1. Newtonian Mechanics: Introduction
8.01
W01D3 2006

2. Système International (SI)
Metric System of Units
Système International (SI)
Length meter (m)
Mass kilogram (kg)
Time second (s)
Electric Current ampere (A)
Temperature Kelvin (K)
Amount of Substance mole (mol)
Luminous Intensity candela (cd)

3. Speed of Light
In 1983 the General Conference on Weights and Measures defined the speed of light to be
This number was chosen to correspond to the most accurately measured value of the speed of light and is well within the experimental uncertainty.

4. Atomic Clock and the Definition of the Second
The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Adopted In 1967

5. Length as a Derived Quantity
The meter was originally defined as 1/10,000,000 of the arc from the Equator to the North Pole along the meridian passing through Paris.
To aid in calibration and ease of comparison, the meter was redefined in terms of a length scale etched into a platinum bar preserved near Paris.
Once laser light was engineered, the meter was redefined to be a certain number of wavelengths of a particular monochromatic laser beam.
The meter (m) is now defined as the distance traveled by a light wave in vacuum in 1/299,792,458 seconds.

6. Inertial Mass Inertial mass is a “quantity of matter”
The SI standard of mass is a platinum-iridium
cylinder assigned a mass ms= 1 kg
The mass of all other bodies will be
determined relative to the mass of
our standard body.
By applying the same action (force) to
the standard body and an unknown body,
the unknown mass is obtained in terms of
ratio of accelerations

7. Group Problem: Proportions of the Standard Kilogram
The standard kilogram is a cylindrical alloy of 90 % platinum and 10 % iridium. The density of alloy is
Your job is to design a strategy for finding the optimal height and radius for the standard kilogram keeping in mind that the surface is occasionally cleaned of unwelcome atoms (dust). You don’t have to solve this.

8. Proportions of Standard Kilogram
Strategy; Since atoms collect on the surface, chose the radius and height to minimize surface area.
Constant volume for cylinder:
The surface area is
Minimize the area with respect to radius:
Radius is one half height:
The volume determined from density
The radius is
The height is

9. Problem Solving
Measure understanding in technical and scientific courses
Problem solving requires factual and procedural knowledge, knowledge of numerous schema, plus skill in overall problem solving.
Schema is loosely defined as a “specific type of problem” such as principal, rate, and interest problems, one-dimensional kinematic problems with constant acceleration, etc..

10. Problem Solving
In most introductory university courses, improving problem solving relies on three things:
increasing domain knowledge, particularly definitions and procedures
learning schema for various types of problems and how to recognize that a particular problem belongs to a known schema
becoming more conscious of and insightful about the process of problem solving.
To improve your problem solving ability in a course, the most essential change of attitude is to focus more on the process of solution rather than on obtaining the answer.

11. General Approach to Problem Solving
George Polya’s How to Solve It, on problem solving.
I. Understand – get a conceptual grasp of the problem
II. Devise a Plan - set up a procedure to I.
III. Carry our your plan – solve the problem!
IV. Look Back – check your solution and method of solution

12. I. Understand – get a conceptual grasp of the problem
What is the problem asking?
What are the given conditions and assumptions?
What domain of knowledge is involved?
What is to be found and how is this determined or constrained by the given conditions?
Model: Real life contains great complexity, so in physics you actually solve a model problem that contains the essential elements of the real problem.

13. II. Devise a Plan - set up a procedure to obtain the desired solution
General
Have you seen a problem like this
Is a part of this problem a known schema?
Could you simplify this problem so that it is?
Can you find any useful results for the given problem and data even if it is not the solution
Can you imagine a route to the solution if only you knew some apparently not given information?
If your solution plan involves equations, count the unknowns and check that you have that many independent equations.

14. III. Carry our your plan – solve the problem!
mathematical manipulations.
keep as simple as possible by not substituting in lengthy algebraic expressions until the end is in sight,
make your work as neat as you can to ease checking and reduce careless mistakes.
Keep a clear idea of where you are going and have been (label the equations and what you have now found),
if possible, check each step as you proceed.

15. IV. Look Back – check your solution and method of solution
Check work:
Check dimensions if analytic, units if numerical.
Check special cases
Is the scaling what you’d expect
Does it depend sensibly on the various quantities
Is the answer physically reasonable
consider special limits (zero, infinity)
Review the schema of your solution:
what is the model,
the physical approximations,
the concepts needed
any tricky math manipulation.

16. Estimation Problems Quantitative estimation of phenomena
Order of magnitude estimations

17. Estimations Strategies
What type of quantity is being estimated?
How is that quantity related to other quantities, which can be estimated more accurately?
Establish an approximate or exact relationship between these quantities and the quantity to be estimated in the problem

18. Estimation Strategies
3) identify a set of quantities that can be estimated or calculated
4) establish an approximate or exact relationship between these quantities and the quantity to be estimated in the problem

19. Concept Question: Estimation Volume of Earth’s Atmosphere
What is your best estimate for the volume of the earth’s atmosphere?
1) between 101 and 105 cubic meters
2) between 105 and 1010 cubic meters
3) between 1010 and 1015 cubic meters
4) between 1015 and 1020 cubic meters
5) between 1020 and 1025 cubic meters
6) between 1025 and 1030 cubic meters

20. Example Estimation: Number of Molecules in Atmosphere
Estimation quantity is a scalar: N number of molecules and is related to volume of atmosphere.
Number of molecules = (number of molecules in a mole)(number of moles in atmosphere)
Number of moles in atmosphere = (volume of atmosphere)/(volume of mole)
number of molecules in a mole
at STP (Standard Temperature and Pressure): one mole of an ideal gas occupies 22.4 L = 22.4 x 10-3 m3.
Number of molecules in atmosphere:

21. Force Law
Force Law: Discover experimental relation between force exerted on object and change in properties of object
Induction: Extend force law from finite measurements to all cases within some range creating a model
Add predictive nature

22. Universal Law of Gravitation
Gravitational force between two bodies with masses m1 and m2
Gravitational force is attractive
The force is proportional to the product of the masses, and inversely proportional to square of the distance of separation, r1,2 .

23. Models in Physics: Fundamental Forces of Nature
Force laws are mathematical models of physical processes
Electromagnetism
Weak Force
Strong Force
Gravity
Fifth Force?

24. Fundamental Units Dimensions and values of the fundamental constants
Planck constant
Speed of light
Universal Gravitation constant
Boltzmann constant

25. Example: Planck Mass
Let’s construct a combination that depends only on mass. The dimension of the product of Planck’s constant and the speed of light is
Thus the following quantity has the dimensions of mass
Value

26. Example: Mass to Length Conversion
What are the dimensions and magnitude of the Gravitational constant divided by the speed of light squared?
This ratio acts as a conversion factor between mass to length in the same manner that speed of light can be used as a conversion factor between length and time. The magnitude of this conversion factor is

27. Example: Planck Length
fundamental length unit, we use the conversion
Thus the following quantity has the dimensions of length
Value

28. Example: Mass to Time Conversion
The dimensions and magnitude of the speed of light cubed divided by Gravitational constant
This ratio acts as a conversion factor between mass to time

29. Example: Planck Time Use the conversion
Thus the following quantity has the dimensions of time
Value