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Dimensional Analysis - Introduction Physics | PHYS 171, Study notes of Physics

University of MarylandPhysics
Prof. Wolfgang Losert

Material Type: Notes; Professor: Losert; Class: INTRO PHYS:MECH&RELATIV; Subject: Physics; University: University of Maryland; Term: Spring 2007;

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

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Physics 171 – Fri 1/26
Information on “Mastering Physics”
I have given you 6 attempts per problem.
For each wrong answer you will loose 3%
of your final score. Then you will be
offered a free “hint” that should help
you solve the problem.
Today: Parts of Chapter 1
Dimensional Analysis
• “Dimensions” of quantities
–Length [L]
–Mass [M]
–Time [T]
• Both sides of equation must have the
same dimensions
pf3
pf4
pf5
pf8

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Physics 171 – Fri 1/

Information on “Mastering Physics”

I have given you 6 attempts per problem. For each wrong answer you will loose 3% of your final score. Then you will be offered a free “hint” that should help you solve the problem.

Today: Parts of Chapter 1

Dimensional Analysis

  • “Dimensions” of quantities
    • Length [L]
    • Mass [M]
    • Time [T]
  • Both sides of equation must have the same dimensions

Dimensional Analysis, example

Given the equation: x = ½ at^2 x: position [L] ; t time [T] What is dimension of acceleration a?

[ ] [ ]

2 Dimensions on both sides of an equation L = ??⋅ T have to be same (ignore prefactors):

Algebraic manipulation of dimensions allowed!

[ ] [^ ]

[ ]

= 2 ⋅[ ]^2

L L T T

Acceleration has dimension Length/(Time) 2

x = at

The equation for the position x of a train starting at x=0 is given by x = a t +1/2 b t 2 The dimensions of b are:

1. LT

2. LT-

3. T-

4. L-1T

5. LT-

Next Basic Tool: Order of Magnitude Estimate

Estimate something very roughly (e.g., how many cells in our body: a million, billion, or trillion?)

-> Calculate result from quantities that can be approximated (e.g.: number of cells = volume of body / (Length of a cell) 3 )

-> Estimate each quantity to within an order of magnitude if possible (order of magnitude is the power of 10 that applies)

Length of cell: 10 micrometers Volume of body: 30cm x 30cm x 2m

Total number of cells: 1.8 x 10 14 cells -> 180 trillion

Example – order of magnitude estimate

  • The city of Los Angeles is in a semi-desert area. It pumps huge amounts of water from Northern California. Estimate how much water all the people in the city of Los Angeles use every day.

Estimated number:

REAL NUMBER: (^) 187,229,086,

Uncertainty in Measurements

There is uncertainty in every measurement (length of foot) this uncertainty “carries over” through the calculations (length of classroom = number of feet * length of foot) -> We will use rules for significant figures to approximate the uncertainty in results of calculations

Phys174 will show you more accurate ways to calculate uncertainty in calculations

Significant Figures, examples

  • 0.0075 m has 2 significant figures
    • The leading zeros are placeholders only
    • to show more clearly: 7.5 x 10- 3 m
  • 10.0 m has 3 significant figures
  • 1500 m has 4 significant figures (for the purposes of this class, more accurate treatment see book) - Use 1.5 x 10 3 m for 2 significant figures - Use 1.50 x 10 3 m for 3 significant figures

Rounding

Last retained digit is increased by 1 if the last digit dropped is 5 or above Last retained digit remains as it is if the last digit dropped is less than 5 Do not round before you get to the final result

Example: Round the sum of 1001 contributions of $0.40 to the nearest $

  • Final result of calculation: $400.
  • Rounded final result: $
  • Round each contribution: $ –> sum (rounded too early) is $

Describing Motion

  • Defined only relative to known reference.
  • Term: “ frame of reference”
  • need to define
    1. origin
    2. one, two or three axes
    3. Measurement units

1 m

Does the reference frame move?

-Tablecloth Demo

Do the plates move or not?

-> Depends on the reference frame

Generally: Measurements in Laboratory reference frame

ToDo

READ: Rest of Chapter 1 –

Chapter 2.1 and 2.

TUE: 2.3-2.

THU: 2.6-2.

FRI: First HW due