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A bowling ball and a ping-pong
ball are rolling towards you with
the same momentum. If you exert
the same force to stop each one,
which takes a longer time to bring
to rest?
 
We know:
 Δp
  Fav  =
 Δt
 
 
p
p
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 
 
p
p
 
 
p
p
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A skier traveling 11.4 m/s reaches the foot of a steady
upward 18.4° incline and glides 11.2 m up along this
slope before coming to rest. What was the average
coefficient of friction? We found on Monday that
µ=
€
1 v2
1
11.4 2
− tanθ =
− tan(18.4) = 0.29
2 gdcos(θ )
2 9.8⋅ 11.2cos(18.4)
The skier turns right around and glides
down the slope. What will be her
speed at the bottom?
PHYS 1021: Chap. 10, Pg 5
New Topic
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 
Initial:
Conserve momentum pX:
V1,i
initial:
V2,i
m1
m1v1,i + m2v2,i = m1v1,f + m2v2,f
Final:
  Conserve kinetic energy:
x
V1,f
m1
final:
1/ m v 2
1
2
1
2
1
2
2
1 1,i + /2 m2v 2,i = /2 m1v 1,f + /2 m2v 2,f
 
m2
V2,f
m2
After some algebra, one can show a general result:
v1,i - v2,i = – (v1,f - v2,f )
The relative velocity before the collision is equal and opposite
to the relative velocity after the collision
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Consider two elastic collisions:
1) a golf ball with speed v hits
a stationary bowling ball head-on.
2) a bowling ball with speed v
hits a stationary golf ball head-on.
In which case does the golf ball
have the greater speed after the
collision?
v
at rest
1
1)  situation 1
2)  situation 2
3)  both the same
at rest
v
2
Consider two elastic collisions:
1) a golf ball with speed v hits
a stationary bowling ball head-on.
2) a bowling ball with speed v
hits a stationary golf ball head-on.
In which case does the golf ball
have the greater speed after the
collision?
Remember that the magnitude of the
relative velocity has to be equal before
and after the collision!
v
1
v
2v
2
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Carefully place a small rubber ball
(mass m) on top of a much bigger
basketball (mass M) and drop these
from some height. What is the
velocity of the smaller ball after the
basketball hits the ground and collides
with small rubber ball?
m
v
v
1)  zero
2)  v
3)  2v
4)  3v
5)  4v
??
v
v
v
(a)
(b)
(c)
Carefully place a small rubber ball (mass
m) on top of a much bigger basketball
(mass M) and drop these from some
height. What is the velocity of the
smaller ball after the basketball hits
the ground and collides with small
rubber ball?
v
m
v
3v
v
v
v
(a)
(b)
(c)
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Now imagine the two balls are dropped
together from a height of 1 m. What
height will the small ball reach after the
basketball hits the ground and collides
with small rubber ball?
1)  zero
2)  1 m
3)  2m
4)  3m
5)  9m
m
v
v
??
v
v
v
(a)
(b)
Now imagine the two balls are dropped
together from a height of 1 m. What
height will the small ball reach after the
basketball hits the ground and collides
with small rubber ball?
(c)
1)  zero
2)  1 m
3)  2m
4)  3m
5)  9m
• 
If the velocity is tripled,
the kinetic energy will by
increased by a factor of
9 and so the final mgh
will be 9 times higher
than the initial.
v
m
v
3v
v
h
v
v
(a)
9h
(b)
(c)
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Imagine two pool balls colliding, the first is moving with velocity v0 and the
second is at rest. Both have the same mass, m. After the collision, the
second ball moves off at a 45 degree angle relative to the path along which
the first one came.
What are the final velocities of the two balls?
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