Physics 121

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Physics 121
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7. Linear Momentum
7.1 Momentum and its relation to Force 7.2
Conservation of Momentum 7.3 Collisions and
Impulse 7.4 Conservation of Energy and
Momentum 7.5 Elastic Collisions 7.6
Inelastic Collisions 7.7 Solving Collision
Problems 7.8 Center of Mass
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Linear Momentum

• Linear Momentum mass x velocity
• p mv

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Conservation of Momentum
Law of Conservation of Momentum In a collision,
momentum BEFORE the collision equals the momentum
AFTER the collision
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Example 7.1 . . . The Odd Couple I
A model railroad car (mass 100 g), moving at 4
m/s, collides and locks onto a similar stationary
car. The coupled cars move as a unit on a
straight and frictionless track. The speed of
the moving cars is most nearly A. 1 m/s B. 2
m/s C. 3 m/s D. 4 m/s
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Solution 7.1 . . . The Odd Couple I
Momentum BEFORE Momentum AFTER 100 x 4 0 200
x v v 2 m/s
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Example 7.2 . . . The Odd Couple II
Is the K.E. BEFORE K.E. AFTER? In other words,
is the K.E. conserved in this collision?
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Solution 7.2 . . . The Odd Couple II
K.E. BEFORE the collision (1/2)(0.1)(16) 0
0.8 J K.E. AFTER the collision
(1/2)(0.2)(4) 0 0.4 J Half of the K.E. has
mysteriously disappeared! Note However, this
does not mean that ENERGY is not conserved! K.E.
was transformed (converted) into other forms of
energy.
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Close collisions of the second kind ...
There are TWO types of collisions I. Momentum
conserved and K.E. also conserved. This type is
called an ELASTIC collision. Elastic collisions
are non-sticky as in billiard balls or steel
ball-bearings. II. Momentum conserved BUT K.E.
NOT conserved. This type is called an INELASTIC
collision. Inelastic collisions are sticky as
in coupled railroad cars and putty.
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Example 7.3 . . . Hockey Puck
Two hockey pucks collide elastically on ice. P2
is at rest and P1 strikes it head-on with a
speed of 3 m/s. A. P1 stops and and P2 moves
forward at 3 m/s B. P1 and P2 move forward at 1.5
m/s C. P1 and P2 move in opposite directions at
1.5 m/s D. P1 moves forward at 1 m/s and P2 moves
forward at 2 m/s
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Solution 7.3 . . . Hockey Puck
A. P1 stops and P2 moves forward at 3 m/s.
Please verify that 1. Momentum is conserved 2.
K.E. is also conserved (elastic)
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Equations for Head-on Collision
Momentum is conserved(Always!) m1 v1 m2 v2 m1
v1' m2 v2' K.E. is conserved (Elastic) 1/2 m1
(v1 )2 1/2 m2 (v2 )2 1/2 m1 (v1')2 1/2
m2(v2')2 Momentum and K.E. BOTH conserved
(Elastic) v1 - v2 v2'- v1'
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Example 7.3 one more time!
Work out Example 7.3 using v1 - v2 v2'-
v1' and see how effortless it is to arrive at
the correct answer!
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Impulse
O.K. good boys and girls. Here is everything you
always wanted to know about momentum but were
afraid to ask! In the beginning there was F
ma So
F m(vf - vi) / t If F 0
mvf mvi If F is ? 0
mvf - mvi F x t Change in
momentum F x t IMPULSE
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Example 7.4 . . . Tiger in the woods
A golf ball has a mass of 48 g. The force
exerted by the club vs. time is a sharp spike
that peaks at 180 N for 0.01 s and then drops
back to zero as the ball leaves the club head at
high speed. It is estimated that the average
force is 90 N over a short time (?t) of 0.04 s.
The speed of the ball is A. 35 m/s B. 75 m/s C.
95 m/s D. 135 m/s
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Solution7.4 . . . Impulse to ride the tiger

• Impulse F ?t 90 x 0.04 3.6 Ns
• Impulse change in momentum
• 3.6 mv -0
• 3.6 0.048 x v
• v 75 m/s

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Example 7.5 . . . Teeter-Totter
FB weighs 180 pounds and sits at the 20 cm. mark.
Where should SP (120 pounds) sit in order to
balance the teeter-totter at the playground?
0 20
50
100
180
120
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Solution 7.5 . . . See-Saw

• 30 x 180 what x 120
• what 45 or 95 cm. mark

0 20
50
100
180
120
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Example 7.6 . . . Center of Mass
The C.M. is a weighted average position of a
distribution of masses where the system can be
balanced. Where is the C.M.?
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Solution 7.6 . . . Center of Mass

• (100)( x -20) (300)(80 - x)
• x (100) (20) (300)( 80) / (100 300)
• x 65

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A formula for C.M.

• C.M. M1 X1 M2 X2
• M1 M2

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Thats all folks!