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Phys141 – Lecture 3 – Wed 9/
Review Chapter 1: Basic tools of classical mechanics:
- Basic, standardized quantities for measurements:
- Dimensions of quantities
- Conversion of units
- Density – an example of derived dimensions
- Dimensional Analysis
- Common sense checks:
- “are results reasonable”
- Order of magnitude estimate
- Uncertainty in measurement and calculation
- Significant figures
- Rounding
ToDo: Read Chapter 2.6; (Skip Chapter 2.7)
Read Chapter 3
Homework DUE FRIDAY (online and printout!)
Operations with Significant Figures
Number of significant figures in the answer:
~ smallest number of significant figures of the
quantities that are multiplied/divided.
Example: 25.57 m x 2.45 m = 62.6 m 2
- The 2.45 m limits your result to 3 significant
figures
Operations with Significant Figures –
Adding or Subtracting
Number of decimal places in the result:
~smallest number of decimal places in
any term in the sum.
Example: 135 cm + 3.258 cm = 138 cm
- The 135 cm limits your answer to the units
decimal value
932m x 0.5 + 12m = ??
478 m 478.0 m 4.8 x 102 m5 x 102 m
0% 0% 0% 0%
- 478 m
- 478.0 m
- 4.8 x 10 2 m
- 5 x 10
2 m
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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 $
Chapter 2: Kinematics
- Kinematics: Basic tools to
characterize motion
DEMO
Position
to known reference.
reference”
- need to define
- origin
- one, two or three axes
- Measurement units Movie Frame by Frame
Example Frame of reference:
Cartesian Coordinate System
coordinate system
intersect at the origin
( x , y )
Instantaneous Velocity
Mathematically: The limit of the average
velocity for infinitesimally short times
(Δt approaches zero)
- The instantaneous velocity can be positive,
negative, or zero
0
x lim
t
x dx v Δ → t^ dt
Velocity from position vs time graphs
- The slope of position vs time graph is
the velocity
Instantaneous Speed
= magnitude of the instantaneous velocity
- scalar quantity ( positive number - see chap. 3)
- same units as velocity
- Does your car show velocity or speed?
Average Speed
not the magnitude of the average velocity
You drive once all around the beltway and after one hour and 55 miles you arrive back in collage park.
- what is the average speed of the whole trip?
- What is the average velocity of the whole trip?
- what is the instantaneous velocity right before the Wilson bridge?
total distance traveled Average speed = total time
Acceleration
Rate of change of the velocity
- Average acceleration:
- Dimensions [L/T 2 ]
- SI units m/s 2
Δ^ −
x^ xf^ xi x
v v^ v a t t
Instantaneous Acceleration
Mathematical definition: Instantaneous
acceleration is the limit of the average
acceleration as Δ t approaches 0
Active Figure 2.10:
Active Figure 2.11 (practice yourself)
2
0 2
lim
x x x (^) t
v dv d x a Δ → t dt dt
Useful equations
i
v t = v + at
i i
x t = x + vt + at
for constant acceleration a:
a t ( ) = a
Need to know:
-Initial velocity v (^) i
Need to know:
-Initial position x (^) i
-Initial velocity v (^) i
Questionnaire answers – Which
physics will you need?
Examples:
- Whatever physics is on the MCAT
- Calculating the movements of cells or chemicals
- Pathologist: how forces affect me – how they affected organisms in the past
- Quantum mechanics for physical chemistry
