1. Chapter 8 Conservation of Linear Momentum Linear momentum; Momentum conservation Impulse Total kinetic energy of a system
March 8, 2010
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Phys 201, Spring 2011

2. Conservation of Linear Momentum
Definition of linear momentum,
Linear momentum is a vector (decompose to x,y,z directions).
Units of linear momentum are kg-m/s.
Can write Newton’s second law in terms of momentum:
A more general form  in the case of variable m
Momentum  force, as if Kinetic energy  work
9/11/2018
Phys 201, Spring 2011

3. Momentum of a system of particles
The total momentum of a system of particles is the vector sum of the momenta of the individual particles:
From Newton’s second law, we obtain
“internal forces” cancel in pair (3rd law).
9/11/2018
Phys 201, Spring 2011

4. Conservation of Momentum
Law of conservation of momentum:
If the sum of the external forces on a system is zero, the total momentum of the system does not change.
If then
Momentum is always conserved when no net “external” force.
(even if “internal” forces are non-conservative).
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Phys 201, Spring 2011

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6. Collisions momentum before collision = momentum after collision
Always -
But only if
9/11/2018
Phys 201, Spring 2011

7. Explosion - I “before” M v2 “after” v1 m1 m2
Example: m1 = M/3 m2 = 2M/3
(same magnitude, opposite)
After explosion, which block has larger momentum?
Which block has larger speed?
m1v1 = - m2v2, so smaller mass has larger speed: v1 > v2.
Is kinetic energy conserved?
NO! K was 0 before, it is greater after the explosion.
(internal non-conservative force does some work.)
9/11/2018
Phys 201, Spring 2011

8. Momentum and Impulse Momentum For single object….
How about p-change?
For single object….
If F = 0, then momentum conserved (p = 0)
For “system” of objects …
Otherwise:
F = I/Δt
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11. Elastic Collision in 1-Dimension
Initial Final
Linear momentum is conserved
Energy conserved
(for elastic collision only)
9/11/2018
Phys 201, Spring 2011

12. Magnitude of relative velocity is conserved.
Elastic Collision
Magnitude of relative velocity is conserved.
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Phys 201, Spring 2011

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14. Is this an elastic collision? (for a hard club and ball)
For elastic collision only:
Yes, the relative speeds
are approximately the same
before and after collision
9/11/2018
Phys 201, Spring 2011

15. What is the speed of the golf ball, in case of an elastic collision
Club speed: 50 m/s
Mass of clubhead: 0.5kg
Mass of golfball: 0.05kg
Two unknowns: after the impact,
speed of club and
speed of golfball
Problem solving strategy:
Momentum conservation
Energy conservation
Or use the derived equation
for relative velocities
9/11/2018
Phys 201, Spring 2011

16. Club speed almost unchanged Ball speed almost 2 x club speed
Result:
Special cases:
Golf shot: m1>>m2
Club speed almost unchanged
Ball speed almost 2 x club speed
2) A ball hits a wall: m1<<m2
the ball bounces back with almost same speed
the wall speed almost unchanged
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Phys 201, Spring 2011

17. Some Terminology n.b. ALL CONSERVE MOMENTUM!! If external forces = 0
Elastic Collisions:
collisions that conserve kinetic energy
Inelastic Collisions:
collisions that do not conserve kinetic energy
Completely Inelastic Collisons:
objects stick together (or split from one into two)
n.b. ALL CONSERVE MOMENTUM!!
If external forces = 0
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18. Kinetic energy of a system of particles:
In terms of the CM velocity and relative velocity to the CM:
Where
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Phys 201, Spring 2011