1. PHYS 172: Modern Mechanics Summer 2011
Lecture 6 – Momentum Conservation, Complex Systems Read

2. Electric force: the electric charges
Charges: property of an object
Two types: positive (+) and negative (-)
Like charges: repel.
Opposite charges: attract
Net charge of a system: algebraic sum of all the charges
Conservation of charge
The force exerted by one point charge on another acts along the line
joining the charges
Charge: measured in C (Coulomb)
Elementary charge: e = 1.602×10-19 C
Charge of electron is –e, of a proton +e 2

3. The electric force law (Coulomb’s law)q1 q2
Coulomb’s law 3

4. Electric force versus gravity
Gravity (Cavendish, 1798)
Electric force (Coulomb, 1795)
G = 6.67×10-11 m3/(kg.s2)
1/(40) = 8.99×109 Nm2/C2
Clicker question: A) Gravity
Which of the two forces is in general stronger? B) Electrical
3 m
3 m
Electric forces are much stronger than gravitational forces 4

5. Predicting the future of a gravitational system
Massive star
And small planets
fixed
Two body: ellipse (or circle)
fixed
Determinism:
If we know the positions and momenta of all particles in the Universe we can predict the future

6. Predicting the future of gravitational system
Solar system
Binary star
Sun, Earth and Moon
Ray Bradbury’s “The Sound of Thunder” – time travelers stepped on butterfly millenia ago, enormous changes in present
Coin – drop the same way from the same height
Problems:
Sensitivity Initial condition and t
Inability to account for all interactions
1025 molecules in glass of water !
Small particles: quantum mechanics

7. Probability and uncertainty
Example: a free neutron decays with ~15 minutes:
Probability t
Clicker:
Can we predict the motion of an electron near a free neutron?
Yes No

8. Probability and uncertainty
Semitransparent mirror
Clicker poll:
The photon will:
Reflect
Pass through
photon
Where is the electron?
Classical
Quantum

9. The Heisenberg uncertainty principle
Werner Karl
Heisenberg
Position and momentum of a particle cannot be exactly measured simultaneously
1927
Nobel Prize: 1932
Planck’s constant
h = 6.6×10-34 kg.m2/s
E=h
1900
Nobel Prize: 1918
Max Planck

10. System consisting of two objects
Momentum principle: +
Clicker question 2:
What is the last term in that equation?
A) Zero
B) Not zero, directed toward the larger object
C) Not zero, directed toward the smaller object
D) It is always positive
E) It is always negative 10

11. System consisting of two objects
Momentum principle: +
Only from surrounding! 11

12. System consisting of many objects
Because all the forces inside the system come in pairs they cancel out.
The only forces left over are forces from the surroundings! 12

13. System consisting of several objects
Total momentum of the system:
The Momentum Principle for a system:
The sum of all external forces
due to surrounding 13

14. Conservation of momentum
system +
In the absence of external forces
system
surrounding
Conservation of momentum

15. Reciprocity: Newton’s 3rd law
Force magnitudes are the same
Directions are opposite
They act on different objects
Consider a very thin layer between mass and spring – there are two forces on that, from spring, and from gravity on the mass. It is still – dp/dt is zero, which means that both forces must be the same!
Reciprocity (Newton’s 3rd law):
The forces of two objects on each other are always equal and are directed in opposite directions
NOTE: Velocity-dependent forces (e.g., magnetic forces) do not obey Newton’s 3rd law! 15

16. Collisions: negligible external forces
1. Sticky ball
Momentum conservation:
Assume =1: m1 m2
What if balls bounce?
Two unknowns, one equation