elastic
Same magnitude as original relative
velocity; opposite sign
Solution:
A
D
e =
! (v1" ! v2" )
v1 ! v2
e = 0 Perfectly ________
e = 1 Perfectly ________
B
EF 151 Spring, 2011 Lecture 3-7
1
Collisions in 2 dimensions
A
vA
vB
y
x
line of _______
x motion - ________
v AX =
vB X =
EF 151 Spring, 2011 Lecture 3-7
! (v1" ! v2" )
v1 ! v2
EF 151 Spring, 2011 Lecture 3-7
2
Given: 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.
A
v A!
B
B
e =
Example: Shooting Pool I
A
plane of _______
C
B
v B!
Required: Determine the speed of
ball B and the angle ! after ball B
hits cushion C.
y motion: Forces and impulse
m A v AY + mB vBY = m A v!AY + mB v!BY
e =
(
! v"AY ! v"BY
If e=1, will ! be:
A.  >30°
B.  =30°
C.  <30°
)
v AY ! vBY
3
EF 151 Spring, 2011 Lecture 3-7
If e=0.6, will ! be:
A.  >30°
B.  =30°
C.  <30°
If e=0, will ! be:
A.  =30°
B.  30°< ! < 90°
C.  =90°
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Example: Shooting Pool I
Example: Shooting Pool II
Solution:
Given: A pool ball moving with a speed of
5 m/s strikes a pool ball moving with a
speed of 3 m/s. The coefficient of
restitution Is 0.90. The line of impact is the
line connecting the centers of the two balls.
Required: Determine the velocity of both
balls after impact.
e=0.6
EF 151 Spring, 2011 Lecture 3-7
5
EF 151 Spring, 2011 Lecture 3-7
3 m/s
5 m/s
Line of
impact
60°
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